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The reaction of bis(thioether) complexes of (octaethylporphyrinato)ruthenium(II) with dioxygen, and the.. Pacheco-Olivella, Arsenio A. 1992-12-31

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THE REACTION OF BIS(THIOETHER) COMPLEXES OF (OCTAETHYLPORPHYRINATO)RUTHENIUM(II) WITH DIOXYGEN, AND THE CATALYZED 0 2-OXIDATION OF THIOETHERS by ARSENIO ANDREW PACHECO-OLIVELLA B.Sc., The University of British Columbia, 1982 M.Sc., The University of British Columbia, 1986 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES THE DEPARTMENT OF CHEMISTRY We accept this thesis as conforming to the required standard  THE UNIVER ITY OF BRITISH COLUMBIA September 1992 Arsenio Andrew Pacheco-Olivella, 1992  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  (Signature)  Department of  ^C ke^r),  The University of British Columbia Vancouver, Canada  Date^becet4er  DE-6 (2/88)  11  ABSTRACT  This thesis describes a detailed study of the reactivity of Ru(OEP)(RR'S) 2 complexes (where OEP ---7= the dianion of 2,3,7,8,12,13,17,18-octaethylporphyrin, R -z--methyl, ethyl or decyl, and R' - =- methyl or ethyl) with 0 2 , in various solvents. Exposure to 02 (or air) of a benzene, toluene or methylene chloride solution containing PhCOOH and Ru(OEP)(RR'S) 2 at ambient conditions, results in the selective oxidation of the axial ligand(s) on the metalloporphyrin complex to the corresponding sulfoxide(s). For a CD 2 C12 solution containing ,-.---, 20 mM of Ru(OEP)(dms)2 (dms a--dimethylsulfide) and-..., 12 mM PhCOOH, exposed to 1 atm of 0 2 at room temperature, 'H-nmr analysis shows that most of the Ru(OEP)(dms) 2 has oxidized to Ru(OEP)(dmso) 2 over a period of 35h. Three detected intermediates are identified as Ru(OEP)(dms)(dmso) (where s indicates S-coordination of the sulfoxide), Ru(OEP)(dms) 2 +PhC000 and Ru(OEP)(dms)(PhC00). To identify the products and intermediates of oxidation, the complexes in the series Ru(OEP)(RR'S) 2 , Ru(OEP)(RR'S0) 2 and Ru(OEP)(RR'S) 2 + BF4, as well as Me41•1 + Ru(OEP)(PhC00)2, were synthesized and characterized by use of 'H-nmr, it and uv/vis spectroscopy, cyclic voltammetry, and elemental analysis; the x-ray crystal stucture of Ru(OEP)(decMS) 2 +13F4 was obtained. The Ru(OEP)(dmso) 2 complex exists as the bis(Sbound) isomer in the solid state, although variable temperature uv/vis studies suggest that isomerization to 0-bound species occurs in solution. The Ru(OEP)(RR'S)(RR'SO) complexes could not be isolated pure, but they were characterized in solution by 'H-nmr, CV, and uv/vis studies. For solutions containing  iii Ru(OEP)(Et 2 SO) 2 , Ru(OEP)(Et 2S)(Et250), Ru(OEP)(Et 2 S) 2 , and varying concentrations of Et2 S and Et2 SO, the equilibrium and rate constants governing the relative solution concentrations of the three species were determined from stopped-flow experiments. The Ru(OEP)(RR'S)(PhCOO) complexes could not be isolated in pure form either, but solutions containing 1:1 mixtures of Ru(OEP)(dms) 2 +13F4 and Me4 N+Ru(OEP)(PhC00)2 were shown by 'H-nmr to generate Ru(OEP)(dms)(PhCOO). On the basis of detected intermediates and their properties, a "three-stage" mechanism is proposed for the O 2 -oxidation of the thioether ligands of Ru(OEP)(RR'S) 2 in acidic organic media. For example, for the bis(dms) system, in the "first stage", 0 2 coordinates to Ru"(OEP)(dms) formed by dissociation of a dms ligand. This is followed by electron transfer from the metal to 0 2 ; the 02 formed is protonated by PhCOOH to yield HO2 , while Ru m (OEP)(dms)(PhC00) is also formed. The HO 2 disproportionates to 02 and H 2 02 , and the latter oxidizes Et 2S to Et 2 SO. In the "second stage", a Ru m species, probably Ru m (OEP)(dms)(PhCOO), is oxidized to Re by another Ru m species, probably Ru m (OEP)(dms) 2 + 1311C00 - (i.e. 2Ru m --> Ru" + Ru 11). During the "third stage", the Ru"' species is thought to be converted to O=Ru"(OEP)(dms), which then reacts with dms to produce Ru ll (OEP)(dms)(dmso). The overall process results in two moles of dms being oxidized to dmso per mole of 0 2 consumed. The basic mechanism appears to be the same for the oxidation of dialkylsulfides in CH2 C1 2 , benzene or toluene, but with some differences in detail. In the presence of excess thioether, solutions of Ru(OEP)(RR'S) 2 in CH2C12, benzene or toluene, containing PhCOOH, catalyze the O 2 -oxidation of thioether to sulfoxide, but light above 480 nm is required. It is believed that, under catalytic  iv conditions, 0 2 -coordination to the metal is inhibited by the presence of excess thioether, and that light is then required to provide energy for the otherwise unfavourable outersphere electron transfer from the metal to 0 2 . After the initial electron transfer, the reaction would follow the same course as in the stoichiometric oxidation. The catalytic system was studied for the case in which RR'S = Et 2S. The stoichiometry: 2Et 2 S + 0 2 --> 2Et2 SO was verified by gas chromatography and by oxygen-uptake experiments. A kinetic analysis of the gas uptake data showed that, under the experimental conditions used, the initial rate approached a maximum value for [Ru] o > 2 mM, [02 ] > 0.14 M, and [PhCOOH] > 54 mM, with the limiting rate being imposed by the complete absorption of the incident light by the reaction solution. The results of a kinetic modelling analysis suggest that the photoexcited state that gives rise to the observed photochemistry has a minimum lifetime of 10-8 s (in the absence of 02), and that Ru(OEP)(Et 2 S)(Et 2S0), which accumulates as the concentration of Et2 SO builds up, is outside of the catalytic cycle.  V TABLE OF CONTENTS  ABSTRACT ^  ii  TABLE OF CONTENTS ^  v  LIST OF TABLES ^  x  LIST OF FIGURES ^  xi  LIST OF ABBREVIATIONS AND SYMBOLS ^  xviii  ACKNOWLEDGEMENTS ^  xx  CHAPTER 1 INTRODUCTION ^  1  1.1 General Introduction ^  1  1.2 Reactivity of Ruthenium Porphyrins with Dioxygen ^ 5 1.3 Reactivity of Dialkylsulfides with Dioxygen ^  14  1.4 Outline of this Thesis ^  19  NOTES AND REFERENCES FOR CHAPTER 1 ^  20  CHAPTER 2 REACTION OF Ru(OEP)(RR'S) 2 COMPLEXES WITH DIOXYGEN IN ACIDIC MEDIA ^  23  2.1 Introduction ^  23  2.2 Experimental ^  24  2.2.1 General Reagents, Gases and Solvents ^  24  2.2.2 Tetramethylammonium Benzoate (Me4N+PhC00 ) ^ 25 -  2.2.3 Tetra-n-butylammonium Tetrafluoroborate (n-Bu4N+BF4)^26 2.2.4 Ruthenium Porphyrin Complexes ^  26  2.2.4.1 Ru(OEP)(dins)2 ^  27  vi  2.2.4.2 Ru(OEP)(Et2S)2 ^ 28 2.2.4.3 Ru(OEP)(dmso) 2 and the dmso-d 6 Analogue ^ 28 2.2.4.4 Ru(OEP)(Et25.0)2 ^  29  2.2.4.5 Ru(OEP)(decMS0) 2  29  ^  2.2.4.6 Ru(OEP)(dms) 2 +BF4 ^  30  2.2.4.7 Ru(OEP)(Et2S)2 + BF4 ^  31  2.2.4.8 Ru(OEP)(decMS) 2 + BF4 ^  31  2.2.4.9 Me 4 N + Ru(OEP)(PhC00) 2  32  ^  2.2.5 Instrumentation ^  32  2.2.5.1 Ultraviolet/Visible Absorption Spectroscopy ^ 32 2.2.5.2 Infrared Spectroscopy ^  33  2.2.5.3 Proton Nuclear Magnetic Resonance Spectroscopy ^33 2.2.5.4 Conductivity ^  33  2.2.5.5 Cyclic Voltammetry ^  33  2.2.5.6 Elemental Analysis ^  36  2.3 Characterization of Ru(OEP)(RR'S0) 2 Complexes ^ 36 2.4 Characterization of Ru m (OEP) Complexes ^ 40 2.5 Reaction of Ru(OEP)(dms) 2 With Dioxygen and Benzoic Acid in Methylene Chloride ^  49  2.6 Reaction of Ru(OEP)(RR'S) 2 Complexes with Dioxygen and Benzoic Acid in Hydrocarbon Solvents ^  71  REFERENCES AND NOTES FOR CHAPTER 2 ^ 81 CHAPTER 3 A MECHANISTIC STUDY OF THE 0 2 -OXIDATION OF DIETHYLSULFIDE CATALYZED BY  Ru(OEP)(Et2S)2 ^  84  3.1 Introduction ^  84  3.2 Experimental ^  85  3.2.1 Materials ^  85  3.2.2 Stopped-Flow Experiments ^  85  3.2.2.1 Sample Handling ^  85  vii 3.2.2.2 Instrumentation ^ 3.2.3 Gas Chromatography ^  86 86  3.2.3.1 Sample Handling ^  86  3.2.3.1 Instrumentation ^  87  3.2.4 Oxygen Uptake Experiments ^  87  3.2.4.1 Sample Handling ^  87  3.2.4.2 Apparatus Setup ^  88  3.2.5 Data Treatment ^  92  3.3 Ru(OEP)(Et2 S) 2-Catalyzed 0 2 -Oxidation of Et 2 S in Benzene Solution General Observations ^  92  3.4 Stopped-Flow Analysis of Et 2 SO Substitution by Et2S in Ru(OEP)(Et 2 SO) 2 in Benzene Solution ^  113  3.4.1 Data Treatment and Results ^  113  3.4.2 Error Analysis ^  129  3.4.2.1 Uncertainties in the Solution Concentrations ^ 129 3.4.2.2 Instrumental Uncertainties ^  129  3.4.2.2.1 Uncertainties on the Millisecond Timescale ^130 3.4.2.2.2 Uncertainties in the One Hundred Second Timescale ^ 3.4.3 Discussion of the Parameter Values ^  134 135  3.5 Catalytic Oxidation of Et2 S - Rate Dependence on [0 2 ] [PhCOOH] and [Ru(OEP)(Et2S)2] ^  138  3.5.1 Data Treatment and Results ^  138  3.5.2 Error Analysis and Discussion ^  153  3.5.2.1 Experimental Uncertainties ^  153  3.5.2.2 Evaluation of the Kinetic Model ^ 154 NOTES AND REFERENCES FOR CHAPTER 3 ^  170  CHAPTER 4 RATE LAW DERIVATION FOR THE 0 2 -OXIDATION OF DIETHYLSULFIDE CATALYZED BY Ru(OEP)(Et2S)2 ^ 172  viii 4.1 Introduction ^  172  4.2 The Equilibria between Ru(OEP)(Et2S) 2 , Ru(OEP)(Et2S)(Et2SO) and Ru(OEP)(Et 2 SO) 2  ^  4.2.1 Rate Law Derivations ^  172 172  4.2.2 Correlation of Uv/Vis Absorbance Changes to the Derived Rate Laws ^  181  4.2.2.1 First Substitution Reaction ^  181  4.2.2.2 Second Substitution Reaction ^ 185 4.3 Catalytic 0 2 -Oxidation of Et 2 S by Ru(OEP)(Et2S)2 ^ 189 4.3.1 General Rate Law Derivation ^ 189 4.3.2 An Approximate Expression for I. ^  196  4.3.3. Modifications to the Proposed Mechanism ^ 202 4.3.3.1 Internal Rearrangement ^  203  4.3.3.2 Photoactivation Via Metal-to-Porphyrin Charge Transfer ^  205  CHAPTER 5 GENERAL CONCLUSIONS AND SUGGESTIONS FOR FURTHER STUDIES ^  209  REFERENCES FOR CHAPTER 5 ^  213  APPENDIX 1 QUICK BASIC PROGRAMS ^  213  A1.1 LINFIT ^  213  A1.2 POLFIT ^  217  A1.3 ONEDMIN ^  221  A1.4 TWODMIN ^  229  A1.5 ODEGRPH ^  237  APPENDIX 2 RESULTS OF STOPPED-FLOW EXPERIMENTS ^ 242 A2.1 Experiments Carried Out Using Light of 400.5 nm Wavelength ^ 242 A2.1.1 Experiments Carried Out Using a Constant [Et 2SO] of  ix 1.18 ± 0.03 mM ^  243  A2.1.2 Experiments Carried Out Using a Constant [Et2SO] of 17.7 + 0.2 mM ^  249  A2.2 Experiments Carried Out Using Light of 402.8 nm Wavelength ^ 254 A2.2.1 Experiments Carried Out Using a Constant [Et2SO] of 1.18 + 0.03 mM ^  255  A2.3 Blank Experiments ^  259  APPENDIX 3 RESULTS OF OXYGEN UPTAKE EXPERIMENTS ^ 260 A3.1 First Data Set ^  260  A3.1.1 [Ru]. Dependence Studies ^  261  A3.1.2 [PhCOOH] Dependence Studies ^  266  A3.1.3 [0 2] Dependence Studies ^  270  A3.2 Second Data Set ^  274  A3.2.1 [Ru]. Dependence Studies ^  274  A3.2.2 [PhCOOH] Dependence Studies ^  278  A3.3 Additional Data Sets ^  282  A3.3.1 Dependence of the Reaction Rates on the Reaction Vessel Shaking Speed ^  282  A3.3.2 Dependence of the Reaction Rates on the Volume of the Reaction Mixture ^  284  x LIST OF TABLES  Table 2.1 Summary of the 'H-nmr Peak Positions in CD 2 C1 2 for the Ru(OEP) Complexes Discussed in Section 2.5 ^  52  Table 2.2 Positions of the 1 1-I-nmr Signals (Sobs), Assigned to Ru11(OEP)(dms)2 + Ru m (OEP)(dms) 2 + PhC00- in the Experiment Illustrated in Figure 2.7, and the Calculated Remaining Mole Fraction of Ru(OEP)(dms) 2 (NI) ^ 57 Table 2.3 Selected Bond Distances (A) and Bond Angles (deg) for Ru(OEP)(decMS) 2 and Ru(OEP)(decMS)2 ÷ BF4 ^  60  Table 2.4 Summary of the 1 1-1-nmr Peak Positions in C 6D 6 for the dms- and dmsoContaining Ru(OEP) Complexes Discussed in Section 2.6 ^ 73 Table 2.5 Summary of the 1 1.1-nmr Peak Positions in C 6D 6 for the Et2 S- and Et2 SO-Containing Ru(OEP) Complexes Discussed in Section 2.6 ^ 76 Table 3.1 Fundamental Parameters Derived from Equations 3.18 and 3.19 ^ 121 Table 3.2 Fundamental Parameters Derived from Equations 3.24 and 3.25 ^ 129 TABLE 3.3 Fundamental Parameters Derived from the Plots of k obs vs. [Ru] o , [PhCOOH] and [0 2] ^  152  xi LIST OF FIGURES  Figure 1.1. Structure of the porphyrin ring skeleton ^  2  Figure 1.2. Sample structures of Ru(OEP)L2 and Ru(TMP)L 2 complexes. a) Ru(OEP)(Ph 2 S)2 (taken from reference 19); b) Ru(TMP)(THF)(N2 ) (taken from reference 8b). ^  9  Figure 1.3. Proposed catalytic cycle for the epoxidation of olefins catalyzed by Ru(TMP)(0) 2 (taken from reference 11) ^  11  Figure 2.1. Cyclic voltammetry cell: (A) platinum bead working electrode; (B) platinum wire spiral auxilliary electrode; (C) non-aqueous salt bridge; (D) aqueous Ag/AgC1 reference electrode; (E) KC1 reservoir; (F) sample preparation flask. ^  35  Figure 2.2. Changes in the visible spectrum of a CH 2 C1 2 solution containing 0.039 mM Ru(OEP)(Et 2 SO) 2 , and 4.72 mM free Et 2 SO, as the temperature is increased in 10° intervals, from 20-50° C. ^  38  Figure 2.3. Uv/vis spectra in CH 2 C12 of (a) Ru(OEP)(dms) 2 and Ru(OEP)(dms) 2 + 13F4, and (b) Me4 N + Ru(OEP)(PhC00)2. ^ 41 Figure 2.4. Cyclic voltammograms in CH 2 C12 /n-Bu4 N + 13F4 for (a) Ru(OEP)(dms) 2 , (b) Ru(OEP)(dmso) 2 , and (c) Me4N + Ru(OEP)(PhC00) 2- . The cyclic voltammograms of the other dialkylsulfide and sulfoxide complexes are virtually indistinguishable from those of the dms and dmso complexes illustrated. Also, a CV identical to (a) was obtained for Ru(OEP)(dms) 2 + BF4. ^  43  Figure 2.5. (a) Visible spectrum of a 1:1 mixture of Ru(OEP)(Et 2 SO) 2 and AgBF4 in CH 2 C1 2 ; (b) 1 1-I-nmr spectrum of a CD 2 C1 2 solution initially containing [Ru(OEP)] 2 (BF4 ) 2 and free dmso in approximately 1:8 ratio; S^solvent, T = 20° C ^  44  Figure 2.6. 'H-nmr spectrum of Ru(OEP)(decMS) 2 + 13F4 in CD 2C12 , taken at 20.0° C; S^solvent. ^  48  xii Figure 2.7. 'H-nmr spectral changes over time after an acidic CD 2 C1 2 solution of Ru(OEP)(dms) 2 is exposed to 1 atm of 0 2 at room temperature (approximately 20° C). The peak assignments for each species are summarized in table 2.2. ^  50  Figure 2.8. 'H-nmr spectrum of a CD 2 C1 2 solution of Ru(OEP)(dms)2 (approximately 5 mM) to which an excess of a mixture containing 3:1 dms/dmso (neat) has been added. Under these conditions, the major Ru(OEP) species in solution is Ru(OEP)(dms)(dmso). ^ 51 Figure 2.9. 1 11-nmr spectrum of an acidic CD 2 C1 2 solution of Ru(OEP)(dms) 2 35 h after exposure to 1 atm of 0 2 at room temperature (cf. figure 2.7); S =solvent. ^  54  Figure 2.10. 1 11-nmr spectrum of Ru(OEP)(dms) 2 13F4; 20.0° C in CD 2 C12 ; S --solvent. ^  56  Figure 2.11. Crystal structure of Ru(OEP)(decMS) 2 +BF4; selected bond lengths and angles are given in table 2.3. ^  59  Figure 2.12. 'H-nmr spectrum of (a) a mixture (approximately 1:1) of Ru(OEP)(dms) 2 +BF4 and Me4 N + Ru(OEP)(PhC00)2 about 1 h after mixing; (b) pure Me4lsr- Ru(OEP)(PhC00)2. Both spectra in CD 2 C1 2 at 20.0° C, and systems sealed under vacuum; S ---2 solvent. ^ 64 Figure 2.13. Cyclic voltammogram of a solution (CH 2 C1 2/n-Bu4 N + BF4 ) initially containing 0.78 mM Ru(OEP)(decMS) 2 , 71 mM decMS, and 25 mM decMSO. ^  69  Figure 2.14. 'H-nmr spectrum of a C 6D6 solution, initially containing 8.2 mM Ru(OEP)(dms) 2 and 8.2 mM PhCOOH, which was exposed to 1 atm of 0 2 for about 36 h at room temperature; S 7--.- solvent, g s--- grease, ? ....unidentifed signals  72  Figure 2.15. 1 H-nmr spectrum of a C 6D 6 solution, initially containing 2.3 mM Ru(OEP)(Et 2 S) 2 and 3.3 mM PhCOOH, which was exposed to 1 atm of 0 2 for about 12 h at 35° C; S 7.--- solvent, g --- grease, ? as unidentified signals. ^  75  xiii Figure 2.16. 1 H-nmr spectrum of a C 6D 6 solution, initially a suspension of Re(OEP)(dms) 2 +BF4 and Me4 N + Ru III (0EP)(PhC00) 2 (approximately 4x106 mol of each), which was allowed to stand overnight under vacuum; S =.---- solvent, ? Fa- unidentified signals. ^  78  Figure 3.1. Apparatus used for gas uptake measurements. (a) Complete setup; (b) Close-up view of the oil bath and housing, showing the orientation of the light source. Key components: (A) Thermostatted and insulated oil bath; (B) Reaction vessel; (C) Oil manometer; (D) Mercury burette and reservoir; (E) Projection lamp; (F) Aluminum foil; (G) Compressed air manifold; (H) Screen. (1)-(12): Various taps and valves; see text for explanations ^  89  Figure 3.2. Dependence of Et 2 SO production rate on reaction vessel illumination. [Ru(OEP)(Et2S) 2 ] = 0.34 mM; [PhCOOH] = 5.3 mM; [Et 2 S] = 0.74 M; the reaction was carried out in benzene solution at 35° C, in a flask exposed to the air. Reaction progress was followed by gas chromatography. ^  94  Figure 3.3. (a) Uv/visible spectra of Ru(OEP)(Et 2 S) 2 , and of the yellow and blue filters used to test which wavelengths are necessary for Et 2 S oxidation to proceed. (b) Effects of the cutoff filters on the rate of Et 2 SO production, as measured by 02 -absorption at 35° C; in each case, a benzene solution initially containing 0.84 mM Ru(OEP)(Et 2 S) 2 , 24 mM PhCOOH, and 0.74 M Et2 S was exposed to 0.81 atm of 0 2 (corrected for benzene vapour pressure). ^  95  Figure 3.4. Scheme showing the types of electronic transitions which can occur in d 6 six-coordinate ruthenium porphyrins (adapted from reference 8). ^ 97 Figure 3.5. Two possible mechanisms for the photochemical stage of the 0 2 oxidation of Et 2 S catalyzed by Ru(OEP)(Et 2 S) 2 : a) porphyrin  7-7r *  transition, followed by transfer of the excited electron to 02 ; b) direct metal-to-porphyrin charge-transfer, followed by transfer of the excited electron to 0 2 ^  98  xiv Figure 3.6. Relationship between the light energy absorbed by Ru(OEP)(Et 2S) 2 at 525 nm, and the relative free energy changes associated with various transformations; see text for details. ^  102  Figure 3.7. Gas chromatographic trace of a benzene solution initially containing 0.42 mM Ru(OEP)(Et 2 S) 2 , 6.5 mM benzoic acid, and 0.74 M Et 2 S, exposed to 0.81 atm of 0 2 (corrected for benzene vapour pressure) at 35° C for 2.5 h. 4.89 min: Et 2S 2 ; 6.05 min: Et 2 SO; 7.11 min: Et 2 SO2 ; 7.90 min: n-undecane; 9.30 min: benzoic acid. The signal at 13.16 min is that of an unidentified product; the rest of the unidentified signals are present at the start of the reaction. ^  104  Figure 3.8. Scheme proposed for the 0 2 -oxidation of Et2 S to Et2 SO, catalyzed by Ru(OEP)(Et 2 S) 2 and PhCOOH (dotted pathways imply that these processes can be neglected under catalytic conditions).  106  Figure 3.9. A typical plot showing the accumulation of Et2 S0 with time, determined by monitoring the 0 2 -uptake (see section 3.5 for full details). For this experiment at 35° C, the initial concentrations of the reagents are: [Ru(OEP)(Et 2 S) 2] = 0.202 mM; [PhCOOH] = 24.4 mM; [Et 2 S] = 0.742 M; p02 = 0.813 atm (corrected for benzene vapour pressure). ^ 108 Figure 3.10. Relationship between the light energy absorbed by Ru(OEP)(Et2S)(Et250) at 525 nm, and the free energy changes associated with various transformations. AG° for the oxidation at the metal of Ru ll (OEP)(Et2 S)(Et 250) was estimated from the CV data for the analogous Ru(OEP)(decMS)(decMS0) system (see section 2.5 and figure 2.13); for the one-electron ring oxidation, AG° is assumed to be the same as in the Ru(OEP)(Et2 S) 2 system (see figure 3.6). ^  110  Figure 3.11 Uvivis spectra of a benzene solution initially containing 0.202 mM Ru(OEP)(Et 2 S) 2 , 0.742 M Et 2 S, and no benzoic acid, at various times after exposure to a light source, and 0.813 atm of 0 2 (corrected for benzene vapour pressure). The same results were obtained ^ 111 Figure 3.12. Scheme showing the proposed mechanisms for the sequential  XV  substitution of two Et2 SO ligands by Et 2S in Ru(OEP)(Et2 SO) 2 . In solution, the bis-sulfoxide species is believed to exist as a mixture of the S- and 0bound linkage isomers (see section 2.3)  114  Figure 3.13. Uv/vis spectral changes observed as: (a) a benzene solution initially containing 3.4x10 6 M Ru(OEP)(Et 2 SO) 2 and 0.19 M free Et2 SO is titrated with neat Et2 S; (b) a benzene solution initially containing 1.7x105 M Ru(OEP)(Et 2 S) 2 and 0.74 M free Et 2 S is titrated with neat Et 2 SO. T = 35° C for both experiments. ^  115  Figure 3.14. A typical, fitted stopped-flow trace of the change in absorbance over 100 ms, at X = 400.5 nm, when Et2 S is substituted for Et 2 SO in Ru(OEP)(Et 2 SO) 2 . [Et2 S] = 9.27+0.09 mM; [Et 2 SO] = 1.18+0.03 mM; [Ru] c, = (3.44+0.07)x10 6 M. The first four points likely are in the dead time of the instrument, and are neglected in the fit. ^ 122 Figure 3.15. Portions of the plots of [Et 2 S]/3 1 vs [Et2 S] for data collected at X = 400.5 nm over 100-ms time-frames. a) [Et 2SO] = 1.18±0.03 mM; b) [Et2 SO] = 17.7±0.2 mM. In each case [Ru] o = (3.44±0.07)x1 0-6 M. The residual plots show the full range of data collected; the main plots show only the region in which $ increases (Q is the goodness of fit given the obtained x2 value). ^  123  Figure 3.16. Portions of the plots of [Et2 S]/v ol vs. [Et2 S] for data collected at X = 400.5 nm over 100-ms time-frames. a) [Et 2SO] = 1.18+0.03 mM; b) [Et2 SO] = 17.7±0.2 mM. In each case, [Ru],, = (3.44±0.07)x1 0-6 M. The residual plots show the full range of data collected; the main plots show only the region in which v ol increases. ^  124  Figure 3.17. A typical, fitted stopped-flow trace of the change in absorbance over 100 s, at X = 402.8 nm, when Et 2 S is substituted for Et 2 SO in Ru(OEP)(Et2 S)(Et2S0). [Et2 S] = 18.6+0.2 mM; [Et 2 SO] = 1.18±0.03 mM; [Ru] o = (3.44+0.07)x10-6 M. 127 Figure 3.18. Portions of the plots of: a) [Et 2 S] 2/13 2 vs [Et2S], and b) [Et 2S] 2ivo2 vs [Et2 S], for data collected at X = 402.8 nm over 100-s time-frames. [Et2SO]  xvi = 1.18+0.03 mM; [Ru] o = (3.44+0.07)x10 -6 M. There is one off-scale point at [Et 2 S] = 0.232+0.002 M for each plot; all of the data are tabulated in appendix 2. ^  128  Figure 3.19. Variation of the parameters 0 1 and 7 1 from experiment to experiment, when all reagent concentrations are held constant. The error bars represent the uncertainties estimated from fitting the raw stopped-flow data ^  131  Figure 3.20. Weakening of 7r-bonds trans to a sulfoxide; 0 - bonds trans to the sulfoxide will also be weakened, since the sulfoxide can transfer more °electron density to the Ru d z2 orbital than a comparable ligand incapable of 7r-bonding (see text) ^  137  Figure 3.21. Visible spectra of pure Ru(OEP)(Et 2 S) 2 (3), a solution containing mostly Ru(OEP)(Et2 S)(Et§0) (2, see text), and pure Ru(OEP)(Et 2 SO) 2 (1 and 1'). The dashed lines indicate the region of all three spectra over which the integrated extinction coefficients were calculated (see text for details) ^  144  Figure 3.22. A plot of [Et2 SO] vs. time, fitted using the least squares procedure described in the text. For this experiment, the initial concentrations of the reagents are: [Ru(OEP)(Et 2S) 2 ] = 0.202 mM; [PhCOOH] = 2.31 mM; [Et2 S] = 0.742 M; p0 2 = 0.813 atm (corrected for benzene vapour pressure). ^  147  Figure 3.23. Plots of k obs vs.: (a) [Ru] o , with [PhCOOH] and [0 2 ] held constant at 24.4 and 7.63 mM, respectively; (b) [PhCOOH], with [Ru] o and [02 ] held constant at 0.408 and 7.63 mM, respectively; (c) [0 2] with [Ru] o and [PhCOOH] held constant at 0.408 and 24.4 mM, respectively. The error bar magnitude in each case is given by a. ^  149  Figure 3.24. Plots of k obs vs.: (a) [Ru] o , with [PhCOOH] and [0 2 ] held constant at 24.4 and 7.63 mM, respectively; (b) [PhCOOH], with [Ru] o and [02 ] held constant at 0.202 and 7.63 mM, respectively. The error bar magnitude in each case is given by a.  151  xvii Figure 3.25. Plots of the goodness of fit parameter (Q) vs.: (a) [Ru] o ; (b) [PhCOOH]; (c) [0 2 ] for the fitting procedures illustrated in figures 3.23 and 3.24, and assuming that 0 = 0.85 (see text for details). ^ 155 Figure 3.26. Plots of the goodness of fit parameter (Q) vs.: (a) [Ru] o ; (b) [PhCOOH]; (c) [0 2 ] for the fitting procedures illustrated in figures 3.21 and 3.22, and assuming that 0 = 0.6 (see text for details). ^ 160 Figure 3.27. A plot of [Et 2 SO] vs. time, fitted using: (a) the least squares procedure described in the text; (b) the function [Et 2 SO] = 2k3 [Ru] ot. For this experiment, the initial concentrations of the reagents are: [Ru(OEP)(Et2 S) 2] = 0.0253 mM; [PhCOOH] = 24.4 mM; [0 2 ] = 7.63 mM; [Et2 S] = 0.742 M. ^  164  Figure 4.1. Mechanism proposed for the sequential substitution of two Et 2 SO ligands by Et2 S, assuming that in solution the bis(sulfoxide) species exists as a mixture of the S- and 0-bound linkage isomers. ^ 174 Figure 4.2. Mechanism proposed for the 0 2 -oxidation of Et2 S to Et 2 SO, catalyzed by Ru(OEP)(Et 2 S) 2 and PhCOOH (dotted pathways imply that these processes can be neglected, or do not occur, under catalytic conditions; see the assumptions on pp. 140-141). ^  190  Figure 4.3. Alternative mechanism for the photochemical stage of the 0 2 -oxidation of Et2 S catalyzed by Ru(OEP)(Et 2 S) 2 ; see text for details. ^ 206  ^  xviii  LIST OF ABBREVIATIONS AND SYMBOLS  Where possible, all abbreviations used are those recommended in: "Handbook for Authors". Amer. Chem. Soc. Publications, Washington, D. C., 1978; pp. 29-47. The following is a list of specialized abbreviations and symbols used in this thesis.  Symbol or Abbreviation^  Meaning  AZBN^  azoisobutyronitrile  Cp^  cyclopentadienyl anion  CT^  charge transfer  CV^  cyclic voltammetry  d^  doublet  decMS^  n-decylmethylsulfide  decMSO^  n-decylmethylsulfoxide  DMA^  N,N'-dimethylacetamide  dms^  dimethylsulfide  dmso^  dimethylsulfoxide  m^  multiplet  NHE^  normal hydrogen electrode  OCP^meso-tetra(2,6-dichlorophenyl)porphyrinato dianion OEP^2,3,7,8,12,13,17,18-octaethylporphyrinato dianion Porp^  any general porphyrinato dianion  xix ppm^  parts per million  py^  pyridine  q^  quartet  qn^  quintet  s^  singlet  SCE^  saturated calomel electrode  sx^  sextet  t^  triplet  TMP^ meso-tetramesitylporphyrinato dianion TPP^  meso-tetraphenylporphyrinato dianion  XX  ACKNOWLEDGEMENTS  I wish to thank all of those who helped me, directly or indirectly, to complete this work. First, I wish to express my deepest gratitude to Professor B. R. James, for his expert guidance and support during the course of my studies; it has been a pleasure to work for him. I also owe special thanks to my wife Muriel, not only for her unfailing moral support, but also for doing the illustrating for the thesis. My thanks to colleagues in both the B. R. James and D. Dolphin research groups, for their friendship and helpful discussions; many an idea crystallized while sharing theories over coffee! In the same vein I wish to thank my good friends K. Barnard and S. Habib, for enduring innumerable questions about numerical analysis, and coming up with helpful answers. I am also grateful to Dr. E. Burnell of this department for his helpful comments and suggestions. The prompt and courteous services provided by the crystallographer Dr. S. Rettig, and by the nmr, Elemental Analysis, Electronic, Glassblowing and Mechanical shop personnel are deeply appreciated. Finally, I would like to thank my family, especially my parents and my brother, for their unfailing love and support.  1 CHAPTER 1 INTRODUCTION  1.1 General Introduction The porphyrin macrocycle (figure 1.1) is a planar 18-electron aromatic system, containing a total of 11 conjugated double bonds. The four pyrrolic nitrogen atoms define an equatorial plane, and the porphyrin dianion, formed by removing the two internal protons, is a planar tetradentate chelating agent capable of forming coordination compounds with all the transition and lanthanide metals, as well as many of the main group metals and semimetals, and a number of actinides.' Iron porphyrins are ubiquitous in natural protein and enzyme systems, and have been identified as vital components in the active sites of such diverse molecules as hemoglobin which is an oxygen transport protein, the cytochromes which perform an assortment of oxidation-reduction tasks, and oxygenases which catalyze selective oxidations using 0 2 . 2 Because of their importance in natural systems, iron porphyrins have been the subject of intense investigation over the last 30 years, and several model (i.e. "protein-free") systems, using a variety of synthetic porphyrins, have been devised.' In addition to their use within model systems for naturally occurring iron porphyrins, studies are now under way to use robust synthetic iron porphyrin catalysts in industrial oxidation processes.' As mentioned, porphyrin systems containing almost every metal in the periodic table have now been synthesized and characterized.' In large part the interest in metalloporphyrins other than Fe(Porp) has also been fuelled by a desire to better  ^  Ri^R2 OEP C7HS TPP^H^C6H5 TMP^H^2, 4, 6-Me3C 6H 2 OCP^H^2, 6-C1,,C6H3  Figure 1.1. Structure of the porphyrin ring skeleton  3 understand the natural porphyrin systems;' much can be learned about one element by comparing and contrasting its behaviour with that of other elements. Because ruthenium is immediately below iron in the periodic table, the possibility of comparing and contrasting ruthenium porphyrins with iron porphyrins is especially intriguing, and since 1969 various ruthenium porphyrins have been synthesized and characterized." Despite the fact that it has been over twenty years since the first ruthenium porphyrin complex was prepared, it still appears too early to assess the full impact of the ruthenium porphyrin studies on the understanding of the naturally occurring iron porphyrin systems; what can be said for sure is that the study of ruthenium porphyrins has developed into a mature and interesting field in its own right. Much of the work done to date has focused on the synthesis of novel ruthenium porphyrins and, in this respect, the dimeric complexes such as [Ru(OEP)] 26 and [Ru(OEP)BF4] 27 (OEP^dianion of octaethylporphyrin), and the four-coordinate Ru(TMP) 8 (TMP^dianion of tetramesitylporphyrin) deserve special mention (see figure 1.1 for porphyrin systems). These complexes are coordinatively unsaturated, and exhibit many remarkable physical and chemical properties." The lack of axial ligands also makes these complexes excellent starting materials for the preparation of other Ru(Porp) complexes (Porp = dianion of a porphyrin in general); indeed, using the dimeric and four-coordinate complexes as starting materials, a wide variety of Ru ° , Ru", Ru m , Ru N and Ru vi materials has now been synthesized." Investigations into the reactivity of various ruthenium porphyrins have also yielded interesting catalytic properties in reactions as diverse as the decarbonylation of aldehydes,' and the 02 -oxidation of various organic compounds, including olefins to  4 epoxides." One problem with some of the catalysis studies carried out to date is that often the reactivity patterns of the ruthenium porphyrins are complex; consequently, many of these studies provided only a rough outline of the possible mechanisms involved; this was the case, for example, in the decarbonylation process,' and in the 02 -oxidation of phosphines (see below).' However, the advances in synthetic methods of recent years, and the isolation and concomitant characterization of higher-valent Ru(Porp) complexes (notably of Ru g , Ru l`' and Ru v1 species) 9 now makes it possible to identify intermediates in complex reaction pathways, which in turn means that detailed mechanistic studies are now feasible. This thesis describes just such a study, on the autoxidation of thioethers to sulfoxides catalyzed by Ru(OEP)(RR'S) 2 complexes (R and R' are alkyl groups). Interest in the possible autoxidation of thioethers to sulfoxides, using Ru(Porp) complexes as catalysts, was sparked by earlier studies in our laboratories which showed that Ru(OEP)(PPh 3) 2 catalyzes the autoxidation of free PPh 3 to OPPh3 (see section l.2). 12 As the subject of a detailed study, the selective oxidation of sulfides to sulfoxides was more attractive than the oxidation of PPh 3 to OPPh 3 , because of the potential commercial value of the former process; 13 ' 14 this consideration played a part in the initial decision of which system to investigate further. As will be seen in the following two sections of this chapter, many advances have been made in the field of catalytic 0 2-oxidation of thioethers since this project was first conceived, and at present two other processes" appear more effective than the process described in this thesis (this topic is discussed in more detail in chapter 5). Nevertheless, this thesis project has revealed some interesting properties of ruthenium porphyrins, some of which may have bearing on the results of  5 earlier investigations on catalyzed 0 2 -oxidation of PPh 3 12 , and the catalyzed decarbonylation of aldehydes,' for which mechanistic details were lacking.  1.2 Reactivity of Ruthenium Porphyrins with Dioxygen  Early studies on the reactivity of Ru(Porp) complexes with dioxygen focused on Ru 11  ^and commented on the high stability of the Re species to oxidation by air  when compared to the then known Fe ll analogues."'" The stability was rationalized in terms of the larger ruthenium d-orbitals leading to greater ligand field stabilization by the porphyrin, as well as to more efficient metal-to-porphyrin ir-backbonding.  16,17 While  Re(Porp) complexes are more thermodynamically stable to oxidation than Fe ll (Porp) complexes, those prepared in the early studies were exceptionally stable, and many airsensitive Ru(Porp) complexes have been prepared since that time, 18 " 9 including species that bind 0 2 reversibly.' The first Re(Porp) complexes isolated contained CO as an axial ligand, and it was proposed that efficient 7-backbonding from the ruthenium dorbitals to the carbonyl 7 orbitals was decreasing the electron density around the metal, .  and thus stabilizing the lower oxidation state (a well-known property of the CO ligand). 21 The next Ru(Porp) complexes to be prepared were of the form Re(Porp)L 2 , where L = py or another nitrogenous base; although these complexes exhibited (Ru m + e ---' Re) reduction potentials as much as 0.6 V lower than those of the Ru(Porp)CO complexes, they also appeared to be rather stable to air-oxidation. 17 Proceeding from the hypothesis that 02 -oxidation required initial coordination of 0 2 to the metal center, the apparent stability of the Ru(Porp)L2 complexes was attributed to the fact  6 that all of these compounds were substitutionally relatively inert; Ru(TPP)py 2 (TPP -rm dianion of tetraphenylporphyrin, see figure 1.1), for instance, took a week under 1 atm CO at room temperature to give the thermodynamically favoured (carbonyl)pyridine product. ° In recent years many Ru(Porp) complexes have been prepared with labile axial ligands such as MeCN, THF, N2 and Ph 2S 8 ' 19 ' 2° and a series of monomeric and dimeric complexes exemplified by Ru(TMP) g , [Ru(OEP)1 2 and [Ru(TPP)]2, 6 which contain no extraneous axial ligands have been isolated; all such complexes are invariably extremely air- sensitive. If a Ru 11 (Porp)L2 complex is substitutionally inert, one could still envision an "outer sphere" electron transfer from Ru n to 0 2 . In fact, such a mechanism has been invoked in several instances; for example, in the 02 -oxidation of PPh3 to OPPh 3 catalyzed by Ru(OEP)(PPh3)2, mentioned at the end of the last section, the initial step in the cycle was proposed to be"  Ru 11 (OEP)(PPh 3 ) 2 + 0 2 c'-'- Ru 111 (OEP)(PPh 3 ) 2 + + °2^  1.1  However, this reaction is highly unfavourable thermodynamically,' and a proton source is required to promote the subsequent reactions:  02 ± H + R--'' H0 2^1.2 -  2H02  -,  H202 + 02  ^  1.3  7 The disproportionation reaction 1.3 is irreversible,  Z2  and it was hypothesized that this  step makes possible the otherwise unfavourable outer sphere oxidation of Ru(OEP)(PPh 3) 2 complexes by 0 2 . The following steps were proposed to account for the phosphine oxidation, and to regenerate the Ru n species and complete the catalytic cycle: 12  H2 02 + PPh 3 Ar-". OPPh 3 + H 2 O  ^  2Re(OEP)(PPh 3 ) 2 ÷ + H2 O + PPh 3  1.4  2Ru 11(OEP)(PPh 3 )2 + 2H+ + OPPh 3 1.5  Equations 1.1-1.5 constitute a net catalytic pathway by which two moles of PPh 3 are oxidized by one mole of 0 2 :  2PPh 3 + 02  2OPPh 3^1.6  Outer sphere electron transfer is a major topic of this thesis, and it will be seen in chapter 3 that, for some systems at least, the presence of a proton source is not thermodynamically sufficient to permit a process such as equation 1.1 to occur; the reaction also requires a light source to provide the necessary energy. The study referred to above mentions difficulty in obtaining reproducible kinetic data, and it is possible that this difficulty arose from an unrecognized light dependence. In the absence of an oxygen atom acceptor such as PPh 3 , 02 -oxidation of Ru(OEP)L2 and Ru(TPP)L2 complexes (where L =--- a neutral ligand such as THF) often  8 leads, in the presence of an anion source X - , ultimately to the formation of the thermodynamically stable [Ru w (Porp)M 20. 9ca" For example, if the complex Ru(OEP)(Ph 2S) 2 is exposed to air, it is rapidly oxidized to [Ru(OEP)OH] 2 0, and the freed thioether axial ligands are recovered intact (trace water is believed to provide the OM.' Complexes such as this one, referred to commonly but incorrectly as "A-oxo dimers", were first prepared in 1981 by Masuda et al.,' and have been characterized extensively since that time. 9c ,23,24 The A-oxo dimers appear to be quite resistant to reduction, and so their formation is a problem if one wants to establish a system for catalytic O 2 -oxidation using Ru(Porp) complexes. Of note, although resistant to reduction, there is evidence that kt-oxo dimers can be slowly demetallated in benzene solution, according to the following reaction: 12  [Ru(OEP)(OH)] 2 0 + H 2O --> 2RuO2 + 2H 2 (OEP)^  1.7  If the ortho (and para) protons on the phenyls of TPP are replaced by methyl groups, the resultant TMP system, when metallated, has sterically crowded axial sites; figure 1.2 shows an OEP system (which is less sterically hindered at the axial sites than TPP systems) and a TMP system. The phenyl rings of TMP are perpendicular to the porphyrin plane, and space filling molecular models show that the o-methyls crowd the  9  (a)  (b)  Figure 1.2. Sample structures of Ru(OEP)L 2 and Ru(TMP)L2 complexes. a) Ru(OEP)(Ph 2 S)2 (taken from reference 19); b) Ru(TMP)(THF)(N 2 ) (taken from reference 8b).  10 axial sites. Of importance, Ru(TMP) is sterically prevented from forming  14 oxo -  dimers,  and the end-product of Ru(TMP) oxidation, and of Ru(TMP)L 2 oxidation when L is a labile axial ligand such as MeCN or THF, has been shown to be the trans-dioxo species Ru v1 (TMP)(0) 2 . 8,9b,ii Unlike the A oxo dimers, which do not act as 0-atom donors, -  Ru v1 (TMP)(0) 2 reacts readily with oxygen atom acceptors such as olefins" and organic sulfides,''' to give the corresponding epoxides and sulfoxides. This type of reaction (0atom transfer from metal-oxo species generated via 02 ) has generated considerable interest in recent years, and several studies have been published on the subject  ;  4,96,11,25,26  two examples will be considered in detail. In their 1985 paper, Groves and Quinn reported that Ru(TMP)(0) 2 will catalyze the 0 2 -oxidation of various alkenes to their corresponding epoxides, with two moles of epoxide being produced for every mole of 0 2 consumed." The trans-dioxo species was also found to oxidize alkenes stoichiometrically in the absence of 0 2 , if pyridine was added to the reaction mixture. Thus the products of the stoichiometric oxidation of norbornene were about 1.6 equivalents of norbornene oxide and Ru 11 (TMP)py 2 ." The mechanism proposed for the catalytic oxidation is shown in figure 1.3. The transRu vldioxo species transfers an 0-atom to an alkene, leaving an epoxide and 0=RuNTMP); this species disproportionates to Ru v1 (TMP)(0) 2 and Ru(TMP), which is immediately oxidized back to 0=Ru"(TMP) by 02 . The intermediacy of the 0=RuNTMP) species has since been verified by independent spectroscopic studies, as has its sensitivity to disproportionation.' Structures of trans-Ru(OCP)(0 2 ) 28 and Ru(OCP(C0)(Styrene Oxide) 29 have been reported also, where OCP  11  VIM  1/2 0 2  Figure 1.3. Proposed catalytic cycle for the epoxidation of olefins catalyzed by Ru(TMP)(0) 2 (taken from reference 11).  12 ("octachioroporphyrin") is the dianion of meso-tetra(2,6-dichlorophenyl)porphyrin (see below). Studies carried out in our laboratories have focused in detail on the reactions of Ru(TMP)(0) 2 with phenol and with dialkylsulfides,"'''' the latter reactions are directly related to the subject of this thesis, and will be discussed in some detail. Uv/vis and 'Hnmr experiments showed that if excess of a dialkylsulfide such as Et 2S was added to a benzene solution of Ru(TMP)(0) 2 under argon (or dioxygen), Ru"(TMP)(QSR 2) 2 , Ru 1 (TMP)(QSR 2)(0SR2), and Ru"(TMP)(0SR2) 2 were produced consecutively (0 and S signify oxygen- and sulfur-bound sulfoxides, respectively). The mechanism (supported by kinetic data) proposed for these transformations was:  Ru(TMP)(0) 2 + SR 2^[O=Ru(TMP)QSR 2]  1.8  [0 =Ru(TMP)QSR 2] + SR 2^Ru(TMP)(QSR2) 2  1.9  Ru(TMP)(QSR 2) 2 - Ru(TMP)(OSR2)(OSR2)  1.10  Ru(TMP)(OSR2)(OSR 2 )^Ru(TMP)(0SR2)2  1.11  The O=Ru(TMP)QSR 2 intermediate was not observed experimentally, and kinetic data implied that reaction 1.9 was much faster than 1.8. Interestingly, this situation is different from that implied by the results obtained for the epoxidation of olefins; in this latter case, the major species present during catalysis was considered to be O=Ru(TMP);  11,27 it  13 appears that the substrate being oxidized plays an important role in determining the preferred oxidation state of the detected ruthenium species. The data imply that Ru vi (TMP)(0) 2 is more effective than Ru w (TMP)0 for olefin epoxidation, while Ru w (TMP)(0)(OSR2 ) is more effective than Re l (TMP)(0) 2 for 0-atom transfer to thioethers. Both reactions 1.8 and 1.9 are much faster than the subsequent axial ligand isomerization reactions 1.10 and 1.11; once formed, Ru(TMP)(0SR 2) 2 is substitutionally inert under the ambient reaction conditions. " 9h 25 '  '  The Ru(TMP)/0 2 system will catalytically oxidize dialkylsulfides selectively to the corresponding sulfoxides; however, the catalysis stops after about 8 turnovers at ambient conditions. 9b " 25 The catalysis was considered to occur via the loss of the 0-bonded '  '  sulfoxides from Ru(TMP)COSR 2)2 to regenerate under 0 2 the trans-dioxo species, while formation of the substitutionally inert Ru(TMP)(0SR 2 ) 2 inhibited the catalytic cycle. At higher temperatures (e.g. 65° C), up to 15 turnovers were recorded; however, under these conditions rapid catalyst degradation occurred. More efficient catalytic oxidation of dialkylsulfides was obtained by using transRu(OCP)(0) 2 as a catalyst instead of the TMP system. 9" The axial sites of Ru(OCP) are sterically hindered as in Ru(TMP), so that again tc oxo dimer formation is prevented. In -  addition, the electron-withdrawing chloro groups on the phenyls make the porphyrin more resistant to self-oxidation, a well established phenomenon.' The greater robustness of Ru(OCP)(0) 2 , compared to the TMP system, allowed its use at temperatures as high as 100° C, and, under these conditions, more than 30 equivalents of dialkylsulfide could be oxidized to sulfoxide, with no observable decomposition of the catalyst. 9"h Of note, in addition to making the catalyst more resistant to self-oxidation, the Cl substituents also  14 make the 0---- Ru =0 moiety more electrophilic, 4 which has two beneficial effects: first, the reactivity toward the thioether substrate is increased, as evidenced by increased reaction rates even at room temperatures, and second, Ru(OCP)(0SR 2) 2 is stabilized relative to the S-bound isomers."'" Previous reports in the 1970s (on non-porphyrin systems) have suggested that S-bonded dimethylsulfoxide (dmso) complexes of ruthenium are favoured in cases where the metal center is electron-rich (in which case Ru- ,S 7rbackbonding can reduce the electron density on the metal), whereas 0-bonding is favoured when the metal center is more electron-deficient: 3°51 however, more recent findings on both dmso and tetramethylenesulfoxide derivatives of Ru ll suggest that steric factors dominate the choice of oxygen- versus sulfur-bonding.'  1.3 Reactivity of Dialkylsulfides with Dioxygen Under ambient conditions and in the absence of a catalyst or radical initiator, dialkylsulfides do not react with  02. 33  In the presence of a free-radical initiator such as  azoisobutyronitrile (AZBN), autoxidation of the dialkylsulfides proceeds via hydrogen atom abstraction; the observed product distribution has been rationalized by the following mechanistic scheme: 33 Stage 1  R'CH 2 SR" + R . --> R'(CH•)SR"^(Chain Initiation)^ 1.12  R'(CH . )SR" + 0 2 --> R'CH(0 2 •)SR"^  1.13  15 R'CH(02)SR" + R'CH 2 SR" --> R'CH(0 2 H)SR" + R'(CH . )SR"  1.14  R'CH(02H)SR" + R'CH 2 SR" --. R'CH(OH)SR" + R'CH 2 (SO)R"  1.15  R'CH(OH)SR" -> R'CHO + R"SH  1.16  R`CH(OH)SR" + R"SH --> H 2 O + Complex sulfides  1.17  Stage 2  Stage 3  As can be seen, the free-radical process yields a fairly complex product distribution, which is generally undesirable. The aim of our investigations, as well as those of other researchers in the field, has been to try to find catalysts which result in the selective (preferably exclusive) production of dialkylsulfoxides, 13 or sometimes dialkylsulfones. 13b In 1985 Riley and Correa reported that, in polar solvents, and under conditions of high temperature (>100° C) and 0 2 pressure (- 40 atm), dialkylsulfides were slowly but selectively oxidized to the corresponding sulfoxides.' The mechanism suggested for this reaction was"  16 R2S + 02 --). R2S + . +  02 -^1.18  R2 S+ . + 02 --a, R2S +00 .^1.19  R2S + 00 + 02 --* R2S + 00 + 02 .  .  R2S + 00 + R2S -" 2R2S 0  ^  1.20  -  ^  1.21  -  Two later papers 15 ' 36 reported that cerium(IV) ammonium nitrate is a very efficient catalyst for the process just described; it was proposed that cerium(IV), being a better oxidant than 0 2 , was now responsible for the initial one-electron oxidation of the R2 S (reaction 1.18). 15 . 3 ' Thus  R2 S + Ce N --* R 2 S+ . + Ce m^1.22  The thioether radical cation could then undergo reaction 1.19, after which the Ce  w  would  be regenerated according to the process  R2 S÷00 . + Ce rn -- R 2 S + 00- + Ce N^1.23  Finally, two sulfoxides would be regenerated according to equation 1.21. This system is reportedly very efficient; thus, for example, in a 9:1 CH 3 CN/H2 0 solution, containing about 0.017 M ceric ammonium nitrate and 1.0 M tetrahydrothiophene under 125 psi 0 2  17 pressure, the thioether was completely oxidized with a half-life of 7 min at 75° C. The Cely systems from Riley's group,'" and those reported from this laboratory and discussed in section 1.2, 9l), ' ,25 appear to be the only ones, apart from a system to be described in this thesis, in which the selective catalytic 0 2 -oxidation of dialkylsulfides to the corresponding sulfoxides is accomplished with potentially useful turnovers. Other systems for the metal-complex catalyzed 0 2 -oxidation of thioethers to sulfoxides have been described,' but in every case a stoichiometric reagent other than 0 2 was also required. Two such systems are given as examples. In 1984 Riley and Shumate reported that cis-RuC1 2 (dmso) 4 and trans-RuBr 2 (dms0) 4 catalyzed selective oxidation of various dialkylsulfides to their corresponding sulfoxides, under 100 psi of 0 2 at 100° C. 37 This reaction proceeded only in alcoholic solvents. From kinetic studies and product analysis, the following mechanistic scheme was proposed:  "Ru n " + 2H+ + 0 2 -, "Ruw" + H202  1.24  R2S +  1.25  H20 2 -*  R2 SO + H2 O  "Re" + Me2 CHOH --> "Re" + Me 2 C=O +2H+  1.26  The 1984 article gave no conclusions as to the nature of the actual catalytic species, but later studies provided evidence which suggested that the trans,trans,transRuX 2 (SR 2) 2 (dmso) 2 species are the starting catalysts.' No further details were given on  18 the possible nature of the Ru iv intermediate. The original paper cited the lack of free radical products of alcohol oxidation, and separate studies with various discrete Ru m species supported the hypothesis that Ru n is oxidized directly to Ru"" via reaction 1.24." Another system in which catalytic oxidation of thioethers was observed involved the autoxidation of diphenylsulfide catalyzed by RhC1 3 (dmso) 3 , in N,N'dimethylformamide (DMA) solvent.' In this case,  H2 was  used as the coreductant,  following earlier work on the use of H2 with Rhin to reduce dmso catalytically to the sulfide.' The following mechanism was proposed for the sulfide oxidation:  Rh mdmso + DMA^RIPDMA + dmso  1.27  Rh mDMA + H2 "'" [RA IDMA] + 2H+  1.28  [Rh iDMAJ + 0 2 -, Rh m (02 2)(DMA)  1.29  Rh m (022-)(DMA) + H2 '- [Rh'DMAJ + H202  1.30  H202 + Ph2S --> H2O + Ph2SO  1.31  Steps 1.27 and 1.28 generate the 0 2 -sensitive catalyst; the catalysis operates via steps 1.29-1.31. Attempts at carrying out these reactions in other solvents, such as 1,2dichloroethane, were not successful. Interestingly, more basic dialkylsulfides were not  19 oxidized by the RhC1 3 (dmso) 3 system. This suggested that, in this case, coordination by sulfides inactivated a potentially catalytic system. 39  1.4 Outline of this Thesis  Earlier work from these laboratories had noted briefly that Ru(OEP)(decMS) 2 (decMS = decylmethylsulfide) could catalyze the air-oxidation of free decMS in benzene; 19 ' 43 this catalysis was very slow, but could be accelerated if the solutions were made acidic. The product distributions observed for the catalytic reaction varied unpredictably, and decMSO was not generally the only product; however, in the absence of excess thioether, exposure of Ru(OEP)(decMS) 2 to air resulted in its slow but clean stoichiometric oxidation to Ru(OEP)(decMS)(decMSO). Furthermore, addition of an excess of decMS to the Ru(OEP)(decMS)(decMSO) solution regenerated the starting Ru(OEP)(decMS) 2 complex, thus constituting one turn of a catalytic cycle.' The first part of the investigation described in this thesis focussed on elucidating the mechanism of the stoichiometric 0 2 -oxidation of Ru(OEP)(decMS) 2 and other Ru(OEP)(RR'S) 2 complexes. This part of the investigation is related in chapter 2. Attention then turned to the problem of using Ru(OEP)(RR'S)2 complexes to catalyze the selective 0 2 -oxidation of free thioethers to the corresponding sulfoxides. The conditions under which such catalysis can take place, along with a detailed kinetic analysis of the catalytic system, are all included in chapter 3. The derivations of rate laws, used in the kinetic analysis described in chapter 3, are given in chapter 4.  20 NOTES AND REFERENCES FOR CHAPTER 1 1. Buchler, J. W. In The Porphyrins, Dolphin, D., Ed., Academic Press, New York, N. Y., 1978; vol. I, p. 389. 2. a) Iron Porphyrins, Lever, A. B. P. and Gray, H. B., Eds.; Addison-Wesley, Massachusetts, Parts 1 and 2, 1981. b) Oxygen Complexes and Oxygen Activation by Transition Metals, Martell, A. E. and Sawyer, D. T., Eds.; Plenum, New York, N. Y., 1988. 3. See for example: a) Collman, J. P. Acc. Chem. Res. 1977, 10, 265. b) Perutz, M. F. Scientific Am. 1978, 239, 256. c) Mansuy, D. Pure and Appl. Chem. 1987, 59, 759. d) Collman, J. P.; Kodadak, T.; Brauman, J. I. J. Am. Chem. Soc. 1986, 108, 2588. 4. See for example: a) Ellis, P. E., Jr.; Lyons, J. E. J. Chem. Soc., Chem. Commun. 1989, 1189. b) Ellis, Jr. P. E.; Lyons, J. E. Coord. Chem. Rev. 1990, 105, 181. 5. Fleischer, E. B.; Thorp, R.; Venerable, D. J. Chem. Soc., Chem. Commun. 1969, 475. 6. Collman, J. P.; Barnes, C. E.; Swepston, P. N.; Ibers, J. A. J. Am. Chem. Soc. 1984, 106, 3500. 7. Collman, J. P.; Prodolliet, J. W.; Leidner, C. R. J. Am. Chem. Soc. 1986, 108, 2916. 8. a) Camenzind, M. J.; James, B. R.; Dolphin, D. J. Chem. Soc., Chem. Commun. 1986, 1137. b) Camenzind, M. J.; James, B. R.; Dolphin, D.; Sparapany, J. W.; Ibers, J. A. Inorg. Chem. 1988, 27, 3054. 9. Several more recent publications on various aspects of ruthenium porphyrin chemistry include: a) Mashiko, T.; Dolphin, D.; In Comprehensive Coordination Chemistry, Wilkinson, G., Gillard, R. D. and McCleverty, J. A., Eds.; Pergamon Press, Oxford, 1987; Vol. 2, p. 813. b) James, B. R.; Chem. Ind. 1992, 47, 245, and references therein. c) Ke, M.; Sishta, C.; James, B. R.; Dolphin, D.; Sparapany, J. W.; Ibers, J. A. Inorg. Chem. 1991, 30, 4766, and references therein. d) Rajapakse, N.; James, B. R.; Dolphin, D. Can. J. Chem. 1990, 68, 2274. e) Huang, J.; Che, C.; Li, Z.; Poon, C. Inorg. Chem. 1992, 31, 1313. f) Seyler, J. W.; Safford, L. K.; Fanwick, P. E.; Leidner, C. E. Inorg. Chem. 1992, 31, 1545. g) Sishta, P. C. Ph.D. Dissertation, The University of British Columbia, Vancouver, B. C., 1990. h) Rajapakse, N. Ph.D. Dissertation, The University of British Columbia, Vancouver, B. C., 1990. 10. a) Domazetis, G.; Tarpey, B.; Dolphin, D.; James, B. R. J. Chem. Soc., Chem. Commun. 1980, 939. b) Domazetis, G.; James, B. R.; Tarpey, B.; Dolphin, D. ACS Symp. Ser. 1981, 152, 243. 11. Groves, J. T.; Quinn, R. J. Am. Chem. Soc. 1985, 107, 5790.  21 12. James, B. R.; Mikkelsen, S. R.; Leung, T. W.; Williams, G. M.; Wong, R. Inorg. Chim. Acta 1984, 85, 209. 13. a) Ranky, W. 0.; Nelson, D. C. In Organic Sulfur Compounds, Karasch N., Ed., Pergamon Press, New York, N. Y., 1961; Vol I, Chapter 17. b) Ledlie, M. A.; Alum, K. G.; Howell, J. V.; Pitkethly, G. J. Chem. Soc., Perkin Trans. 1 1976, 1734. 14. Riley, D. P.; Correa, P. E. J. Chem. Soc., Chem. Commun. 1986, 1097. 15. Riley, D. P.; Smith, M. R.; Correa, P. E. J. Am. Chem. Soc. 1988, 110, 177. 16. Chow, B. C.; Cohen, I. A. Bioinorg. Chem. 1971, 1, 57. 17. a) Brown, G. M.; Hopf, F. R.; Ferguson, J. A.; Meyer, T. J.; Whitten, D. G. J. Am. Chem. Soc. 1973, 95, 5939. b) Brown, G. M.; Hopf, F. R.; Meyer, T. J.; Whitten, D. G. J. Am. Chem. Soc. 1975, 97, 5385. 18. See for example, references 6 or 8. 19. James, B. R.; Pacheco, A. A.; Rettig, S. J.; Ibers, J. A. Inorg. Chem. 1988, 27, 2414. 20. a) Farrell, N. P.; Dolphin, D.; James, B. R. J. Am. Chem. Soc. 1978, 100, 324. b) Barringer, L. F.; Rillema, D. P.; Ham, J. H. J. Inorg. Biochem. 1984, 21, 195. 21. See for example: Collman, J. P.; Hegedus, L. S. Principles and Applications of Organotransition Metal Chemistry, University Science Books, Mill Valley, CA, 1980; p. 27. 22. Sawyer, D. T.; Valentine, J. S. Acc. Chem. Res. 1981, 14, 393. 23. Collman, J. P.; Barnes, C. E.; Brothers, P. J.; Collins, T. J.; Ozawa, T.; Gallucci, J. C.; Ibers, J. A. J. Am. Chem. Soc. 1984, 106, 5151. 24. a) Masuda, H.; Taga, T.; Osaki, K.; Sugimoto, H.; Mori, M.; Ogoshi, H. J. Am. Chem. Soc. 1981, 103, 2199. b) Masuda, H.; Taga, T.; Osaki, K.; Sugimoto, H.; Mori, M.; Ogoshi, H. Bull. Chem. Soc. Jap. 1982, 55, 3887. 25. a) Rajapakse, N.; James, B. R.; Dolphin, D. Catal. Lett. 1989, 2, 219. b) Rajapakse, N.; James, B. R.; Dolphin, D. Stud. Suf. Sci. Catal. 1990, 66, 109. 26. Tavares, M.; Ramasseul, R.; Marchon, J. C. Catal. Lett. 1990, 4, 163. 27. Groves, J. T.; Ahn, K. H. Inorg. Chem. 1987, 26, 3833. 28. Groves, J. T. Lecture K6 presented at the 8 th International Symposium on Homogeneous Catalysis, Amsterdam, August, 1992. 29. Groves, J. T.; Han, Y; Engen, D. V. J. Chem. Soc., Chem. Commun. 1990, 436.  22 30. a) McMillan, R. S.; Mercer, A.; James, B. R.; Trotter, J. J. Chem. Soc., Dalton Trans. 1975, 1006. b) Mercer, A.; Trotter, J. J. Chem. Soc., Dalton Trans. 1975, 2480. 31. Davies, A. R.; Einstein, F. W. B.; Farrell, N. P.; James, B. R.; McMillan, R. S. Inorg. Chem. 1978, 17, 1965. 32. a) Yapp, D. T. T.; Jaswal, J.; Rettig, S. J.; James, B. R.; Skov, K. A. Inorg. Chim. Acta 1990, 177, 199. b) Alessio, E.; Milani, B.; Mestroni, G.; Calligaris, M.; Faleschini, P.; Attia, W. M. Inorg. Chim. Acta 1990, 177, 255. 33. Barnard, D.; Bateman, L.; Cuneen, J. I. In Organic Sulfur Compounds, Karasch N., Ed., Pergamon Press, New York, N. Y., 1961; Vol. I, Chapter 21. 34. Correa, P. E.; Riley, D. P. J. Org. Chem. 1985, 50, 1787. 35. Correa, P. E.; Hardy, G.; Riley, D. P. J. Org. Chem. 1988, 53, 1695. 36. Riley, D. P.; Correa, P. E. J. Chem. Soc., Chem. Commun. 1986, 1097. 37. Riley, D. P.; Shumate, R. S. J. Am. Chem. Soc. 1984, 106, 3179. 38. Riley, D. P.; Oliver, J. D. Inorg. Chem. 1986, 25, 1814. 39. a) Gamage, S. N. Ph.D. Dissertation, The University of British Columbia, Vancouver, B. C., 1985. b) Gamage, S. N.; James, B. R.; J. Chem. Soc., Chem. Commun. 1989, 1624. 40. James, B. R.; Ng, F. T. T.; Rempel, G. L. Can. J. Chem. 1969, 47, 4521. 41. Srivastava, R. S.; Milani, B.; Alessio, E.; Mestroni, G. Inorg. Chim. Acta 1992, 191, 15, and references therein. 42. Taqui-Khan, M. M.; Bajaj, H. C.; Chatterjee, D. J. Mol. Catal. 1992, 71, 177, and references therein. 43. James, B. R.; Pacheco, A.; Rettig, S. J.; Thorburn, I. S.; Ball, R. G.; Ibers, J. A. J. Mol. Catal. 1987, 41, 147.  23 CHAPTER 2 REACTION OF Ru(OEP)(RR'S) 2 COMPLEXES WITH DIOXYGEN IN ACIDIC MEDIA  2.1 Introduction  Previous studies carried out in our laboratories showed that if a benzene solution of Ru(OEP)(decMS) 2 (decMS -= n-decylmethylsulfide) was exposed to air for an extended period of time (from a week to a few months), the complex underwent ligand oxidation to give Ru(OEP)(decMS)(decMSO) and Ru(OEP)(decMSO) 2 (decMSO --n-decylmethylsulfoxide) as the major products, along with other minor products." Later studies have shown that Ru(OEP)(dms) 2 (dms :----: dimethylsulfide) and Ru(OEP)(Et2 S) 2 have similar reactivity, both in benzene and other solvent systems.' The degree of reactivity of the complex, as well as the exact product distribution observed, depend not only on the dialkylsulfide and solvent used, but also on the dryness of the solvent and other variables which are difficult to quantify. Because of this it is difficult to get reproducible results when studying such systems. On the other hand, if an acidic solution of Ru(OEP)(RR'S) 2 (where R E-- methyl, ethyl or decyl and R' ---: - methyl or ethyl) is -  exposed to air, the axial ligands are oxidized to the corresponding sulfoxides in a highly reproducible manner, both in benzene (or toluene) and in methylene chloride. Furthermore, several intermediates are observable over the course of the oxidation process. In this chapter these intermediates are identified and characterized, and a mechanism for the oxidation of the Ru(OEP)(RR'S) 2 complexes is proposed based on the presence of the intermediates and other observations.  24 2.2 Experimental 2.2.1 General Reagents, Gases and Solvents  All non-deuterated solvents were obtained from BDH. Hydrocarbon solvents were reagent grade, and were stored in-vacuo over sodium benzophenone ketyl; all other solvents were glass-distilled spectroscopic grade, and were stored in-vacuo over 3 A molecular sieves. Deuterated solvents were obtained from MSD Isotopes or from CIL, and were stored in the same way as the non-deuterated solvents. Gases were supplied by Union Carbide of Canada Ltd. Dinitrogen for the glovebox was prepurified grade, all others were USP grade. Unless otherwise specified, all gases were used without further purification. A gas could be dried by passing it through a drying tower containing 3 A molecular sieves; for especially air-sensitive solutions, argon was passed down a Ridox deoxygenation column prior to use. Air- or moisture-sensitive solids were stored in a glove-box, the N2 atmosphere of which was continuously recirculated through a Dri-Train HE-439 purification tower packed with 2.4 kg of 3 A molecular sieves, 1.5 kg of 7 A molecular sieves, and 2 kg of Ridox deoxygenation catalyst. This treatment kept the concentration of 0 2 and H2 O below 1 ppm, as evidenced by the long lifetime of an exposed 25-W light bulb filament within the box. 2 The thioethers dms and Et 2 S were obtained from Aldrich, while decMS was obtained from Fairfield chemicals; all three were distilled prior to use,and their purity checked by gas chromatography and 'H-nmr spectroscopy. Dimethylsulfoxide (dmso) was spectrograde from BDH, while dmso-d 6 was from MSD isotopes. Diethylsulfoxide and decMSO were synthesized according to standard procedures."' 3 Both dmso and Et2SO  25 were stored under argon over 3  A molecular sieves; decMSO is a solid and not  particularly hygroscopic, so no special storage precautions were employed. Benzoic acid (PhCOOH) was of uncertain origin, but its purity was verified by 1 H-nmr  spectroscopy, melting point comparison with literature values, and titration with  NaOH. Tetrafluoroboric acid (HBF4) was obtained as a 48% aqueous solution from MCB, and used without further purification. Tetramethylammonium hydroxide (Me 4 N + OH-) was obtained from Anachemia chemicals as a nominally 25% aqueous solution; tetra-n-butylammonium hydroxide was nominally a 40% aqueous solution from BDH. Both were used without further purification. Silver tetrafluoroborate (AgBF 4) was obtained from Aldrich chemicals, and was opened and stored in the glove-box.  2.2.2 Tetramethylammonium Benzoate (Me 4N+PhC001 A 0.9 M solution of PhCOOH in ethanol was added dropwise to about 4 g of 25% aqueous Me4 N+OH - until the resultant mixture was slightly acidic to litmus (approximately 14 mL of acid solution were required). The water and ethanol were removed using a rotary evaporator, and the resultant solid was redissolved in ethanol (125 mL); the mixture was refluxed for about 10-15 min, and then filtered to remove a greyish-white flaky precipitate. The volume of the filtered solution was reduced to approximately 2 mL using a rotary evaporator, at which point 40 mL of diethyl ether were added. The desired product was obtained as a white precipitate, which was filtered and dried overnight at 80° C. Me4N + PhC00 - is extremely hygroscopic, and had to be  26 stored and handled in a glove-box; in solution, the salt was handled exclusively in-vacuo. It is stable indefinitely in acetonitrile solution, but slowly degrades in methylene chloride. Yield: 2.13 g (95% relative to Me 4N+OH - used) Anal. Calcd. for C II H I7NO 2 : C, 67.66; H, 8.78; N, 7.17. Found: C, 67.76; H, 8.60; N, 6.99. NMR (S; CD 3 CN or CD 2 C1 2 , 20° C): 7.29 m (11„,, p), 7.96 m (H o), 3.48 s (NCH 3 ).  2.2.3 Tetra n butylammonium Tetrafluoroborate (n Bu 4N+13F41 -  -  -  To about 95 g (0.146 mol) of n-Bu 4N + OH - solution was added enough HBF4 solution to produce a pH-neutral mixture (checked by litmus test). The resulting white precipitate was filtered off, washed with three 50-mL aliquots of ice-cold water, and then dried in-vacuo for 24 h. The dry powder was dissolved in 45 mL of ethyl acetate, passed through a filter paper to remove cloudiness, and then recrystallized by adding approximately 0.6 equivalents of n-pentane, and cooling at -5° C for lh. After a second recrystallization procedure, the product was dried in-vacuo at room temperature for 48 h. Prepared in this way, n-Bu 4 N + 13F4 showed no electrochemical activity in cyclic voltammetric scans from -1.6 to +1.6 V.  2.2.4 Ruthenium Porphyrin Complexes  Ruthenium was obtained on loan from Johnson, Matthey Ltd, in the form of RuC1 3 .3H 2 0 (approximately 40% by weight). H 2 OEP was kindly provided by Dr. D. Dolphin of this department. Ru 3 C0 12 , 4 Ru(OEP)(CO)py, 5 and Ru(OEP)py 2 , 5 the necessary precursors to make [Ru(OEP)] 26 and [Ru(OEP)] 2 (BF4) 2 , 7 were made by the literature procedures cited; for  27 all these compounds the spectroscopic data (nmr, uv/vis, ir) were in excellent agreement with those reported previously, and elemental analysis for C, H, and N was within 0.3% of the theoretical values. A detailed description of the specialized high pressure and photolysis equipment used in our laboratories for the syntheses of Ru 3 CO 12 and Ru(OEP)py 2 can be found in reference la. The dimer [Ru(OEP)] 2 was prepared by high-vacuum pyrolysis of Ru(OEP)py2 , 6 while the oxidized dimer [Ru(OEP)) 2 (BF4) 2 was prepared by adding 2 equivalents of AgBF4 to a benzene solution of [Ru(OEP)]2 . 7 Removal of metallic silver from the oxidized dimer required that a CH 2C1 2 solution of the complex be filtered through a Celite pad; the fine frits available in our laboratories were not fine enough to prevent the passage of finely divided metallic silver. Both dimers are extremely air-sensitive, both in solution and in the solid state. The solids were stored in the glove-box. In solution the dimers were handled using vacuum-transfer techniques where possible; when this was impractical, manipulations were carried out as fast as possible under dry, deoxygenated argon, using a combination of Schlenk and syringe techniques.' The synthesis and characterization of Ru(OEP)(decMS) 2 has been previously described.'  2.2.4.1 Ru(OEP)(chns) 2  Approximately 25 AL (0.34 mmol) of dms and 5 mL of methylene chloride were vacuum-transferred onto 0.1083 g (0.085 mmol) of [Ru(OEP)] 2 , which immediately gave a red solution. The volume was increased to about 15 mL with n-hexane, and then slowly reduced until traces of precipitate appeared. The solution was filtered, and the volume  28 further decreased until considerable precipitation occurred. This concentrate was now heated to redissolve the complex, and then allowed to cool slowly, first to room temperature and then to 0° C. The dark purple crystalline Ru(OEP)(dms) 2 was filtered off and dried in vacuo at 70° C overnight. Yield: 0.104 g (0.137 mmol, 81%). Anal. calcd. for C40H56 N4 S 2 Ru: C, 63.37; H, 7.45; N, 7.39. Found: C, 63.47; H, 7.48; N, 7.20. NMR (5; CD 2 C12 , 20.0° C): OEP, 1.81 t (CH 3 ), 3.85 q (CH 2 ), 9.32 s (Hineso); dms, -2.66 s. Uv/vis (0.0445 mM soln. in C 6 H6 containing 68 mM dms) Xmax (log E): 407.5 (5.34)(Soret), 498 (4.17), 525 (4.42) nm.  2.2.4.2 Ru(OEP)(Et 2S) 2  The procedure for the synthesis of Ru(OEP)(Et 2S) 2 was analogous to that of Ru(OEP)(dms) 2 . Yield: 0.257 g (0.315 mmol, 85%). Anal. calcd. for C 44H64 N4 S 2Ru: C, 64.91; H, 7.92, N, 6.88. Found: C,64.73; H,7.87; N,6.68. NMR (6; CD 2 C12 , 20.0° C): OEP, 1.78 t (CH3 ), 3.96 q (CH 2 ), 9.25 s (Knew); Et2S, 1 .32 t (CH 3 ), -2.47 q (CH2). -  Uv/vis (0.0340 mM soln. in C 6H 6 containing 74 mM Et2S) Xma. (log E): 409 (5.23) (Soret), 499 (4.13), 525 (4.39) nm.  2.2.4.3 Ru(OEP)(dmso) 2 and the dmso d 6 Analogue -  Ru(OEP)(dmso) 2 (where s implies s-bonded) was prepared by adding 16 AL (0.23 mmol) of dry, degassed dmso, and 8 mL of methylene chloride to 0.072 g (.057 mmol) of [Ru(OEP)] 2 . To the deep red solution product were added 10 mL of n-hexane, and then the solvents were slowly removed until solid just appeared. The solution was filtered, and the volume further reduced until considerable precipitation occurred. The  29 microcrystalline product was filtered, and then dried in-vacuo overnight at 70° C. The dmso-perdeuterated analogue was prepared in an identical manner, using dmso-d 6 as the sulfoxide source. Yields: approximately 80% in each case.' Anal. Calcd. for C40H56N402S2Ru: C, 60.81; H, 7.14; N, 7.09. Found: C, 60.39; H, 7.40; N, 6.78. NMR (5;  CD 2 C1 2 , 20.0° C): OEP, 1.87 t (CH 3), 3.98 q (CH2), 9.78 s (H mem,.);, dmso, -2.18 s.  IR (cm- ', in Nujol): vso , 1105. Uv/vis (0.0169 mM soln. in C 6 H6 containing 22.6 mM dmso) X.. (log E): 397.5 (5.44) (Soret), 533 (4.04) nm.  2.2.4.4 Ru(OEP)(Et 2S0) 2  Ru(OEP)(Et 250) 2 was prepared in a manner analogous to that for Ru(OEP)(dmso) 2 . Yield: approximately 80%. 10 Anal. calcd. for C 44H64 N4 02 S 2Ru: C, 62.45; H, 7.62; N, 6.62. Found: C, 62.32; H, 7.58; N, 6.68. NMR (45; CD 2 C1 2 , 20.0° C): OEP, 1.84 t (CH 3 ), 3.96 q (CH 2), 9.70 s (H meso); Et2 SO, -1.55 br (CH 3 ), -2.12 br (CH2)444 -2.74 br (CH 2) b . Uv/vis (0.0390 mM soln. in C6H6 containing 4.7 mM Et 2 SO) X ^(log 6): 399.5 (5.49) (Soret), 527 (4.10) nm.  2.2.4.5 Ru(OEP)(decMS0) 2  To 0.0692 g (0.0545 mmol) of [Ru(OEP)] 2 were added 0.0501 g (0.245 mmol) of decMSO, and about 5 mL of benzene. The solution immediately became a bright, ruby red. After about 10 minutes the solvent was removed, the solid redissolved in about 6 mL of n-pentane, and the resulting solution filtered to remove small amounts of a brown solid. The filtrate was then cooled to -100° C for 15 min to effect precipitation of the desired product. Ru(OEP)(decMS0) 2 was filtered off at - 100° C as a scarlet powder, and  30 dried in-vacuo overnight. Note- the complex is extremely lipophilic, and great care had to be taken to avoid contamination with stopcock grease. Yield: approximately 80%.  10  Anal.  Calcd. for C 581-1 92N4 0 2 S 2Ru: C, 66.82; H, 8.89; N, 5.37; S, 6.15. Found: C, 66.89; H, 8.89; N, 5.18; S, 5.95. NMR (3; C 7D 8 20.0° C): OEP, 1.86 t (CH 3 ), 3.96 q (CH 2 ), 9.72 s (imeso) ; decMSO, -2.34 s (SCH3 ), -2.78 m ( 1 CH2), -1.11 m (2 CH 2), -0.02 m (3 CH2), 0.37 qn (4 CH 2 ), 0.73 qn (5 CH2 ), 0.95 qn ( 6 CH2 ), 1.0-1.25 m ( -9 CH 2 ), 0.839 t ( 1°CH3 ). Uv/vis (0.0101 mM soln. in C 6D 6 containing 0.20 mM decMSO) X...„ (log c): 399 (5.59) (Soret), 530 (4.15) nm.  2.2.4.6 Ru(OEP)(dms) 2 + BF4 To 0.0529 g (0.0368 mmol) of [Ru(OEP))2(BF4)2 were added about 10.7 /LI, (0.147 mmol) and 5 mL of methylene chloride. The solution was stirred for 30 min, during which time it became a dark orange colour. At this point about 5 mL of n-hexane were added, and the total volume reduced until precipitation just occurred. The solution was filtered, and the volume further reduced until most of the desired complex had precipitated, and the supernatant was a very pale orange. The brownish-purple needles were filtered off, washed with n-pentane, and then dried in vacuo at 70° C overnight. Yield: approximately 80%. 10 Anal. calcd. for C 40H5 6 N4 S 2RuBF4 : C, 56.86; H, 6.68; N, 6.63. Found: C, 56.67; H, 6.70; N, 6.44. NMR (6; CD 2 C1 2 , 20.0° C): OEP, 1.52 br (CH3 ), 23.85 br (CH2 ), 1.73 br (1-1.30); dms, -0.174 br. Uv/vis (0.111 mM soln. in CH2C 1 2) X., (log c): 394 (5.05) (Soret), 505 (4.05), 533 (4.03) nm.  31 2.2.4.7 Ru(OEP)(Et 2 S) 2 + BF4  The preparation of this complex was analogous to that described for Ru(OEP)(dms) 2 +13F4. Yield: approximately 80%. 10 Anal. calcd. for C 44H 64N4 S 2RuBF 4 : C, 58.66; H, 7.16; N, 6.22. Found: C, 58.39; H, 7.17; N, 6.15. NMR (6; CD 2 C12 , 20.0° C): OEP, 1.31 br (CH 3 ), 23.09 br (CH 2 ), 1.61 br (H. es.); Et 2 S, 3.57 br (CH 2), 7.82 br (CH3 ). Uv/vis (0.0838 mM soln. in CH 2 C12 ) Xi. (log e): 394 (4.98) (Soret), 505 (4.01), 533 (3.98) nm.  2.2.4.8 Ru(OEP)(decMS) 2 + BFi  To 0.171 g (0.119 mmol) of [Ru(OEP)] 2 (BF4 ) 2 were added 110 AL (0.474 mmol) of decMS, and benzene. The purple, insoluble [Ru(OEP)] 2 (BF4) 2 was slowly converted to the orange soluble Ru(OEP)(decMS) 2 + 13F4. This product was recrystallized from benzene/n-heptane, in a manner analogous to that described for Ru(OEP)(dms) 2 13F4. Crystals suitable for an x-ray structure determination were obtained by reducing the volume of a benzene/heptane solution until precipitation just occurred, heating to redissolve the precipitate, then allowing the solution to cool slowly. Approximate yield: 80%. 10 Anal. calcd. for C 68 H92 N4 S 2RuBF4 : C, 63.48; H, 8.45; N, 5.11; S, 5.84. Found: C, 63.69; H, 8.62; N, 5.19; S, 5.66. NMR (6; CD 2C1 2 , 20.0° C): OEP, 1.44 br (CH3), 23.13 br (CH 2), 1.83 br (H. eso)1: decMS, 0.50 br (SCH 3), 0.92 t ( 1°CH 3 ); {Tentative: 9.06 ,  br ( 1 CH2), 4.39 br ( 2 CH 2 ), 2.22 br (3 CH2 ), 1.96 br (4 CH 2 ), 1.60 br ( 5 CH 2); signals are progressively sharper, with the last two beginning to show fine structure; 1.44 br (6-9 CH2)}. Uv/vis (0.0921 mM soln. in CH2 C1 2) X.., (log c): 394 (5.10) (Soret), 505 (4.11), 533 (4.09) nm. Molar conductivity (1 mM soln. in CH 2 C1 2 ) A = 52 fricm2mol-1.  32 2.2.4.9 Me 4N + Ru(OEP)(PhC00)2 To 0.104 g (0.0725 mmol) of [Ru(OEP)]2+(BF4)2 were added 0.0629 g (0.322 mmol) of Me4N -ThC00- , and about 10 mL of methylene chloride. The colour changed immediately from purple to a greenish-yellow colour, then after about 1 h to a bright red. The solution was cooled to 0° C, filtered to remove solid Me 4N + 13F4, then further cooled to -100° C to precipitate the desired, crimson product. This was filtered off, washed with n-pentane, and then dried in-vacuo overnight at room temperature. Me4N + Ru(OEP)(PhC00)2 is highly air-sensitive in solution, and the solid was stored in the glove-box as a precautionary measure. Yield: 0.102g (0.108 mmol, 74%). Anal. calcd. for C54H66N5O4Ru: C, 68.26; H, 7.00; N, 7.37. Found: C, 68.57; H, 7.16; N, 7.29. NMR (5; CD 2 C1 2 , 20° C): OEP, -0.72 br (CH 3 ), 8.08 br (CH 2), 2.72 br (H 1: meso, PhC00 - , 17.86 br (110), 10.74 br (H.), 9.35 br (H p); 5.64 br N(CH) 3 . Uv/vis (CH2C 12) Xma, (log capprox): 401 (5.0) (Soret), 520 (3.9) nm.  2.2.5 Instrumentation Where uv/vis or nmr spectra of air- or moisture-sensitive materials were required, special apparatus, described generally in reference 9, or more specifically in reference la was used.  2.2.5.1 Ultraviolet/Visible Absorption Spectroscopy  Uv/vis spectra were recorded at 20.0° C on a Perkin-Elmer 552A spectrophotometer with the slit width adjusted to allow 2 nm resolution. To obtain extinction coefficients, the absorbance maximum was scanned manually to avoid errors due to  33 delays in recorder response. Typically the Soret bands were obtained using a 0.1 cm cell, while for the visible bands, which are about 10 times weaker, a 1.0 cm cell was used.  2.2.5.2 Infrared Spectroscopy  The ir spectra of Ru(OEP)(dms) 2 , Ru(OEP)(dmso) 2 and its dmso-perdeuterated analogue were obtained on a Nicolet 5DX single beam ir spectrometer, operating in Fourier transform mode. Samples were mulled in Nujol, and sandwiched between KBr plates.  2.2.5.3 Proton Nuclear Magnetic Resonance Spectroscopy  'H nmr spectra were collected at 20.0° C, using a Varian XL-300 FT instrument.  2.2.5.4 Conductivity  The conductivity measurement was performed using a model RCM 15B1 conductivity bridge from the Arthur H. Thomas company; the conductivity cell was of a commercial design (Yellow Springs instrument company), with a cell constant of 1.00 cm-I .  2.2.5.5 Cyclic Voltammetry  Cyclic voltammetric measurements were carried out using an EG and G PAR Model 175 Universal programmer to control the potential sweep; this unit was linked to a Model 173 PAR potentiostat equipped with a model 176 current-to-voltage converter and a model 178 electrometer probe. Voltammetric traces were recorded on a Hewlett-  34 Packard Model 7005B X-Y recorder. Scan speed was 100 mV/s unless otherwise indicated. All electrochemical experiments were carried out in methylene chloride solution, with approximately 0.12 M n-Bu 4N+BF4 acting as the supporting electrolyte. The electrochemical cell, based on a design described by Van Duyne and Reilley," was made by S. Rak of this department, and was devised for use with minimal volumes of solution (cyclic voltammograms could be obtained with as little as 2 mL), and to allow manipulation of highly air-sensitive samples where necessary. Figure 2.1 illustrates the cell. The Ag/AgCI reference electrode was a commercial design by Metrohm, and was filled with aqueous saturated KC1. Under the experimental conditions employed throughout this work, the Cp2 Fe/Cp 2Fe+ and Ru(OEP)py 2 +/Ru(OEP)PY 212 couples occurred at E°' = 0.58 ± 0.02 and 0.10 ± 0.02 V, respectively, relative to the reference. In a typical experiment involving air-sensitive compounds, a solution containing the material to be analyzed and the supporting electrolyte was first prepared in flask (F), using vacuum transfer techniques. The flask was then filled with dry, deoxygenated argon, and connected to the electrochemical cell at joint 4. Joint 5 was stoppered, the cell was connected to a vacuum pump at joint 3, and evacuated. At this point tap 7 was opened to introduce the electroactive solution into the cell, and then argon was introduced via (3). Finally, under an argon purge, the salt bridge/reference electrode combination and the working/auxiliary electrode housing were installed at joints 4 and 5 as shown in the illustration. Tap 1 was closed, the assembled cell was connected to the instruments, and the cv was obtained. In all experiments carried out in this work, tap 2 was always left open. One could envision, however, that if a solvent  35  Figure 2.1. Cyclic voltammetry cell: (A) platinum bead working electrode; (B) platinum wire spiral auxilliary electrode; (C) non-aqueous salt bridge; (D) aqueous Ag/AgC1 reference electrode; (E) KC1 reservoir; (F) sample preparation flask.  36 with more viscosity than methylene chloride were used, it might not flow easily through the Luggin capillary. In that case, closing tap 2 and pressurizing the reference electrode compartment might succeed in driving the solution through.  2.2.5.6 Elemental Analysis Elemental analyses were carried out by P. Borda of this department.  2.3 Characterization of Ru(OEP)(RR'S0) 2 Complexes A sulfoxide ligand can conceivably bind to a metal center via either its sulfur or oxygen atom; experimentally, both types of complex have been observed, and theories have been proposed to explain the bonding in each case." The bonding between sulfur and oxygen in a free sulfoxide is represented by the following canonical structures:  RR'S=O <^-> RR'S+-0  -  I^II  In the molecular orbital picture, the bonding is seen to consist of a a interaction and a (17-pa interaction, and the S-0 bond order is somewhere between one and two. Coordination of a sulfoxide to a metal via the oxygen atom would tend to stabilize canonical structure II, and thus decrease the S-0 bond order relative to that of the free sulfoxide. On the other hand, coordination via sulfur would tend to intensify the positive charge on the sulfur atom, thus destabilizing canonical structure II, and consequently increasing the S-0 bond order relative to that of the free sulfoxide. As might be expected  37 then, S-bound and 0-bound metal sulfoxide complexes can be readily distinguished by ir spectroscopy: 14 in the S-bound case the S-0 stretching frequency is higher than in the free sulfoxide, whereas in the 0-bound case it is lower. The ir spectrum of Ru(OEP)(dmso) 2 shows a strong band, assigned to v so , at 1105 cm -1 , as compared with 1055 cm -1 in free dmso; hence it is characterized as an Sbound complex, at least in the solid state. The ir spectra of the other two Ru(OEP)(RR'S0) 2 complexes were not obtained; however, all three complexes had similar nmr and uv/vis spectra, as well as electrochemical properties (see the next section), which suggests that they share the same bonding patterns. In solution, there is evidence that some isomerization may be taking place. Kinetic studies of substitution of the bis(sulfoxide) systems by dialkylsulfides show that one of the sulfoxides is strongly bound, but the other is extremely labile and can easily be replaced by other ligands. These studies will be dealt with in considerable detail in section 3.4, but of more immediate interest is possible evidence that an S-bound sulfoxide can revert to, or be replaced by, an 0-bound sulfoxide in solution. The uv/vis spectra of each of the three bis(sulfoxide) complexes prepared vary somewhat with temperature, even in the presence of a large excess of free sulfoxide ligand; to give an example, figure 2.2 shows the temperature dependence of the Ru(OEP)(Et§0) 2 uv/vis spectrum. These variations are reversible, and are not due simply to ligand dissociation, although evidence for the latter process is also observed for dilute solutions containing no added free ligand (see section 3.4). The best explanation for the temperature dependence of the uv/vis spectra is that in solution one of the sulfoxides can be either S-bound or 0-bound, and that the ratio of isomeric forms depends on the temperature. Despite these observations, it will be shown  38  527 Increasing Temperature  420^500^A,(nm)^600  Figure 2.2. Changes in the visible spectrum of a CH 2 C1 2 solution containing 0.039 mM Ru(OEP)(Et2 SO) 2 , and 4.72 mM free Et 2 SO, as the temperature is increased in 10° intervals, from 20-50° C.  39 in section 3.4 that, for the purposes of the present study, Ru(OEP)(RR'SO) 2 complexes in solution can be thought of as containing only S-bound sulfoxides without changing any conclusions. It should be added that the 1 H-nmr spectra of Ru(OEP)(Et 2 SO) 2 and Ru(OEP)(decMSO) 2 (see sections 2.2.4.4 and 2.2.4.5) are also somewhat temperature dependent, and also solvent dependent. As an example of solvent dependence, at room temperature in CD 2 C1 2 , the sulfoxide methyl and methylene 'H-nmr signals of Ru(OEP)(Et 2SO) 2 are broad and lacking in fine structure; on the other hand, at the same temperature but in C 6D 6 , the same signals are resolved multiplets. This topic will not be discussed further, as no systematic studies were done; however, it is an interesting subject which deserves more study in the future. The assignment of the pso ir band requires some comment. Previous studies have mentioned the potential difficulty in distinguishing p so from the p cH, signals of the sulfoxide, and reported that this difficulty could be overcome by comparing data for the dmso complex with those for its dmso-perdeuterated analogue. 13 '" The p oi, modes are isotopically shifted when the perdeuterated analogue is used, whereas the  Pso  signals  remain unchanged. In the case of Ru(OEP)(dmso) 2 and Ru(OEP)(dmso-d 6 ) 2 , the spectra obtained are essentially identical in the region from 500-1500 cm -1 . Presumably the C-H and C-D rocking modes in these complexes are buried under signals attributable to Ru(OEP). When the ir spectra of Ru(OEP)(dmso) 2 and the perdeuterated analogue are compared with that of Ru(OEP)(dms) 2 , the only difference in the region mentioned is that the spectrum of Ru(OEP)(dms) 2 lacks the strong 1105 cm -1 band; the rest of the spectrum is virtually identical for Ru(OEP)(dms) 2 , Ru(OEP)(dmso) 2 , and Ru(OEP)(dmso-d6) 2 . This  40 confirms the assignment of this band as PSO• The peak positions of all the Ru(OEP)(RR'SO) 2 'H-nmr signals are typical of those observed for other related Ru n (OEP) species; in fact, the most complex spectrum collected, that of Ru(OEP)(decMS0)2 , was assigned by direct analogy with the previously reported spectrum of Ru(OEP)(decMS) 2 . 9 The predominant factor which determines the peak positions of any diamagnetic porphyrin species is the ring current generated by the porphyrin 7 electrons, 15 °' 6 and the ring current effect as it relates specifically to Ru(OEP)(decMS) 2 is discussed in detail in reference 9. This effect will not be discussed further at this time, but it has been extensively investigated, and several semi-quantitative models have been published."'"  2.4 Characterization of Ru m (OEP) Complexes  Oxidation of metalloporphyrins can occur either at the metal center or at the porphyrin ring, and again there is precedent for both possibilities.' Fuhrhop et al. first observed in 1973 that a uv/vis spectrum consisting of 2-3 broad bands covering the visible range from 500 to 700 nm seemed to be characteristic of an organic  7  radical,  while one with reasonably localized bands in the region between 500 and 580 nm, which looked very much like those of an unoxidized precursor, indicated that oxidation had occurred at the metal." This qualitative test for oxidation site location is now widely recognized as one of the primary methods of distinguishing the two possibilities.' Figure 2.3a shows that the uv/vis spectra of Ru(OEP)(dms) 2 and Ru(OEP)(dms) 2 13F4 are quite similar, suggesting that oxidation in synthesis of the latter has occurred at the metal. The spectra of the other Ru(OEP)(RR'S) 2 13F4 - complexes were essentially identical to that of  41  (a)  525  ^Run  X10 1.0-  (OEP)(dms),  Ru m (0E13 )(clins); BF, -  407.5  498 394  I  1505‘.  / 11  533  I 0.0 320  400  X(nm)  500  6 01 0  700  00 320^ 400500  X(nm)  600  Figure 2.3. Uv/vis spectra in CH 2 Cl 2 of (a) Ru(OEP)(dms) 2 and Ru(OEP)(dms)2 + BF4, and (b) Me4N+Ru(OEP)(PhC00)2  42 the dms one; the spectrum of Me4/4+12.u(OEP)(PhC00)2 (figure 2.3b) could not be compared to that of the reduced analogue, but also exhibits a fairly localized absorption maximum at 520 nm, and no significant absorption above 600 nm. Again this is suggestive of oxidation at the metal. To the author's knowledge, all Ru"(Porp) 7-cation radical complexes observed to date contain CO as a 7-accepting axial ligand. It is believed that metal to carbonyl backbonding in these complexes stabilizes the metal d orbitals of  7  symmetry to the point  where they are at lower energy than the highest occupied  7  and that this is why the ring is preferentially oxidized.  Previous studies in our  19,20  orbital of the porphyrin ring,  laboratories and elsewhere have shown that dialkylsulfide ligands do not partake in significant metal to ligand 7-7* back-bonding,' and the cyclic voltammetric (CV) studies show (figure 2.4a) that the standard reduction potentials of all three Ru(OEP)(RR'S) 2 13F4 complexes prepared occur at around 0.22 ± 0.02 V relative to Ag/AgC1; 21 such values are comparable to those obtained for systems such as Ru(OEP)py 2 + /Ru(OEP)py 2 , which are known to undergo oxidation at the Metal, 19 ' 22 but are well below the reduction potentials of the Ru(OEP) + (CO)L/Ru(OEP)(CO)L systems (L --== a general ligand or a vacant site), which have typically been recorded at around 0.65-0.70V. 19 ' 23 a A further interesting question arises from the above discussion. Although dialkylsulfides do not partake in significant metal-ligand 7-7* backbonding, there is quite a body of evidence that sulfoxides do.' Would this cause sulfoxide complexes to undergo ring oxidation? An in situ redox titration of Ru(OEP)(Et0) 2 with AgBF 4 , gave a uv/vis spectrum (figure 2.5a) very similar to those of the Ru(OEP)(RIVS)2+13F4  43  1.28  (a)  (b) 0.74  0.20  C  1.31 1.0  -1.0  E vs. Ag/AgC1 la  (C) 0.25  Figure 2.4. Cyclic voltammograms in CH 2 C1 2/n-Bu4N + 13F4 for (a) Ru(OEP)(dms) 2 , (b) Ru(OEP)(dmso) 2 , and (c) Me4N + Ru(OEP)(PhC00) 2 - . The cyclic voltammograms of the other dialkylsulfide and sulfoxide complexes are virtually indistinguishable from those of the dms and dmso complexes illustrated. Also, a CV identical to (a) was obtained for Ru(OEP)(dms)2+BF4.  44  (a)^0.5  = Ru(OEP)(Et,SO), = Ru(OEP)(Et,S0), + AgBF 4 (1 equivalent) czt  525  0 cA ss.  .......  0  ■••■  ■roo ra■■  -  450  (b)  700  600  Ä,(nm)  0 II/ CH s S  /. CH 3  ■•• Cl. H„„„,^/ O  H3C  B F4  -  Ha C H3)OEP  Free Sulfoxide 26^24 H meso  — OS CH3 r  8  I  el,  I T:  '1  4  TIT  2  /ft  0 PPM  ^  Figure 2.5. (a) Visible spectrum of a 1:1 mixture of Ru(OEP)(Et2 SO) 2 and AgBF 4 in CH 2 C1 2 ; (b) 'H-nmr spectrum of a CD 2 C1 2 solution initially containing [Ru(OEP)]2(BF4)2 and free dmso in approximately 1:8 ratio; S ^solvent, T = 20° C.  —2  45 complexes (see figure 2.3a), suggesting that oxidation of the sulfoxide complexes also results in Rum derivatives. Figure 2.5b shows the 1 11-nmr spectrum of an in situ mixture of [Ru(OEP)] 2 (BF4 ) 2 and dmso, in CD 2 C12 at 20° C; this spectrum has several features quite similar to those seen in the corresponding Ru(OEP)(dms) 2 +13F4 spectrum (see figure 2.10, and the discussion later in this section). However, the presence of two signals for the OEP methylenes indicates that the two faces of the porphyrin are inequivalent (ie: the porphyrin plane is not a plane of symmetry in this complex). There are also several small signals, some of which can probably be assigned to another minor Ru(OEP) paramagnetic product. The presence of these extra signals complicates the assignment of any signals due to coordinated dmso; however, the signals at 0.02 and 10.20 ppm each have the correct integration for one sulfoxide. Furthermore, if the whole experiment is repeated using dmso-d 6 , both these signals are absent from the resulting spectrum. Based on this uv/vis and 1 H-nmr evidence, the major product of Ru(OEP)(RR'S0) 2 oxidation is tentatively assigned as Ru m (OEP)(RR'S0)(RR'S0) + BF4; the nmr signal at 0.02 ppm is assigned to the S-bound sulfoxide by comparison with the Ru(OEP)(dms) 2 +13F4 system (see figure 2.10 in the next section), while the signal at 10.2 ppm is assigned to the 0bound sulfoxide. The cyclic voltammograms for the Ru(OEP)(RR'S0) 2 complexes (figure 2.4b) also show evidence of a change in coordination on changing the oxidation state; the oxidation wave has a maximum current at 0.74 V vs. Ag/AgC1, while the reduction maximum occurs at 0.53 V vs. Ag/AgCl. The large peak to peak separation indicates that the complex being reduced is not the same one that was oxidized, but the shape of the CV does not change regardless of how many times the scan is repeated, which suggests that upon reduction the original complex is recovered intact. This is consistent with the  46 postulated mechanism:'  Ru 1 (OEP)(RR'S0) 2^Ru ili (OEP)(RR'S0) 2 4- + e^E°' .-- 0.74 V  2.1  Ru m (OEP)(RR'50) 2 + ‘='-' Ru m (OEP)(RR'S0)(RR'S0) +  2.2  Ru m (OEP)(RR'S0)(RR'S0) + + e rr—' Ru n (OEP)(RR'S0)(RR'SO)^E°' ---,, 0.53 V  Ru ll (OEP)(RR'S0)(RR'SO)-=*.' Ru(OEP)(RR'S0)2  2.3  2.4  Note that 0.74 V is actually higher than the E°' values reported for Ru(OEP)(C0), 19,23a and so if both sulfoxides were to remain S-bound, ring oxidation might be predicted. It is possible that ring oxidation does occur initially, and that internal electron transfer takes place after one of the sulfoxides rearranges to yield the 0-bound isomer. Internal electron transfer upon modification of the coordination sphere has been previously documented for ruthenium porphyrins.'''' Both the Ru(OEP)(RR'S) 2 and Ru(OEP)(RR'S0) 2 complexes exhibit a second redox couple at around 1.3 V (figures 2.4a,b). No further investigation of this couple was carried out in this work, but previous studies in our laboratories have yielded evidence that the second oxidation of similar complexes containing two neutral axial ligands  47 occurred at the ring at around 1.3 V, to yield the Ru m 7-cation radical. 23 a Figure 2.3c shows the corresponding redox couple (0.23 V) for Me 4N+Ru(OEP)(PhC00)2. Notice that the coordination of two anionic ligands on the metal center renders the complex much more easily oxidizable; in fact, oxidation of the bis(benzoate) ruthenium(III) species is as easy as the one-electron oxidation of the Ru 11 (OEP)(RR'S) 2 complexes. This point will be very important in the following section. Presumably, given the ease of oxidation, electron abstraction from Me4 N+Ru(OEP)(PhC00)2 takes place at the metal to generate Ru(IV) species. Corresponding potentials for the related Ru(OEP)X 2 species (X -= Cl, Br) occur at 0.40 and 0.42 V, respectively;' the 0.2 V difference relative to Ru(OEP)(PhCOO) 2 can be attributed to the stronger basicity of PhC00 - relative to Cl and Br. The signals in the paramagnetic 'H-nmr spectra of Ru(OEP)(dms) 2 13F4, Ru(OEP)(Et 2 S) 2 + BF4, Ru(OEP)(decMS)2 +BF4 and Me 4N+Ru(OEP)(PhC00)2 are shifted considerably from their characteristic diamagnetic positions, which is typical for paramagnetic complexes. 258 The magnitudes and directions of the observed paramagnetic shifts (from 0-20 ppm, with the methylene proton signals shifting downfield, and the meso proton signals shifting upfield) are fairly representative of those seen for Ru m (OEP) low spin complexes (no Ru m (Porp) high spin complexes have ever been observed); 26 Ru 1"(OEP) complexes generally (but not always) show much greater shifts (as high as 100 ppm). 27 The spectra of Ru(OEP)(dms) 2 13F4, Ru(OEP)(Et2 S) 2 +BF4 and Me4 N + Ru(OEP)(PhC00) 2 - are assigned primarily based on the relative intensities of all the signals. The spectrum for Ru(OEP)(decMS) 2 +13F4 (figure 2.6) was more difficult to interpret. The porphyrin signals and the SCH 3 signals are assigned by analogy to the  9^7^5^3^1  /N./N.,..N.,N7NS'''  I  10^8^6^4  li meso—MM  Ru  '  (CH  ,CH 3 Elm--  CH,  BF  3)6EP.,,  ^ ;  69  (CH 2  / s NrN/NVNVN./  ( CH,  )  0a„  10(CH, ) 1111,1111111  24^22  '( C H, )  SCH 3  1111111-11111111-1r111 1 111111-111 1 11111-1111 1 1111 1 1117 1 111 11 1111 1 1111 11111- 11/11111111111111111111111111111111111111 10^9^8^7^6^5^ 4^3^^–^1^0^-1  `PPM  Figure 2.6. 'H-nmr spectrum of Ru(OEP)(decMS) 2 + 13F4 - in CD 2C12 , taken at 20.0° C; S E solvent.  49 simpler systems, while the signal due to the thioether 1° CH 3 is unshifted relative to either that of the free ligand or the Ru"-coordinated analogue.' A peak at 9.06 ppm is tentatively assigned to ( 1 CH 2), based on its integration and the fact that it is the broadest of the unassigned signals. A series of progressively sharper signals at 4.39, 2.22, 1.96, and 1.60 ppm are assigned to (2 CH 2)-(5 CH2); the last two actually show some fine structure. Finally, the signals for ( 6-9 CH 2 ) are buried beneath the porphyrin methyl signal, although a broad multiplet is just discernible at 1.38 ppm.  2.5 Reaction of Ru(OEP)(dms) 2 With Dioxygen and Benzoic Acid in Methylene Chloride Figure 2.7 shows the 'H-nmr spectral changes over time as a solution containing about 20 mM Ru(OEP)(dms)2 and 12 mM benzoic acid in CD 2 C1 2 is exposed to 1 atm of 02 at room temperature. For simplicity only part of the spectrum is shown, but comparable changes are seen throughout the spectrum, from -3 to 25 ppm (see table 2.1). When the other dialkylsulfide complexes are exposed to the same conditions, spectral changes analogous to those illustrated in figure 2.5 are observed, at least in the 5-25 ppm region; below this, the spectra of the reaction mixtures are too complicated to interpret readily. The two sharp singlets seen between 9.5 and 10 ppm are assigned to the OEP meso protons of Ru(OEP)(dms)(dmso) and Ru(OEP)(dmso) 2 , respectively. Ru(OEP)(dms)(dmso) could not be obtained pure, but in titrations of Ru(OEP)(dms) 2 with dmso, or of Ru(OEP)(dmso) 2 with dms, the mixed species could be unequivocally identified by uv/vis or 'H-nmr data (see for example figure 2.8). In fact, for the  O  0  0 PhC  Ru — ■  The two small signals at around 11.8 and 16 ppm are due to uncharacterized impurities present before reaction began.  O  — Rum ■  of  0  ms s / s ■ I ,^I 11.■ Ru - ■^ — Ru lill■ + e -  I^1  35 h 360 min 312 min 234 min 97 min 28 min  / r I 1.111^ T II(  /1111111^r^I^ 1  16^  Trill-ill-III  th^14^  A' im  I^r^tirtyririvrtrit  ^  I  a PPM Figure 2.7. 1 1-1-nmr spectral changes over time after an acidic CD 2 C1 2 solution of Ru(OEP)(dms) 2 is exposed to 1 atm of 0 2 at room temperature (approximately 20° C). The peak assignments for each species are summarized in table 2.2.  H3 C  A  0  II  Free dms  CH 3  CH3 Ru Hmeso^  CH,  I  H3C  .•  -  Free d  CH3  0  0  N Ru m  II N  H meso  0  [  10  6  Figure 2.8. 1 H-nmr spectrum of a CD 2 C1 2  I^- I^I^I^T^1^I^I  4  Frill'  2  1^ I 0  I^I^  I^F  1^I^I^I —2 PPM  II[ri  —4  solution of Ru(OEP)(dms) 2 (approximately 5 mM) containing 3:1 dms/dmso (neat) has been added. Under these conditions, the major Ru(OEP) to which an excess of a mixture Ru(OEP)(dms)(dmso). species in solution is  Table 2.1 Summary of the 'H-nmr Peak Positions in CD 2 C12 for the Ru(OEP) Complexes Discussed in Section 2.5  OEP Signals (ppm) CH3^C H 2  Axial Ligand Signals (ppm) Hineso  dms^dmso^PhCOO H.^H.  Ru(OEP)(dms) 2  1.81,t  3.85,q  9.32,s  -2.66,s  Ru(OEP)(dms)(dmso)  1.83,t  3.92,m  9.60,s  -2.87,s  Ru(OEP)(dnig) 2  1.87,t  3.98,q  9.78,s  Ru(OEP)(dms)2 4- BF4- a  1.52 b  23.85  1.73  -0.17  -  Ru(OEP)(dms)(PhCOO)  0.46  16.75,12.87  4.07  -0.49  -  Me4 N + Ru(OEP)(PhC00)2c  -0.72  8.08  2.72  -  -  Hp  -2.07,s -2.18,s  _  _  15.34  9.84  8.75  17.86  10.74  9.35  (a) The signal positions are assumed to be essentially unchanged regardless of the counterion. (b) All of the signals attributed to Rum complexes are broad, and lacking in fine structure. (c) The signal for the Me 4 N + counterion is seen at 5.64 ppm.  53 analogous system involving Et 2 S and Et2 SO, the equilibrium constants as well as the rate constants for the substitution processes were determined by stopped-flow spectrophotometry; this will be fully discussed in section 3.4. Initially, very little of the bis sulfoxide complex is seen. In fact, in all of the spectra collected up to 360 min the Ru(OEP)(dmso) 2 signals are barely discernible; however, figure 2.9 shows that in the final spectrum taken, after 35 h, the bis-sulfoxide is the major Ru(OEP) product. Another important point seen in figure 2.9 is that after 35 h the phenyl signals for the benzoate/benzoic acid are at the same position as at the start; that is, the benzoic acid is recovered intact. The only difference is that the COOH proton, clearly identifiable at 11.4 ppm before the reaction was initiated, is no longer visible. A broad, underlying hump is visible around 5 ppm in figure 2.9 (most clearly seen in the integral scan), which suggests that water is now present, and the COOH proton is rapidly exchanging with it. In the spectra collected from 28 to 360 min, the benzoate phenyl proton signals are shifted significantly from their positions in benzoic acid; this is likely due to interaction of PhC00 - anions with paramagnetic Ru m (OEP) (and possibly RU N) species (see below). Presumably PhC00 - counter-ions would exchange rapidly with PhCOOH, and only time-averaged 1 H-nmr phenyl signals would be observed. In all of the spectra collected between 28 min and 35 h, a broad signal, presumably due to the acid proton of PhCOOH exchanging with H 2O, is observed in the region between 5 and 7 ppm. The broad signal in figure 2.7 that shifts over time (black shading) is one of four, attributable to a time-averaged spectrum of rapidly exchanging Ru(OEP)(dms) 2 + 13 11C00 and Ru(OEP)(dms) 2 (all of the peak positions, for all of the spectra collected, are listed in  ^  IIIIIIIIFIT1ri UI j I I I I^I 1 I (TT 1littlurt - trr - ttItiri  Fl  E  Tr l^II II I IA 1 I] I 11 I I -1 -1 4 1  A^16^14^tk^10^  ^FIT-1-141-T1-11-11-1/1111111111111  4^  - PR4^-4  Figure 2.9. 'H-nmr spectrum of an acidic CD 2 C1 2 solution of Ru(OEP)(dms) 2 35 h after exposure to 1 atm of 0 2 at room temperature (cf. figure 2.7); S ^solvent.  55 table 2.2). Figure 2.10 shows the spectrum of pure Ru(OEP)(dms) 2 + 13F4. When this complex was mixed with Ru(OEP)(dms) 2 , only time-averaged signals could be seen in the 'H-nmr spectrum, and the location of all four signals depended exclusively on the concentration ratio of Ru m/Ru n . This shows that electron transfer between Ru(OEP)(dms) 2 and Ru(OEP)(dms) 2 + X - (X^PhCOO, BF4) at 20° C is very rapid. The following analysis provides an idea of just how fast the electron transfer is. For the case in which a proton can be at one of two sites (in this case either in a Ru m environment or a Ru ll environment), the necessary condition for detecting separate resonances for the proton in each environment is given by r' > 2"/(27,6a,), where  T1  is the lifetime of the proton at  each site, and Ai) is the separation of the peaks (in Hz) when no exchange is taking place.' For the OEP methylene protons, the peak separation between the Ru ll and the Ru m positions is 20 ppm (see table 2.1), or 6000 Hz when a 300 MHz machine is used. Since separate resonances are not observed for the OEP methylenes of Ru(OEP)(dms) 2 and Ru(OEP)(dms) 2 + 13F4 in a mixture of the two species, r cannot be larger than '  3.8)(10' s at 20° C. In figure 2.7, the OEP methylene signal shifts over time towards the Ru m position, at the same time decreasing in overall intensity. This shows that the overall concentration of the two species is decreasing, while the ratio of Ru m/Ru ll is increasing with time; table 2.2 lists the calculated value of the fraction N,, (where Islu = [Ru(OEP)(dms) 2 ]/([Ru(OEP)(dms) 2] + [Ru(OEP)(dms) 2 +PhCOO-D) for each spectrum collected. Based on the oxidation mechanism proposed later in this section, we hypothesize that the concentration of Ru(OEP)(dms)2 ÷PhC00 - is in a steady state for most of the reaction, while that of Ru(OEP)(dms) 2 decreases steadily.  CH3...... ,.... CH3 S  I ,, ■ Ru  ..,  Hmeso  /  CH2  ,  S H3C^CH3 00.0  (CH3)oEP  CH3 B F4  "S,,,...,  .---------  (CH2)0EP  L  inummoninLaj i  agliga".86"a"...""w"risA•^  Figure 2.10. 'H-nmr spectrum of Ru(OEP)(dms) 2 13F4; 20.0° C in CD 2 C1 2 ; S ---- solvent.  meso  Table 2.2 Positions of the 1H-mnr Signals (b obs), Assigned to Ru1 (OEP)(dms) 2 + Ru111 (OEP)(dms) 2 + PhC00 in the Experiment Illustrated in Figure 2.7, and the Calculated Remaining Mole Fraction of Ru(OEP)(dms) 2 (Nur Sa,„ (NH)  Time (min)  CH3  CH2  Hmeso  SCH3  28  1.73, (0.72)  9.67, (0.71)  7.10, (0.71)  -1.92, (0.70)  97  1.68, (0.55)  11.76, (0.61)  6.33, (0.61)  -1.62, (0.58)  234  1.67, (0.51)  14.26, (0.48)  5.39, (0.48)  -1.31, (0.46)  312  1.66, (0.48)  15.29, (0.43)  5.00, (0.43)  -1.19, (0.41)  360  1.64, (0.41)  16.02, (0.39)  4.71, (0.39)  -1.10, (0.37)  (a) The mole fraction is calculated by the formula: N n = (sobs - (5m)/(Sin - (in), where bn and O m are the values of 6 (in ppm) for Ru"(OEP)(dms) 2 and Ru m (OEP)(dins)2 + BE4, respectively (6 for Ru(OEP)(dms) 2 + is assumed to be the same whether the counter-ion is PhC00 - or BEI--  58 The rapid electron transfer giving rise to the observed time-averaged nmr spectrum almost certainly occurs via an outer-sphere process. Such processes have been extensively documented in porphyrin systems, and the porphyrin ring is thought to mediate facile electron transfer from a donor to the metal center or vice-versa.' We have obtained the crystal structure of Ru(OEP)(decMS) 2 +13F4 (figure 2.11), which is expected to be closely analogous to that of Ru(OEP)(dms)2 13F4. 29 Table 2.3 compares selected bond lengths and angles of the Ru m complex with those of Ru(OEP)(decMS)2 , whose crystal structure we previously obtained.' The differences in corresponding bond length between the two species are within about 0.020 A, while the corresponding bond angles are within 5° of each other. In our report on the structure of Ru(OEP)(decMS) 2 , we included a fairly extensive survey of crystal structures of Rull (OEP) complexes, as well as other complexes containing Ru-S bonds.' The geometrical differences between Ru(OEP)(decMS) 2 and Ru(OEP)(decMS) 2 +13F4 are not significant when compared to the variations found in this survey. It is clear that the change in oxidation state does not significantly affect the geometry of the complex. Thus electron transfer between the two Ru species requires minimal bond reorganization, and this leads to fast and efficient electron exchange." Note that in a 1971 article,' Stynes and Ibers point out that a change in spin state upon oxidation or reduction will reduce the electron exchange rate to a much greater extent than even a relatively large change in bond lengths. As mentioned previously, no Ru m (OEP) high spin complex has ever been detected, and all of the available spectroscopic data for Ru(OEP)(dms) 2 +13F4 are similar to those of previously reported Ru m (OEP) low spin d 5 complexes; the fast electron exchange between Ru ll and Ru m provides further evidence that both complexes are low spin.  Figure 2.11. Crystal structure of Ru(OEP)(decMS) 2 +BF4 ; selected bond lengths and angles are given in table 2.3. -  60 Table 2.3 Selected Bond Distances (A) and Bond Angles (deg) for Ru(OEP)(decMS) 2 and Ru(OEP)(decMS) 2 + BF4 a  Ru(OEP)(decMS) 2  Ru(OEP)(decMS)2+BF4  Distances Ru-S(1) Ru-S(2) Ru-N(1) Ru-N(2) Ru-N(3) Ru-N(4)  2.376 (1) 2.361 (1) 2.044 (3) 2.044 (3) 2.056 (3) 2.041 (3)  2.383 (6) (b) 2.029 (6) 2.045 (5) (b) (b)  90.2 (1) 86.9 (1) 90.9 (1) 94.0 (1) 90.7 (1) 94.7 (1) 88.3 (1) 84.5 (1) 178.27 (3)  85.6 (2) 90.1 (2) (b) (b) 94.4 (2) 89.9 (2) (b) (b) 180.00  Angles N(1)-Ru-S(1) N(2)-Ru-S(1) N(3)-Ru-S(1) N(4)-Ru-S(1) N(1)-Ru-S(2) N(2)-Ru-S(2) N(3)-Ru-S(2) N(4)-Ru-S(2) S(1)-Ru-S(2)  (a) Standard deviations in parentheses. (b) Ru(OEP)(decMS) 2 +13F4 has a crystallographic inversion center.  61 The two major signals in figure 2.7 which are shaded grey are attributable to the OEP methylene protons of a paramagnetic complex of formulation Ru(OEP)(dms)(PhCOO) (see below); two signals are observed since in this case the two axial ligands are different, which makes the methylene protons magnetically inequivalent. The other signals which are shaded grey are also attributed to the same complex; the complete assignment is listed in table 2.1, and is discussed below. The signals due to Ru(OEP)(dms)(PhCOO) maintain approximately the same intensity (e.g. relative to the impurity at 16 ppm) until the last (35 h) spectrum, in which their intensity is greatly diminished (figure 2.9). At this point the signals are also slightly but significantly shifted relative to their position in earlier spectra. No immediate explanation is available for this observation; all of the signals initially assigned to the Ru(OEP)(dms)(PhCOO) complex are still present in the final spectrum, but shifted to varying degrees. It is possible that in the first five spectra the signals are actually time-averages due to exchange between Ru(OEP)(dms)(PhCOO) and some other complex, and that by the time of the final collected spectrum the concentration of this exchanging complex is negligible. The presence of Ru(OEP)(dms)(PhCOO) and Ru(OEP)(dms) 2 +PhC00 - is best explained by the following reaction sequence:  2Ru ll (OEP)(dms) 2 + 02 + 2PhCOOH -3 2Ru m (0EP)(dms) 2 + PhC00 - + H2 0 2 2.5  Ru m (OEP)(dms) 2 +PhC00 - T'—' Ru m (OEP)(dms)(PhCOO) + dms^2.6  62 Step one would involve initial electron transfer from Re to 0 2 to form Ru m and the superoxide anion, followed by superoxide protonation and subsequent disproportionation to give hydrogen peroxide and dioxygen. The latter process is known to be very fast, and irreversible,' so it would drive the process to completion. Note that in equations 2.5, 2.6 and throughout this thesis, ionic species are always written with the cation and associated anion. This is convenient for book-keeping purposes, but it is also meant to suggest a physical picture: given the low dielectric constant of the CH 2 C12 solvent (8.93)," all of the ionic species are probably best described as ion pairs." The initial electron transfer in equation 2.5 could occur either following initial coordination of 02 to the metal center (inner-sphere), or by direct outer-sphere electron transfer; there is precedence for both mechanisms.' For the stoichiometric process being discussed here, the inner sphere mechanism is almost certainly the only significant pathway, as evidenced by the fact that the reaction can be stopped completely if an excess of dms is added (at least in the absence of an intense light source; see below). Presumably, the excess thiother ligand is competing with the dioxygen for the axial binding site. Thermodynamically, the direct formation of superoxide via an outer-sphere electron transfer is extremely unfavourable; the (0 2 + e^02) standard reduction potential in dry, non-aqueous media has been measured at -0.8 V vs. Ag/AgC1 32 which, when combined with the Ru l11 (0EP)(RR'S) 2 /Rull (OEP)(RR'S) 2 couple of about 0.22 V reported in section 2.4, gives a cell potential of about -1 V. This translates to an equilibrium constant value of about 10' 7 (for Re + 0 2 -"-=' Ru m + 0 2 -). Theoretically, even a highly unfavourable equilibrium can be overcome if the product removal in a  63 subsequent step (e.g. in this case, by protonation of superoxide) is faster than the reverse reaction; however, product removal cannot overcome the effect of an initial, slow forward reaction. In this case it appears that outer sphere electron transfer from Ru ll to 02 is not only thermodynamically unfavourable, but also kinetically slow, at least under normal laboratory conditions. In chapter 3 it will be seen that Ru(OEP)(RR'S) 2 complexes can react with 02 and PhCOOH in the presence of excess dialkylsulfide, if the solution is irradiated with a reasonably intense source of visible light; in this case, the reaction is  hypothesized to take place via an outer sphere process, but light is required to supply the extra energy. Hydrogen peroxide is known to react rapidly with dialkylsulfides, especially in non-hydroxylic solvents.' Thus the H 2 02 produced in reaction 2.5 is expected to react rapidly with free dms (produced in reaction 2.6) to give water and dmso:  H2 02 + dms --> H 2 O + dmso^  2.7  Hydrogen peroxide could also react with coordinated dms, but free dms is a stronger nucleophile. Numerous unsuccessful attempts were made to prepare Ru(OEP)(dms)(PhCOO) pure; figure 2.12a, which shows the 1 1-1-nmr spectrum obtained for an approximately 1:1 mixture of Ru(OEP)(dms) 2 + 13F4 and Me4 N + Ru(OEP)(PhC00) 2- , illustrates the basic problem (figure 2.12b shows the spectrum of pure Me 4 N+Ru(OEP)(PhC00)2 for comparison). The major signals in the spectrum are attributable to the desired complex Ru(OEP)(dms)(PhCOO). Signals due to residual Me4N+Ru(OEP)(PhC00)2 are also  64  (a)  A O  PhC7 0 Ru m  Me4N+  0 ,C.Ph 0  ,13^'^'^'^16^'i'd'1  1  1",1  1  -  PPM  (b)  ( CH; )0EP  ( CH2 )o EP  N N CH,  HP Ho  U  L•%—..)  Figure 2.12. 'H-nmr spectrum of (a) a mixture (approximately 1:1) of Ru(OEP)(dms) 2 + BF4 and Me4 1•1 + 12u(OEP)(PhC00) 2 - about 1 h after mixing; (b) pure Me4 N+Ru(OEP)(PhC00)2. Both spectra in CD 2 C1 2 at 20.0° C, and systems sealed under vacuum; S == solvent.  65  present because the original mixture was not exactly 1:1, but this is not a factor when the reaction is scaled up, as the starting materials can then be weighed out more accurately. The problem is that figure 2.12a shows small amounts of Ru(OEP)(dms) 2 and Ru(OEP)(dms)(dmso) to be present as well, in essentially a 1:1 proportion. Attempts to crystallize out the desired product using hydrocarbon solvents resulted in a dramatic increase in the concentrations of Re species, this time with a predominance of Ru(OEP)(dms) 2 . In every attempt to prepare Ru(OEP)(dms)(PhCOO), Ru(OEP)(dms) 2 and Ru(OEP)(dms)(dmso) were obtained as co-products; in CH 2 C1 2 the species were in trace amounts and 1:1 proportion, but as soon as hydrocarbons were added, large amounts of Ru(OEP)(dms) 2 were recovered (this will be discussed further in section 2.6). Although the desired Ru(OEP)(dms)(PhCOO) could not be prepared pure, experiments such as that illustrated in figure 2.12a, which certainly demonstrate its existence, also provide a valuable clue as to the nature of the overall reaction of interest (i.e. the stoichiometric oxidation of Ru(OEP)(dms) 2 ). We speculate that a disproportionation such as the following can take place:  Ru m (OEP)(dms) 2 + PhC00- + Ru m(OEP)(dms)(PhCOO) ‘=-'' Ru ll (OEP)(dms) 2 + Ru iv (OEP)(dms)(PhC00) + PhC00-^2.8  In this scenario, coordination of the benzoate to the Ru m metal center brings the Ru m/Ru w redox couple into the range of the Ru(OEP)(dms)2 + /Ru(OEP)(dms) 2 couple; the CV studies discussed in section 2.4 already show how coordination of two benzoates to  66 Ru m can decrease its oxidation potential from about 1.3 to 0.22 V, making it almost as easy to oxidize to RIP as it is to oxidize Ru n (OEP)(Et 2S) 2 to the corresponding Ru m species. The presence of Ru N could well explain the slight shifts observed in the Ru(OEP)(dms)(PhCOO) 'H-nmr signals while the stoichiometric oxidation reaction is under way (see figures 2.7 and 2.9), if the equilibrium 2.8 is very fast. After reaction 2.8, the Re species could be converted to one equivalent of Ru(OEP)(dms)(dmso) by the following sequence of reactions:  Ruiv (OEP)(dms)(PhC00) + PhC00 - + H 2O cz--' 0=Ru N (OEP)(dms) + 2PhCOOH  2.9  0=RuNOEP)(dms) + dms --> Ru ll (OEP)(dms)(dmso)  2.10  Run (OEP)(dms)(dmso)^Ru n (OEP)(dms) + dmso  2.11  Ru il (OEP)(dms) + dmso^Ru il (OEP)(dms)(dmso)  2.12  The conversion of coordinated dmso to dmso could alternatively involve an intramolecular process and a 7-bonded S =0 moiety in the transition state,' although some kinetic findings imply otherwise; this will be discussed in section 3.5.2.2. Finally, as free dmso accumulates, the bis sulfoxide complex would be formed via  67 Ru(OEP)(dms)(dmso) + dmso --='' Ru(OEP)(dmso) 2 + dms^2.13  Equation 2.8 can be thought of as an acid-base reaction leaving a hydroxide as counterion to the Ru N cationic species, followed by nucleophilic addition of the hydroxide to the coordinated benzoate, and subsequent displacement of the Ru"-oxo. Alternatively, the acid-base reaction could be followed by a simple displacement of the coordinated benzoate by the hydroxide, followed by deprotonation of the coordinated ligand. Water in the required stoichiometric amount of reaction 2.9 would be produced in reaction 2.7. The reactivity suggested in equations 2.10-2.12 has precedent in Ru(porphyrin) chemistry (see section 1.2). 36 Notice that the overall stoichiometry for equations 2.5-2.13 is  R u n (OEP)(dm s ) 2 + 0 2 R u ll (OEP)(dm50) 2  ^  2.14  As previously mentioned, the benzoic acid is not consumed in the reaction, and acts merely as a catalyst. It should be emphasized that although equations 2.8 and 2.9 fit well into the scheme for the observed reactivity of Ru(OEP)(dms) 2 , they are meant to suggest a general "Ru w =0" mechanism whereby the reaction takes place, and not necessarily the exact mechanism. There are a considerable number of variations which could be proposed for equations 2.8 and 2.9; a particularly plausible example might be:  Ru m (OEP)(dms)(PhC00) + H 2 O - "- Ru m (OEP)(dms)(OH) + PhCOOH^2.8'  68 Ru m (OEP)(dms)(OH) + Ru m (OEP)(dms) 2 ÷ PhC00 - 7.--"Ru il (OEP)(dms) 2 + 0 =Ru Iv (OEP)(dms) + PhCOOH^2.9'  In this scenario, reaction 2.6 is viewed, in effect, as a side equilibrium, and not really as part of the reaction pathway. Further equilibria might arise as free dmso accumulates from reaction 2.7. Some of the sulfoxide might tend to coordinate to Re:  Ru m (OEP)(dms) 2 + PhC00- + dmso Ru m (OEP)(dms)(dmso) + PhC00 - + dms 2.15  The cyclic voltammetry experiments show (figure 2.4b) that coordination of a sulfoxide to Ru n' makes the metal much more reducible than its dialkylsulfide counterpart; thus if a species such as Ru(OEP)(dms)(dmso) + PhC00 - is formed during the Ru(OEP)(dms)2 oxidation sequence, it will be rapidly and preferentially reduced to the Ru" form, either in a step analogous to step 2.8, or via electron transfer from a Ru"(OEP)(dms) 2 molecule. Figure 2.13 shows the cyclic voltammogram of a solution containing primarily Ru(OEP)(decMS)(decMS0) prepared by mixing 0.78 mM Ru(OEP)(decMS) 2 , 71 mM decMS, and 25 mM decMSO (all three Ru(OEP)(RR'S)(RR'SO) complexes have a distinctive band at 404 nm in their uv/vis spectra, and this can be used to investigate the composition of the above mixture). Initially, as the potential is scanned in the positive direction, the major signal, attributed to the oxidation of Ru(OEP)(decMS)(DecMS0), is found at 0.59 V; the signal at 0.28, attributed to Ru(OEP)(decMS) 2 oxidation, is minor  69  0.21  0.59  Figure 2.13. Cyclic voltammogram of a solution (CH 2 C1 2/n-Bu4N + BF4) initially containing 0.78 mM Ru(OEP)(decMS) 2 , 71 mM decMS, and 25 mM decMSO.  70 by comparison. As the potential is scanned back in the negative direction, the peak due to Ru m (OEP)(decMS) 2 + reduction (at 0.21 V) is now the major one, while that due to Ru m (OEP)(decMS)(decMS0) + reduction (at 0.50 V) is comparatively minor. The observation is explained by the following reaction sequence:  Ru ll (OEP)(decMS)(decMS0) Ru m (OEP)(decMS)(decMS0) -1- + e^2.16  Ru m (OEP)(decMS)(decMSO) + decMS Ru m (OEP)(decMS) 2 + + decMSO 2.17  Ru m (OEP)(decMS) 2 + + e-  Ru ll (OEP)(decMS) 2^2.18  This experiment shows that sulfide coordination to Ru m is preferred over sulfoxide coordination; thus equation 2.15 should not play an important role in the stoichiometric oxidation, except possibly at the point when most of the sulfide has been converted to sulfoxide. All of the alternate reaction pathways proposed, though different in detail to equations 2.8-2.9, nevertheless share the essential feature: Ru m (OEP)(dms)(L) + PhC00 (L^dms, dmso) is reduced to Ru t' by a Ru m species which has had its oxidation potential lowered upon replacement of one coordinated thioether by an anionic ligand, and the resulting Ru Iv species is converted to O=Ru"(OEP)(dms).  71 2.6 Reaction of Ru(OEP)(RR'S) 2 Complexes with Dioxygen and Benzoic Acid in Hydrocarbon Solvents  In benzene or toluene containing benzoic acid, exposure of Ru(OEP)(dms) 2 , Ru(OEP)(Et 2 S) 2 or Ru(OEP)(decMS) 2 to 0 2 , under conditions analogous to those described for the reactions in methylene chloride, also ultimately results in the production of the Ru(OEP) mono- and bis- sulfoxide complexes. In a general sense, the mechanism suggested in equations 2.5-2.13 is consistent with the reactivity observed in benzene or toluene; however, the lower polarity of these solvents (dielectric constant ,--r- 2) does result in some minor, but interesting, differences between what is observed in methylene chloride, and what is observed in, say, benzene. Figure 2.14 shows the 'H-nmr spectrum of a C 6D6 solution containing 8.2 mM Ru(OEP)(dms) 2 and 8.2 mM PhCOOH, which was exposed to 1 atm of 0 2 for about 36 h at room temperature (table 2.4 summarizes the peak assignments). Several points are noteworthy about this reaction. First, it is much slower than the analogous reaction in methylene chloride; figure 2.9 shows that, after 35 h, a substantial proportion of the Ru(OEP) has been converted to Ru(OEP)(dmso) 2 , and no Ru(OEP)(dms) 2 can be detected. In the reaction illustrated in figure 2.14, only about 66% of the original complex has reacted to give Ru(OEP)(dms)(dmso), and the bis(sulfoxide) is present in trace amounts. A second point is that no significant amounts of Ru m complexes are visible in the reaction mixture (actually, trace amounts of Ru(OEP)(dms)(PhCOO) are detectable, if the spectrum is expanded sufficiently). In a separate experiment, in which [PhCOOH] was 20 times that of Ru(OEP)(dms) 2 , the characteristic signals of Ru m (OEP)(dms)(PhC00) (table 2.4) could be detected in significant quantities, but even  A I  un.  A 0  A 0 PhCOOH r•■■-••■  11111- T^  1.1D^  PhCOOH  rA-N  1'^r rrirl r  6  I  r  111  -1--  11  - 11111i1  -11I -  1-  1- 11 -  1  T2Pkr-r-r"T"1-r-r-rT  Figure 2.14. 'H-nmr spectrum of a C 6D 6 solution, initially containing 8.2 mM Ru(OEP)(dms) 2 and 8.2 mM PhCOOH, which was exposed to 1 atm of 0 2 for about 36 h at room temperature; S^solvent, g^grease, ?^unidentifed signals.  Table 2.4 Summary of the 'H-nmr Peak Positions in C 6D6 for the dms- and dmso-Containing Ru(OEP) Complexes Discussed in Section 2.6  OEP Signals (ppm)^Axial Ligand Signals (ppm) CH 3^CH2^Hmeso^dms^dmso^PhCOO H o^H.^Hp Ru(OEP)(dms) 2  1.90,t  3.90,q  9.62,s  -2.68,s  Ru(OEP)(dms)(dmso)  1.88,t  3.93,m  9.85,s  -2.94,s  Ru(OEP)(dm50) 2 a  1.93,t  3.99,q  9.94,s  Ru(OEP)(dms)(PhCOO) b  0.30  15.73, 12.33  4.12  -2.08,s -2.32,s  0.20  -  16.88  9.77  —8.45'  (a) This spectrum was obtained in C 7D 8 ; note that Ru(OEP)(dmso) 2 is sparingly soluble in all hydrocarbon solvents. (b) All of the signals for this paramagnetic complex are broad, and lacking in fine structure. (c) This signal overlaps another set of signals attributed to unidentified diamagnetic species, which makes it difficult to establish the exact peak position.  74 under these conditions there was no evidence for the presence of Ru m (OEP)(dms) 2 ÷ PhC00 - . Clearly the Re species are much more difficult to generate in the non-polar benzene solvent, and also equation 2.6, in which Ru(OEP)(dms) 2 +13 11C00 - is considered to dissociate dms and form Ru(OEP)(dms)(PhCOO) must lie far to the right. Both of these factors would contribute to making the overall reaction slower in hydrocarbon solvents (cf. equation 2.8). A third feature of figure 2.14 worth pointing out is the presence of the trace signals at 4.3 and 10.1 ppm. The presence of both these signals was noted in our earlier studies on the oxidation of Ru(OEP)(decMS) 2 ," although the signals were much more prominent l a There is no immediately apparent assignment for the signal at 4.3 ppm, but that at 10.1 ppm is almost certainly attributable to the meso proton of a Ru ll (OEP) complex.' It is impossible to be sure which complex is giving rise to this signal, but it may be a Ru(OEP)(CO)L species (L --.. a neutral ligand, possibly dms or dmso), as such species exhibit an H ines, signal at around 10.1 ppm in benzene.' It is well known that the CO-containing complexes are thermodynamic sinks in Ru(Porp) chemistry, and the appearance of Ru(OEP)(CO)L under conditions where there is no obvious source of CO has been documented, although often without explanation (but see below). 1a,22,38,39 The presence of end-products other than the sulfoxide complexes (which are desired within the catalytic 0 2 -oxidation of thioethers to sulfoxide; see chapter 3) seems to be characteristic of the reactions carried out in hydrocarbon solvents. Figure 2.15 shows the result of exposing a solution containing 2.3 mM Ru(OEP)(Et 2 S) 2 and 3.3 mM  A  s  13  s 1  Ru  PhC  Free Et 2 S and Et 2 S0 g  -4  Figure 2.15. 'H-nmr spectrum of a C 6D 6 solution, initially containing 2.3 mM Ru(OEP)(Et 2S) 2 and 3.3 mM PhCOOH, which was exposed to 1 atm of 0 2 for about 12 h at 35° C; S^solvent, g^grease, ?^unidentified signals.  Table 2.5 Summary of the 'H-nmr Peak Positions in C 6D6 for the Et2S- and Et2SO-Containing Ru(OEP) Complexes Discussed in Section 2.6  OEP Signals (ppm)^ Axial Ligand Signals (ppm) CH 3  CH2  HMESO  CH2^CH3^CH2^CH3 Ru(OEP)(Et 2 S) 2  1.91,t  3.91,q  9.65,s  Ru(OEP)(Et 2 S)(Et25.0)  1.91,t  3.96,m  9.85,s  Ru(OEP)(Et 2_SO) 2 b  1.90,t  3.94,q  9.90,s  Ru(OEP)(Et 2 S)(PhC00)  0.24  15.40, 12.36  — 4.1 6  PhCOO  Et2S^Et2 S 0  Ho  Hm  Hp  -  -2.34,q^-1.49,t -1.4 to -2.7'^-1.4 to -2.7' -(2.11,2.68)c -1.65,t 8.22^— 4.1 d  17.00  9.80  8.556  (a) These signals have not yet been unequivocably assigned. (b) This spectrum was obtained in C71:0 8 . (c) For Ru(OEP)(Et 250) 2 the sulfoxide methylene protons are magnetically inequivalent, and give rise to two separate multiplets. (d) Tentative positions; overlap of signals makes it difficult to determine the exact positions of these signals.  al,  77 PhCOOH, to 1 atm of 0 2 for 12 h at 35° C (these are the conditions under which the experiments described in the next chapter were run, except that in the latter an excess of thioether was added). The peak assignments for figure 2.15 are given in table 2.5. For the Et 2 S system, Ru ffi (OEP)(Et 2S)(PhC00) does accumulate significantly (in fact the signals attributable to this complex were present within 20 min of starting the reaction). It appears that Ru m (OEP)(Et 2 S)(PhC00) is significantly more "stable" than its dms counterpart under the reaction conditions. Still, there is no evidence in figure 2.15 for the presence of Ru m (OEP)(Et2 S) 2 + PhC00 - ; thus even for the Et 2 S complex, the ionic species is not stable in the less polar solvent, so that the Et 2 S equivalent of equation 2.6 lies far to the right. What little Ru(OEP)(Et 2S) 2 +13 11C00- is produced perhaps rapidly undergoes the disproportionation reaction 2.8 and subsequent reactions, to give neutral species such as 0=Ru(OEP)(Et 2S), and eventually Ru(OEP)(Et2 S)(Et2S0). Figure 2.15 also shows the signals at about 4.3 and 10.1 ppm (note that here the 4.3 signal is quite intense), and also two other signals of about equal intensity near 9.5 ppm. Again, one can only speculate as to the identity of the complexes which give rise to these signals, but previous studies have shown that the meso protons of complexes having the form [Ru N (OEP)L] 20 (L an anionic ligand) have signals around 9.5 ppm in benzene solution.' These so-called Aoxo dimers are well known thermodynamic sinks in ruthenium porphyrin chemistry when 0 2 and H 2 O are present, and so it is likely that the two signals at around 9.5 ppm in figure 2.15 are due to two complexes of this type (perhaps with L^PhCOO and/or OH)." There are other studies which shed some light on the observations made about the 'H-nmr data of figures 2.14 and 2.15. Figure 2.16 shows the 'H-nmr spectrum of a  A s I  ow R u  13  s  s  Ru  Rums  / 11  0  0  PhC  A  O  _P-  Ilifir I rIr IfT FT114T-111] ^  IV.^T  ^lb  S PhCOOH PhCOOH  rg^r-ri  11111i^  r^I 1  -  r - r-  r  tlitTliFfil PPM^-4  Figure 2.16. 'H-nmr spectrum of a C 6D 6 Me4N+Rum (OEP)(PhC00)2(approximatelsolution, initially a suspension of Ru m(OEP)(dms) 2 +13F4 and y 4x10 6 solvent, ?^unidentified signals. mol of each), which was allowed to stand overnight under vacuum; S  79 solution obtained by allowing a suspension of Ru(OEP)(dms) 2 + 13F4 and Me4 N+Ru(0Ep)(phC00) 2 " (approximately 4x10' mol of each in about 0.6 mL of solvent) to stand overnight under vacuum in thoroughly dried C 6 D6 . At the time the spectrum was taken, all of the solid had dissolved, and the resulting solution was dark red-orange. The spectrum shows that Ru(OEP)(dms) 2 and Ru(OEP)(dms)(dmso) are formed in an approximately 3:1 ratio, along with comparatively small amounts of Ru(OEP)(dms)(PhCOO), and other unidentified Re products. This is a very different product distribution from that obtained when Ru(OEP)(dms) 2 + 13F4 and Me4 N+Ru(OEP)(PhC00)2 are mixed under vacuum in CD 2 C12 (see figure 2.12a in the previous section); in this solvent, the major product is Ru(OEP)(dms)(PhCOO), and the small quantities of Ru(OEP)(dms) 2 and Ru(OEP)(dms)(dmso) observed can be attributed to the presence of a trace amount of water, which presumably allows reactions 2.8-2.13 to take place to a limited extent. It appears that in benzene, the Ru  m  species are  sufficiently unstable in solution that, even in the absence of H2 O, an alternative reduction pathway is being used to generate substantial amounts of Ru(II). One plausible route is via a process formally described by:  Ru m (OEP)(dms) 2 + BF4 " + Me 4 N + Ru(OEP)(PhC00)2 -' Ru"(OEP)(dms) 2 + "(PhCOO) 2 " + Me4 N + BF4 + Unidentified Ru n Products 2.19  In practice, benzoyl peroxide is not observed; however, this could be because the benzoyl radicals react further with other compounds in solution, which would explain the presence of the other unidentified products, and also of coordinated dmso. In hydrocarbon solvent,  80 such free-radical processes might take place to a limited extent under even under 0 2 atmospheres, when H 2 O is available (from the reaction of dms with H 2 02 , equation 2.7), which could also help explain the formation of unidentified Ru(OEP) products obtained in the aerobic oxidations of Ru(OEP)(dms)2 and Ru(OEP)(Et 2 S) 2 in hydrocarbon solutions. For example, the presence of the PhCOO radical in aerobic conditions could initiate autooxidation of the thioethers. This is known to produce, among other products, aldehydes, 35 and it has been shown that Ru(OEP) complexes can catalyze the decarbonylation of aldehydes.'" Thus Ru(OEP)(CO)L could indeed be giving rise to the signal at 10.1 ppm, with the CO resulting from free-radical autoxidation of the thioethers, and subsequent decarbonylation of the primary auto-oxidation products. Despite the minor side products which are observed when Ru(OEP)(RR'S) 2 complexes react with 0 2 and PhCOOH, it does appear that the major oxidation pathway can be described by equations 2.5-2.13, whether the oxidation is carried out in methylene chloride or benzene. This conclusion becomes a key assumption in the experiments described in the following chapter.  81 REFERENCES AND NOTES FOR CHAPTER 2  1. a)Pacheco, A. A. M.Sc. Dissertation, The University of British Columbia, Vancouver, B. C., 1986. b) Pacheco, A. A. Unpublished data. 2. Sekutowski, D. G.; Stucky, G. D. J. Chem. Educ. 1976, 53, 110. 3. Fieser, L. F. and Fieser, M. Reagents for Organic Synthesis, J. Wiley and Sons, Inc, New York, 1967; vol I, pp 471 and 472. 4.Bruce, M. I.; Matisons, J. G.; Wallis, R. C.; Patrick, J. M.; Skelton, B. W.; White, A. M. J. Chem. Soc., Dalton Trans. 1983, 2365. 5. Antipas, A.; Buchler, J. W.; Gouterman, M.; Smith, P. D. J. Am. Chem. Soc. 1978, 100, 3015. 6. Collman, J. P.; Barnes, C. E.; Sweptson, P. N.; Ibers, J. A. J. Am. Chem. Soc. 1984, 106, 3500. 7. Collman, J. P.; Prodolliet, J. W.; Leidner, C. R. J. Am. Chem. Soc. 1986, 108, 2916. 8. A good reference on the subject of handling air-sensitive compounds is: Shriver, D. F. The Manipulation of Air Sensitive Compounds, McGraw-Hill, New York, N.Y., 1969. 9. James, B. R.; Pacheco, A. A.; Rettig, S. J.; Ibers, J. A. Inorg. Chem. 1988, 27, 2414. 10. The yields for these complexes were not explicitly determined; however, the supernatants after recrystallization showed only negligible color, which suggests that any losses in yield were due primarily to incomplete transfer of the precipitate from the filter to the weighing vial. For approximately 100 mg quantities of a precipitate, 80-90% transfer was commonly obtained. 11.Van Duyne, R. P.; Reilley, C. N. Anal. Chem. 1972, 44, 142. 12. This couple was previously recorded at 0.08 V vs. SCE (see references 19 and 20 below), which is the same within experimental error; the SCE is 0.04V higher than that of Ag/AgC1 (relative to NHE) in aqueous solution (Brady, J. E.; Humiston, G. E. General Chemistry, Principles and Structure, 2" ed., John Wiley and Sons, New York, N. Y., 1978; p. 463). 13. J. A. Davies, Adv. in Inorg. Chem. Radiochem. 1981, 24, 115 and references therein.  82 14. See for example: James, B. R.; Morris, R. H.; Reimer, K. J. Can. J. Chem. 1977, 55, 2352, and references therein. 15. Janson, T.R.; Katz, J. In The Porphyrins, Dolphin, D., Ed, Academic Press, New York, N. Y., 1978; vol. VI, chapter 1. 16. Scheer, H.; Katz, J. In Porphyrins and Metalloporphyrins, Smith, K. M., Ed., Elsevier Scientific, Amsterdam, The Netherlands, 1975; Chapter 10. 17. Davis, D. G. In The Porphyrins, Dolphin, D., Ed., Academic Press, New York, N. Y., 1978; vol. V, chapter 4. 18. Fuhrhop, J. H.; Kadish, K. M.; Davis, D. G. J. Am. Chem. Soc. 1973, 95, 5140. 19. Brown, G. M.; Hopf, F. R.; Ferguson, J. A.; Meyer, T. J.; Whitten, D. G. J. Am. Chem. Soc. 1973, 95, 5939. 20. Brown, G. M., Hopf, F. R., Meyer, T. J., Whitten, D. G. J. Am Chem. Soc., 1975, 97, 5385. 21. The X-Y recorder used for the CV studies was not ideal for obtaining precise data, and the experimental uncertainty in the obtained E°' values is estimated at +0.02 V. Therefore the E°' values for all three complexes are the same within experimental error. 22. Sishta, P. C. Ph.D. Dissertation, The University of British Columbia, Vancouver B. C., 1990. 23. a) Barley, M.; Becker, J. Y.; Domazetis, G.; Dolphin, D.; James, B. R. Can. J. Chem. 1983, 61, 2389. b) Barley, M.; Dolphin, D.; James, B. R. J. Chem. Soc., Chem. Commun. 1984, 1499. 24. a) See reference 9 and references therein. b) Rearrangement of S-bound sulfoxide to the 0-bound isomer in Ru(dmso) complexes after metal-centered oxidation was previously observed for Ru n (NH 3 )5 (dmso) in aqueous solution: Scott, A. Y. N.; Taube, H. Inorg. Chem. 1982, 21, 2542. A 7-coordinate transition state was postulated for the isomerization process. 25. Drago, R. S. Physical Methods in Chemistry, W. B. Saunders, Philadelphia, PA, 1977; a) Chapter 12; b) Chapter 8. 26. Ke, M.; Rettig, S. J.; James, B. R.; Dolphin, D. J. Chem. Soc., Chem. Commun. 1987, 1110. 27. Sishta, C.; Ke, M.; James, B. R.; Dolphin, D. J. Chem. Soc., Chem. Commun. 1986, 787.  83 28. Castro, C. E. In The Porphyrins, Dolphin, D., Ed., Academic Press, New York, N. Y., 1978; Vol. V, Chapter 1. 29. A complete analysis of the crystal structure is described elsewhere; Pacheco, A. A.; Rettig, S. J.; James, B. R. To be Published. 30. Wilkins, R. G. Kinetics and Mechanisms of Reactions of Transition Metal Complexes, VCH, Weinheim, 1991; Chapter 5. 31. Stynes, H. C.; Ibers, J. A. Jnorg. Chem. 1971, 10, 2304. 32. Sawyer, D. T.; Valentine, J. S. Acc. Chem. Res. 1981, 14, 393. 33. Sawyer, D. T.; Roberts, Jr. J. L. Experimental Electrochemistry for Chemists, John Wiley and Sons, New York, N. Y., 1974; Chapter 4. 34. A good review of this subject is provided in reference 28; another useful review is found in: Chu, M. M. L.; Castro, C. E.; Hathaway, G. M. Biochem. 1978, 17, 481. 35. Barnard, D.; Bateman, L.; Cuneen, J. I. In Organic Sulfur Compounds, Kharasch N., Ed., Pergamon Press, New York, N. Y., 1961; Vol. I, Chapter 21. 36. Rajapakse, N.; James, B. R.; Dolphin, D. Catal. Lett. 1989, 2, 219. 37. A singlet between 9.0 and 10.5 ppm in the 'H-nmr of Ru(OEP) complexes is characteristic of the meso protons; see reference 9 and references therein. 38. Ke, M. Ph.D. Dissertation, The University of British Columbia, Vancouver B. C., 1988. 39. In one study, it was even shown that Ru(Porp) complexes can react with CO present in the walls of the reaction vessel: Corsini, A.; Mehdi, H.; Chan, A. Can. J. Chem. 1980, 58, 527. 40. Collman, J. P.; Barnes, C. E.; Brothers, P. J.; Collins, T. J.; Ozawa, T.; Gallucci, J. C.; Ibers, J. A. J. Am. Chem. Soc. 1984, 106, 5151. 41. Domazetis, G.; Tarpey, B.; Dolphin, D.; James, B. R. J. Chem. Soc., Chem. Commun. 1980, 939.  84 CHAPTER 3 A MECHANISTIC STUDY OF THE 0 2 -OXIDATION OF DIETHYLSULFIDE CATALYZED BY Ru(OEP)(Et 2S) 2  3.1 Introduction  In the previous chapter a mechanism was proposed for the stoichiometric oxidation of Ru(OEP)(RR'S) 2 complexes to Ru(OEP)(RR'S)(RR'50) and Ru(OEP)(Et 250) 2 by dioxygen in acidic organic media. It is clear that, in the presence of a large excess of dialkylsulfide, the starting bis(thioether) complex could be regenerated from Ru(OEP)(RR'S)(RIV50), thus making the process catalytic. This assumption was confirmed experimentally, and in the process new insights were obtained. In particular, a completely new and interesting feature of the catalytic reaction became apparent, namely its rate dependence on visible light. This chapter begins by summarizing qualitative features peculiar to the catalytic process. Based on these, and on the conclusions drawn in chapter 2 about the stoichiometric oxidations, a mechanism for the catalytic oxidation of dialkylsulfides is proposed. The second part of the chapter deals with the kinetic analysis of quantitative stopped-flow and oxygen-uptake experiments, which were used to monitor the catalytic process. The data are fitted to a rate law derived from the proposed mechanism; the actual derivation of the rate law is deferred to chapter 4. All of the studies discussed in this chapter refer specifically to Et2S oxidation catalyzed by Ru(OEP)(Et 2 S) 2 , in benzene. Qualitatively, excess dms in the presence of Ru(OEP)(dms) 2 and decMS in the presence of Ru(OEP)(decMS) 2 were found be oxidized in the same way as Et2 S in the presence of Ru(OEP)(Et2 S) 2 , and the systems exhibited  85 qualitative dependences on the same variables. Furthermore, all the reactions proceeded in either methylene chloride or toluene; in fact, it was already shown in chapter 2 that the stoichiometric reaction proceeds more cleanly in methylene chloride than in benzene, and this is probably true of the catalytic system as well; unfortunately the high vapour pressure of methylene chloride was a problem when quantitative studies were attempted. Dimethylsulfide also had the problem of high vapour pressure.  3.2 Experimental 3.2.1 Materials  n-Undecane, used as an internal standard for the GC measurements, was from Aldrich. The origins or methods of preparation of all other materials used in the experiments described in this chapter were previously described in chapter 2.  3.2.2 Stopped-Flow Experiments 3.2.2.1 Sample Handling  All experiments were carried out under aerobic conditions; no special precautions were taken to exclude air or water. It is assumed that side-reactions with these potential reagents are slow enough to be ignored under the conditions of high sulfide and sulfoxide concentrations used, and indeed the excellent reproducibility of the results verifies this assumption (see section 3.4). For any given experiment, one of the drive syringes was filled with a benzene solution of Et 2 S, and the other with a benzene solution of Ru(OEP)(Et 2 SO) 2 and Et2 SO. One experiment was taken to be the average of five stopped-flow runs done at constant concentration of all reagents. In any given series of  86 experiments, the concentration of Et 2 S was varied, while the concentrations of the reagents in the other syringe were held constant. A blank run in which the Et 2S syringe contained only benzene was carried out for each series. The free ligand concentrations (Et2 S and Et2 SO) were always held high enough so that they would remain effectively constant for the duration of an experiment.  3.2.2.2 Instrumentation  All stopped-flow experiments were carried out on an Applied Photophysics model SF.17MV stopped-flow spectrophotometer, equipped with 2.5 mL drive syringes. A pressure of 650 kPa was used to drive the syringes.' A constant temperature of 35.0+0.1° C was achieved using a Grant LTD 6 constant-temperature bath connected to the stopped-flow sample handling unit via Tygon tubing. Changes in the reaction mixture were monitored by following the absorbance change at one of two wavelengths: 400.5, or 402.8 nm (see section 3.4.1). The absorbance change with time was monitored across a 1.00 cm path-length cell. The monochromator entrance and exit slits were both set at 0.2 mm. A high brightness 150-W Xenon arc lamp was used as the light source.  3.2.3 Gas Chromatography 3.2.3.1 Sample Handling  Sample preparation and handling for gas chromatographic experiments was essentially identical to that described below for the gas uptake experiments. The only significant difference was that samples to be analyzed by gas chromatography had 23.7  87 mM n-undecane added to them as an internal standard.  3.2.3.1 Instrumentation  Gas chromatography was carried out on a Hewlett-Packard HP 5890A gas chromatograph, equipped with a 15 m x 0.20 mm HP-1 capillary column (0.33 Am film thickness), a split capillary inlet (insert packed with 3% OV-1 on 100/120 chromosorb W-HP), and a flame ionization detector. Helium was used as the carrier and makeup gas. Other chromatographic conditions were as follows: sample volume, 2 AL; column flow, 0.33 mL/min; split ratio, 45:1; injector temperature, 220° C; detector temperature, 325° C; oven temperature program, 80° C for 5 min then increased at a rate of 20° C per min to 170° C, and held for 15 min.  3.2.4 Oxygen Uptake Experiments 3.2.4.1 Sample Handling  Unless otherwise stated, all the gas uptake experiments were carried out in 10.0 mL aliquots of a benzene solution, containing an initial Et 2 S concentration of 0.742 M. For experiments in which Ru(OEP)(Et2 S) 2 concentrations of less than 0.5 mM were required, a stock solution containing about 5 mM Ru(OEP)(Et 2 S) 2 and 0.742 M Et2 S was first made up. The appropriate amount of this solution was then added to the reaction vessel using a Unimetrics microliter syringe, and the total volume made up to 10.0 ml with a 0.742 M solution of Et 2S in benzene. Between experiments, the stock Ru(OEP)(Et 2S) 2 solutions were kept in the dark, and all stock was used up in a maximum of three days. For experiments requiring Ru(OEP)(Et2 S) 2 concentrations greater than 0.5  88 mM, the appropriate amount of crystalline complex was weighed out and added directly to the reaction vessel. Crystalline benzoic acid was weighed out into a small glass bucket, which was suspended above the reaction mixture by means of a dropping sidearm (see fig.3.1a), until the moment when the reaction was to be initiated. Prior to reaction, the solution was subjected to two freeze/pump/thaw degassing cycles in order to remove dissolved nitrogen.  3.2.4.2 Apparatus Setup  The gas uptake apparatus used for this series of experiments was simply a modified version of a design which has seen extensive use in our laboratories,' so that a full written description of all the parts and basic operation is omitted here. Nevertheless, there are a sufficient number of procedural differences in the way the modified apparatus was used to warrant some discussion. The complete apparatus is illustrated in figure 3.1. The principal design difference between this apparatus and its predecessors is in the use of high-vacuum Teflon valves at positions 3 and 4, in place of standard greased stopcocks (figure 3.1a). When Teflon valve 3 is closed to seal off the small volume of gas in the right arm of the oil manometer, a significant pressure is exerted, causing a very noticeable change in the oil levels. Thus the oil manometer must be re-levelled before proceeding (see below). In addition, when valve 4 is closed, a much smaller but still measurable pressure change takes place. This too must be compensated for (see below). Additional modifications to the apparatus were peculiar to this series of  89  (a)  to mercury manometer to mercury manometer  (b)  ,,Reaction flask V assembly  Figure 3.1. Apparatus used for gas uptake measurements. (a) Complete setup; (b) Closeup view of the oil bath and housing, showing the orientation of the light source. Key components: (A) Thermostatted and insulated oil bath; (B) Reaction vessel; (C) Oil manometer; (D) Mercury burette and reservoir; (E) Projection lamp; (F) Aluminum foil; (G) Compressed air manifold; (H) Screen. (1)-(12): Various taps and valves; see text for explanations.  90 experiments, and were required to keep the reaction solution intensely and constantly illuminated. These modifications are illustrated in figure 3.1b. A GTE/Sylvania ENX 360 Watt projection lamp (E), of the type commonly used in Kodak carousel slide projectors, was used as a source of light. The solution was illuminated via a hole in the oil bath housing insulation, normally used to inspect visually the reaction mixture. A Powerstat variable transformer was used to supply 30 V AC to the lamp. The insulation and the outside walls of the oil bath housing had to be covered in foil (F) to protect them from excessive heating by the projection lamp. In addition, the lamp and exterior of the oil bath housing were constantly cooled by blowing compressed air over them via the funnel G, which was a common laboratory glass funnel. During operation, the operator was protected from the intense light by the screen (H), which was simply a sheet of cardboard covered in aluminum foil. Normally a thermostatted heat source is required to keep the oil bath temperature constant. In this case a cooling source also had to be supplied to counteract the uncontrolled heat provided by the projection lamp. The oil bath was cooled by water, supplied from a separate constant-temperature bath, and fed through a copper coil immersed in the oil. With this setup, the temperature could be kept constant at 34.85+0.15° C (but see sections 3.5.2.1 and 3.5.2.2). Finally, because the average surface of reaction solution exposed to the light would tend to vary with the shaking rate, special care was taken to keep this constant at 164 ± 10 cycles/min, unless otherwise stated. The same flask and bucket were used in all of the experiments for the same reason. As benzene and Et2 S both have a significant vapour pressure at the reaction temperature, a measurable pressure change occurs as the temperature cycles between  91 34.70 and 35.00° C. This change is visible as an oscillatory motion of the levels in the oil manometer, in the absence of any gas uptake or evolution due to chemical reactions. This phenomenon would incorporate an additional uncertainty in the uptake readings if these were taken at random times. To prevent this, all gas burette readings were taken when the temperature was at the minimum of 34.70° C. A typical experimental run proceeded as follows. The initial sample preparation was identical to that used with prior versions of the apparatus.' Once the reaction vessel (B) was immersed in the oil bath (A), the solution was allowed to equilibrate for about 10 minutes with the projection lamp off (30 minutes for gas pressures of 0.6 atm or less) at a pressure about 10 ton below that desired for the reaction. During this time, valves 7, 8, 10 and 11 were closed, while all others were open. After this time, valve 3 was closed. Oxygen was introduced through needle valve 10, until the oil manometer (C) was nearly levelled (to within 3mm). The total pressure reading at the mercury manometer was recorded; this reading was taken to be the total pressure under which the reaction was carried out, and p0 2 was calculated by subtracting the benzene vapour pressure (147.66 mm Hg) 3 a from this value (the solubility of 0 2 in benzene, at 35° C, is 9.279 mM/ate b). Valves 4 and 6 were now closed, and from this point onward valve 6 was used to introduce or remove oxygen from the part of the apparatus to its left, as required to keep the oil manometer level. The projection lamp was now turned on. This sometimes altered the temperature cycle slightly, and so at the next temperature minimum the oil manometer was checked and re-levelled if necessary. The initial reading was taken on the mercury burette (D), the shaker stopped momentarily, and the reaction started by dropping the bucket containing the benzoic acid into the solution. After the shaker was  92 re-started, the experiment proceeded in the same way as it would with other versions of the gas uptake apparatus, with uptake readings taken each time a temperature minimum was passed (approximately every 6-10 minutes). In experiments for which very little uptake occurred over this time period, the oil level difference was first artificially enhanced by drawing a very slight vacuum via valve 6. Subsequent re-levelling was much easier than via a direct attempt to adjust for a very small level difference. This technique could also be used if too much 0 2 was introduced via valve 6, so that the level in the right hand side of the oil manometer was higher than that of the left.  3.2.5 Data Treatment  Raw data from the stopped-flow experiments were analyzed on an Archimedes workstation using a non-linear least squares fitting program, supplied with the stoppedflow instrumentation, which implements the Levenberg-Marquardt algorithm.''' All other data analyses, including least-squares methods and numerical solution of differential equations, were carried out on a PC using customized implementations of the programs found in "Numerical Recipes, the Art of Scientific Computing (Quick Basic versions)".  6  The complete customized programs are listed in appendix 1.  3.3 Ru(OEP)(Et 2S) 2 -Catalyzed 0 2 -Oxidation of Et 2 S in Benzene Solution - General Observations  Gas chromatographic studies show that in oxygenated solutions containing Ru(OEP)(Et 2 S) 2 , benzoic acid, and an excess of free Et 2 S at room temperature or at 35° C, the thioether is catalytically oxidized to Et 2 SO. However, early attempts to study the  93 kinetics of this catalytic oxidation yielded erratic and generally irreproducible results. Eventually it was found that if the reaction mixture was irradiated by intense visible light at all times, Et 2SO was produced selectively and reproducibly. Figure 3.2 dramatically illustrates the effect light has on the reaction rate. For a benzene solution exposed to the air at 35° C, initially containing 0.34 mM Ru(OEP)(Et 2 S) 2 , 5.3 mM PhCOOH, and 0.74 M Et2S, sulfoxide production (followed by GC) stops completely whenever the irradiating lamp is turned off, and starts again at the same rate whenever the lamp is turned on again. This phenomenon is only observed in the case of catalytic oxidation, where a large excess of dialkylsulfide is present; the stoichiometric oxidation of Ru(OEP)(RR'S) 2 complexes, described in detail in the previous chapter, proceeds equally readily in the presence or absence of light. Assuming that the fate of the metalloporphyrin during the catalytic oxidation of Et2 S is similar to that observed in the absence of excess thioether (see sections 2.5 and 2.6), a likely candidate for the light-dependent step is the initial one-electron transfer from Ru(OEP)(Et 2S) 2 with 02 . In the presence of a large excess of sulfide, this step probably cannot proceed at any appreciable rate via the inner sphere mechanism proposed for the stoichiometric oxidation, because of competition for the axial sites of the complex by the sulfide. On the other hand, light could provide the extra energy required to proceed via an outer-sphere process, previously shown to be highly unfavourable (see section 2.5). To establish which of the Ru(Porp) bands are responsible for the observed photochemistry, two gas uptake experiments were carried out using different cut-off filters (figure 3.3a). Of interest, light above about 480 nm is found to be essential for  94  0.018 0.015 -  -1  0.012 off o  0 0.009C/2 C\1  0  -4-J  C4  0.006 off 0.003 -  /  -o on  o 0 0.000 0.0  on 3.0  ^  6.0  9.0  12.0^1 5 .0  Time (h)  Figure 3.2. Dependence of Et 2 SO production rate on reaction vessel illumination. [Ru(OEP)(Et 2 S) 2] = 0.34 mM; [PhCOOH] = 5.3 mM; [Et 2 S] = 0.74 M; the reaction was carried out in benzene solution at 35° C, in a flask exposed to the air. Reaction progress was followed by gas chromatography.  18.0  95  (a)  2 .0 -------------  Ru(OEP)(Et 2 S) 2 spectrum — — — Blue filter Yellow filter  X10  400^500600  320  1  (n m)  700^800  (b) 0.035 ^ 0.030 –  •  0.025 –  • —• Blue filter  0.020  • No filter  • —• Yellow filter  0.015 – O ciS 0.010– FL4 0.005 – 0.000 –0.005 ^ 0  500^1000^1500^2000^2500^3000 t(s) Figure 3.3. (a) Uv/visible spectra of Ru(OEP)(Et 2 S)2 , and of the yellow and blue filters used to test which wavelengths are necessary for Et 2 S oxidation to proceed. (b) Effects of the cutoff filters on the rate of Et 2 SO production, as measured by 0 2 -absorption at 35° C; in each case, a benzene solution initially containing 0.84 mM Ru(OEP)(Et 2 S) 2 , 24 mM PhCOOH, and 0.74 M Et 2 S was exposed to 0.81 atm of 0 2 (corrected for benzene vapour pressure).  96 reaction; when the blue filter absorbing all light above about 480 nm is used, no catalysis at all takes place. Cutting off irradiation of the Soret band (the most intense and energetic in the Ru(OEP) spectrum) with a yellow filter slows (by about 60%), but does not stop, reactivity (figure 3.3b). The slow-down is probably due to the fact that the yellow filter is not completely transparent above 480 nm. Moreover, because of the experimental setup, the light hits the filter at an estimated angle of 30°, so that considerable loss of light intensity due to reflectance is expected. Figure 3.4 is a qualitative molecular orbital diagram showing the types of transitions which give rise to the uv/vis spectrum of d 6 six-coordinate ruthenium porphyrins.''' Both the Soret and the a bands are assigned to  ir-ir*  transitions in the  porphyrin ring (a l „,a2 „ —> eg *), and are common to all porphyrins and metalloporphyrins; the /3 band is attributed to the addition of one mode of vibrational excitation to the transition which gives rise to the a band.' In addition to the 7r-7r" transitions, many metalloporphyrin spectra,' including those of ruthenium porphyrins,' have low intensity "extra" bands; in the case of ruthenium porphyrins, these bands are attributed to metal(d)-to-porphyrin(a") charge transfer bands (see figure 3.4). 8 Theoretical studies suggest that the dz2 and d x2,2 orbitals in Ru(Porp) complexes are too high in energy to play any role in low energy light absorption.' Based on the available electronic transitions (figure 3.4), figure 3.5 illustrates two possible mechanisms for the photochemical effect observed in the catalytic 02 -oxidation (the reason for the choice of subscripts for the rate constants will become apparent when the full catalytic cycle is considered, later in this section). In figure 3.5a, the first step (k5 ) represents a lr-ir* transition on the porphyrin ring. The excited electron is more easily  97  d7 2  e (n*)  d x 2_ y 2  A(CFSE)  (d,d)  S oretband  a2.(n)  ••  •  II^ II ii  d xz ,d yz (eg )  ^dxy (b e g )  V  a lu (n) Porphyrin  Metal  Figure 3.4. Scheme showing the types of electronic transitions which can occur in d 6 sixcoordinate ruthenium porphyrins (adapted from reference 8).  98 ff Ru (0EP)(Et S) 2 ,  (a) RuntuEr) • ---• * (Et ,S), 6'  [Ril i (OEP) + (Et ,S) 2 ]0 2 k 7^k-7  [Ru lii (OEP) Et , S)21 +02 PhCOOH k 8^ HO  0.5 0 2  k  0.5 H2O,  f.1( (OEP)(Et 2 S)21 -ThC00 -  0.5 H 2 0  0.5 Et,S 0.5 Et,S0  (b) Ru ll (O EP) + tEt 2 S),0, -  Ru ttt (OEP) . (Et 2 S),  III  (0EP)(Et 2S)2l + 02 k7  PhCOOH^0.5 0 2 '^---)o. HO  kd  [Ru in (OEP)(Et 2S)21 + PhC00 -  0.5 H O  kox  > 0.5 H2O  0.5 Et,S 0.5 Et,S0  Figure 3.5. Two possible mechanisms for the photochemical stage of the 02 -oxidation of Et2 S catalyzed by Ru(OEP)(Et 2 S) 2 : a) porphyrin 7 - 7 * transition, followed by transfer of the excited electron to 0 2 ; b) direct metal-to-porphyrin charge-transfer, followed by transfer of the excited electron to 02.  99 abstracted by 02 in the second step (k 6), leaving a 7-cation radical. As mentioned in section 2.4, the metal d orbitals lie at higher energy than the porphyrin  7  orbitals under  most conditions, and so the cation radical soon rearranges to the more stable Ru m species (10. Finally, protonation (k 8 ) and subsequent irreversible disproportionation (1( d) of the superoxide drive the reaction forward. The reaction k_ 6 , represents a pathway by which Ru(OEP)(Et 2 S) 2 + 02 can revert back to Ru(OEP)(Et 2 S) 2 ; the prime emphasizes the fact that this is not the reverse of k 6 . Figure 3.5b illustrates an alternative mechanism, in which the initial light absorption gives rise to a metal-to-porphyrin charge transfer (k 5 ). The resultant zwitterion then reacts with 02 to produce the Ru(OEP)(Et 2 S)2 +02 species directly (k6), which reacts with PhCOOH as before (k 7). Apart from the a,$ bands, the only other band resolved in the visible spectrum of Ru(OEP)(Et2 S) 2 (figure 3.3a) is at approximately 450 nm; this band cannot be responsible for the observed photochemistry, because it is completely cut off by the yellow filter, but not by the blue one (figure 3.3a). Nevertheless, there might be a charge-transfer band somewhere in the 480-540 nm region, and this band might be hidden by the more intense ot,f3 bands. Metal(d)-toporphyrin(7*) charge-transfer is symmetry forbidden, so the bands arising from this process would be weak and easily masked. If a 7-7 * transition is giving rise to the photochemical effect, then on the basis of figure 3.4, it is difficult to rationalize why light absorption in the Soret region does not lead to reaction; nevertheless, this would not be the first instance in which the Soret and the c«, f3 bands behave differently, even when the simple molecular orbital picture predicts that they should behave in the same way. For example, it is well established that for many metalloporphyrins, 7 including Ru n porphyrins, 8 the 0/03 bands are hypsochromically  100 shifted (i.e. to shorter wavelength) relative to those of the free-base porphyrins. Based on the simple molecular orbital rationale portrayed in figure 3.4, this phenomenon has been attributed to back-donation of electron density from the metal e g d-orbitals to the porphyrin eg le-orbitals, which would raise the energy of the latter. This simple model is quite useful, and has been used to rationalize, for example, the fact that the a,f3 bands shift progressively closer to their free-base positions as axial ligands with stronger  7r-  accepting properties, such as CO or NO, are used. The explanation put forth is that as the axial ligand accepts more electron density from the metal, less density will be transferred to the porphyrin Ir a orbitals, and their energy will drop: 7 ' 8 Despite its usefulness, the simple model has one serious flaw: a review of the electronic spectra of several Ru n (OEP) complexes' shows that their Soret bands are not hypsochromically shifted from the free-base position, and there is no obvious correlation between Soret peak position and the ir-acidity of the axial ligands. The simple model predicts that metalto-porphyrin 7- 7 * backbonding should cause the Soret to shift hypsochromically by the same amount (in energy units) as the cr,(3 bands. The fact that this is not the observed behaviour suggests that there is some kind of interaction between the metal and the porphyrin, which is unique to the excited species generated by irradiating the 0/03 bands. This same unique interaction could be a requirement for the photochemical process. The question of which band is responsible for the observed photochemistry is discussed again in section 3.5.2.2, at which point kinetic evidence is presented which tends to rule out the 7-7 *  transition mediated mechanism shown in figure 3.5a. At this point it is worth looking at the predicted thermodynamics of some of the  reactions shown in figures 3.5. Recall that in section 2.5 the cell potential for a one-  101 electron transfer from Ru(OEP)(Et 2 S) 2 to 0 2 was estimated at about -1 V, which translates to a free energy barrier of about 95 kJ/mol. Assuming for the moment that Ru(OEP)(Et 2 S) 2 absorbs only at X = 525 nm, this will supply the porphyrin complex with 228 kJ/mole. Combining these two relationships allows us to write  Ru n (OEP) * (Et2 S) 2 + 02 Ru m (OEP)(Et 2S) 2 +02 AG° = -133 kJ/mol^3.1  Hence light of wavelength around 525 nm provides more than enough energy to allow the overall process of interest to proceed. Moreover, the standard reduction potential for the process Ru ll (OEP)'(Et 2S) 2/Ru ll (OEP)(Et 2 S) 2 is expected to have a value around 0.64 V, which is the standard reduction potential for the Ru ll (OEP)+•(C0)/Ru n(OEP)(CO) system (recall section 2.4).' ° At the very most, the ring reduction potential might be as high as that of the free base (0EPH 2 + 10EPH2), which was previously recorded as 0.83 V.' 0 The latter value (using a value of -0.8 V for the 0 2 /02 - couple, see section 2.5) gives a cell potential of about -1.6 V for the one-electron transfer from the porphyrin ring to 0 2 , which translates to an energy barrier of 154 kJ/mol. Light of 525 nm provides enough energy to overcome even this high barrier:  Ru ll (OEP)*(Et2 S) 2 + 02  Ru ll (OEP)•(Et2 S) 2 02 AG° = -74 kJ/mol^3.2  Figure 3.6 summarizes the suggested free energy relationships, which relate directly to the mechanism shown in figure 3.5a. The same general relationships will hold if the  Ru ll (OEP)*(Et 2 S) 2 02  AG° = -74 kJ/mol  AG°= -133 kJ/mol  [R uII( OE P)- (Et2S) 21 0 2  AEabs  = 228 kJ/mol  AG°= -59 kJ/mol AG° = 154 kJ/mo  [Rum(OEP )(Et2S ) 21 + 0 2 -  AG° = 95 kJ/mol  Ru n (OE P )(E t2 S) 2 02  Figure 3.6. Relationship between the light energy absorbed by Ru(OEP)(Et2S) 2 at 525 nm, and the relative free energy changes associated with various transformations; see text for details.  103 photochemical reaction is proceeding via an initial metal-to-ligand charge transfer (figure 3.5b), assuming that the charge transfer absorption band is hidden under the «,0 bands, somewhere in the region of 525 nm. Figure 3.7 shows a gas chromatographic trace of a benzene solution initially containing 0.42 mM Ru(OEP)(Et 2S) 2 , 6.5 mM benzoic acid, and 0.74 M Et 2 S, which was exposed to 0.81 atm of oxygen (corrected for benzene vapour pressure) at 35° C for 2.5 h under irradiation. The major oxidation product is Et 2 SO, with minor amounts of Et2SO 2 , Et2 S 2 , and one other unidentified side product. Initially, the way in which Et 2 SO was selectively produced came as a surprise. Earlier studies carried out in our laboratories, which looked at 0 2 -oxidation of decMS catalyzed by Ru(OEP)(decMS) 2 , revealed sulfur product distributions which were akin to those of dialkylsulfide freeradical autoxidation ll (for example, didecyldisulfide was a major product); sulfoxide was not obtained as a single product.' In the present case, an autoxidation type of reaction would be expected to initially produce EtSH in concentrations comparable to those of Et2 SO; the thiol would then further react to produce Et 2 S 2 (see section 1.3). 11,12 Therefore, the lack of a significant Et2 S 2 signal in figure 3.7 also suggests that thiol was never a major product of reaction. In a series of experiments in which total oxygen uptake for a reaction was compared to Et 2 SO produced (as determined by gas chromatography) over 1.8-2.5 h periods, the stoichiometry of 2 moles of Et 2 SO produced for every mole of 02 consumed, which is implicitly suggested by the type of mechanism being proposed, was confirmed. As an example, when a solution containing 0.420 mM Ru(OEP)(Et 2 S) 2 , 9.86 mM PhCOOH, and 0.742 M Et 2 S was irradiated under 0.812 atm of oxygen (corrected for benzene vapour pressure) at 34.85° C for 1.9 h,  104  111  H  Ti t (min)  Figure 3.7. Gas chromatographic trace of a benzene solution initially containing 0.42 mM Ru(OEP)(Et 2 S) 2 , 6.5 mM benzoic acid, and 0.74 M Et 2S, exposed to 0.81 atm of 02 (corrected for benzene vapour pressure) at 35° C for 2.5 h. 4.89 min: Et 2 S 2 ; 6.05 min: Et 2 SO; 7.11 min: Et 2 S02 ; 7.90 min: n-undecane; 9.30 min: benzoic acid. The signal at 13.16 min is that of an unidentified product; the rest of the unidentified signals are present at the start of the reaction.  105 32.9 ± 0.4 mM Et 2 SO were produced, and 16.8 ± 0.2 mM of 0 2 were consumed. In light of the results discussed in the previous paragraph, the decMS used in the early experiments was carefully re-examined by GC, and found to contain some decanethiol and other impurities; this almost certainly explains the presence of didecyldisulfide as a reaction product in those experiments. Figure 3.8 provides a scheme for the overall catalytic cycle, which takes into account the conclusions of chapter 2, and the observed light dependence when excess sulfide is present. The reaction path flows counterclockwise, starting at Ru(OEP)(Et 2 S) 2 , which is just left of the top of the circle. The first four steps (k 5 to k8 ) correspond to the photochemical mechanism portrayed in figure 3.5a, and result in the production of one mole of Et 2 SO, one of H 2 O, and two moles of Ru(OEP)(Et 2S) 2 +13hC00 - for every two moles of Ru(OEP)(Et 2S) 2 oxidized. At this stage, no evidence has been given to favour either mechanism 3.5a or 3.5b; figure 3.8 incorporates mechanism 3.5a because, as will be seen in sections 3.5 and 4.3.2, this mechanism can be tested directly. The next two steps in the catalytic cycle (k 9 and k 10) represent one of the possible disproportionation processes suggested in the previous chapter (section 2.5). Whichever process (or combination of processes) is actually going on, disproportionation will give rise to one mole of a R  e  species for every two moles of Ru(OEP)(Et 2 S) 2 originally  oxidized (with regeneration of one mole of Ru(OEP)(Et 2 S) 2). Note that all of the steps beyond superoxide protonation are portrayed as irreversible; it is assumed that, in the presence of high concentrations of Et 2 S, all of the Ru ifi and Re species will be consumed as rapidly as they are produced.  106 Et, SO II Ru H (OEP)(Et SO),^ii^Ru II (0EP)(Et,SOXEt2S 0) , ""Ig k-1^ 4,„.■ Ru il (OEP)(Et ,S0) Et 2 S - -^1114 k, I Ru il (OEP)(Et ,S)(Et,S0) -4re^Internal Rearrangement k 3 IL. 3 Et2S Et, SO Ru ll (OEP)(Et ,S ) k_ 6 ,^2Ru11(OEP)(El 2S)2  by^k_s  r  k1 4  02 coordination  /  RUII (OENEt-)S)(E00)  Ru(OEP)(Et ,S)(0 2 )  1°1\(.13  2Ru II (OEPAEt 2 S),  ^ Et, S  0=Ruiv (OEP)(Et ,S) PhCOOH 2[Rul 1 (OEP)t(Et ,S),]0 2 k  [Ru iv (OEP)(Et 2 S )(PhC00)] +Off PhCOOH PhCOOH •••  2[R u lli(OEP)(E t 2S)21 +02 -  X  HO, <  PhCOOH  H,0 [Ru lv(OEP)(Et 2S)(PhC00)113hC00  -  k 10 41/4 Ru  2[Ru m (OEP)(Et 2S)2 rPhC00 . 2H0, ^ ky Ica ^ 0,  III  (0EP)(Et,S)(PhC00)  Et,S  H, 0,  1,-Ox  r•-•--- Et ,S ,S0  H,0  Figure 3.8. Scheme proposed for the 0 2 -oxidation of Et2 S to Et 2 SO, catalyzed by Ru(OEP)(Et2S) 2 and PhCOOH (dotted pathways imply that these processes can be neglected, or do not occur, under catalytic conditions).  107 Reaction of the Ru"' species with water and free Et2 S produces Ru(OEP)(Et 2 S)(Et 2S0) (k 11 to 1( 13 ), which can either isomerize to give Ru(OEP)(Et 2 S)(a250), or react with Et 2S to regenerate Ru(OEP)(Et 2 S) 2 . In the latter case, another mole of free sulfoxide is liberated, to give a total of two moles of free Et2 SO produced for every turn of the catalytic cycle. In either case, the two moles of PhCOOH used to "trap" the high valent Ru species are regenerated at the end of the cycle, and the net result of the process is to produce 2 moles of Et 2 SO for every mole of 02 consumed. The production of two of the possible isomers of Ru(OEP)(Et2 SO) 2 (at the top of the scheme), and direct 02 coordination to Ru" (vertical pathway), are both portrayed using dashed arrows. This emphasizes that although both processes are known to occur when the concentration of free Et 2 S is low, they are probably not important under catalytic conditions. The equilibria between Ru(OEP)(Et 2 S) 2 , Ru(OEP)(Et 2S)(Et 250) and Ru(OEP)(Et 2 SO) 2 , and the possibility of internal rearrangement of Ru(OEP)(Et2 S)(Et 2 SQ) to the S-bound isomer, also portrayed with a dashed arrow in the figure, will be further discussed in the next two sections. In the scheme portrayed in figure 3.8, any possible reaction of Ru(OEP)(Et2 S)(Et250) (or indeed Ru(OEP)(Et 2 SO) 2 ) with dioxygen is neglected; these complexes are outside of the catalytic cycle. This means that, according to the model, as Et2 SO is produced, it should have an inhibitory effect on the reaction rate, depending on the equilibria governing formation of the sulfoxide-containing complexes. Figure 3.9 shows a plot of [Et2 SO] vs. time, obtained from an oxygen uptake experiment, and the reaction rate is indeed found to decrease with time (this decrease is not accounted for by the drop in [Et 2 S] with time, which is less than 5% over the whole measured interval).  108  t (s)  Figure 3.9. A typical plot showing the accumulation of Et 2 S0 with time, determined by monitoring the 0 2 -uptake (see section 3.5 for full details). For this experiment at 35° C, the initial concentrations of the reagents are: [Ru(OEP)(Et 2 S) 2 ] = 0.202 mM; [PhC001-1] = 24.4 mM; [Et2 S] = 0.742 M; p0 2 = 0.813 atm (corrected for benzene vapour pressure).  109 Section 3.5 describes how the data in figure 3.9, and about 50 other sets of similar data, can be fitted to a rate law derived from the mechanism shown in figure 3.8. As will be seen, the derived rate law fits the experimental data remarkably well; however, the same reasoning used earlier to show that electron transfer from Ru(OEP)(Et 2 S) 2 to 0 2 is energetically quite feasible in solutions irradiated by visible light, shows that the less favourable electron transfer from Ru(OEP)(Et 2 S)(Et 250) to 0 2 is also possible under these conditions. Figure 3.10 summarizes the relevant energy relationships; a full discussion on the possible role of electron transfer from Ru(OEP)(Et2 S)(Et250) directly to oxygen is deferred to section 3.5.2.2. A second omission in figure 3.8 is any mention of catalyst degradation (this is a common weakness of nearly all postulated catalytic cycles). In chapter 2 it was pointed out that the stoichiometric reaction of 0 2 with Ru(OEP)(RR'S) 2 complexes in acidic benzene solutions was not as clean as in methylene chloride, and that small amounts of unidentified Ru(OEP) side products were produced along with Ru(OEP)(RR'S)(RR'SO) and Ru(OEP)(RR'S0) 2 . One might expect such side reactions to occur also to some extent in the catalytic system and, indeed, monitoring the reaction mixtures for extended periods (20 h) by uv/vis, clearly showed that catalyst degradation occurred, but at a slow rate compared to the catalytic rate. Of interest, this catalyst degradation is not acid dependent, and proceeds at about the same rate with or without added acid, provided that the reaction solution is illuminated (see below). The uv/vis spectrum of a reaction mixture, initially containing 0.202 mM Ru(OEP)(Et 2 S) 2 and 0.742 M Et 2 S (but no benzoic acid), after a 24 h exposure to 02 and light at 34.85° C, is shown in figure 3.11; this spectrum is similar to those seen in earlier studies of corresponding  Ru(OEP)*(Et 2 S)(Et 2 S0) 02  0111•11•■  AG°_ -74kJ/mol  AG°= -94kJ/mol  [Rull(OEP)'(Et2S)(Et2S0)102 AG°= [Ru11l(OEP)(Et2S)(Et2S0)]+02-^ -2OkJ/mol  AE ab , 228kJ/mol AG°= 154kJ/mol  AG°= 134kJ/mol  Rul l(OEP)(Et 2 S)(Et 2 S0 ) 0,  Figure 3.10. Relationship between the light energy absorbed by Ru(OEP)(Et 2 S)(Et250) at 525 nm, and the free energy changes associated with various transformations. AG° for the oxidation at the metal of RAOEP)(Et 2 S)(Et250) was estimated from the CV data for the analogous Ru(OEP)(decMS)(decMS0) system (see section 2.5 and figure 2.13); for the one-electron ring oxidation, AG° is assumed to be the same as in the Ru(OEP)(Et 2S) 2 system (see figure 3.6).  8  0.55 -/  .......... .........  o,^  1  420^ 500^  k( nrr )^600^  700  Figure 3.11 Uv/vis spectra of a benzene solution initially containing 0.202 mM Ru(OEP)(Et 2 S) 2 , 0.742 M Et2 S, and no benzoic acid, at various times after exposure to a light source, and 0.813 atm of 0 2 (corrected for benzene vapour pressure). The same results were obtained in the presence of up to 48 mM of PhCOOH.  112 Ru(OEP)(decMS) 2/decMS systems.' The spectrum shows broad bands extending to 700 nm, and no major band at 525 nm, which suggests that very little or none of Ru(OEP)(Et2 S) 2 , Ru(OEP)(Et2S)(Et 25.0) or Ru(OEP)(Et 2 SO) 2 remain in solution (the visible spectra of the three Ru ll species are illustrated later in figure 3.21, p.144). The relatively sharp band at 549 nm is notable, since this is the position (551 ± 4 nm) at which all known Ru(OEP)(CO)L (L = a neutral ligand) have their a bands;' recall from section 2.6 that there is evidence of a Ru(OEP)(CO)L complex being a minor product in the stoichiometric oxidation of Ru(OEP)(RR'S) 2 in benzene and toluene solutions. Since none of Ru(OEP)(Et2 S) 2 , Ru(OEP)(Et2 S)(Et250) or Ru(OEP)(Et 2SO) 2 absorb significantly above 600 nm, the absorbance in this region by a reaction mixture at any given time can be used as a crude estimate of catalyst degradation, with the absorbance after 24 h representing maximum degradation. Such an analysis was carried out on the spectrum in figure 3.11, and on several catalytic reaction mixtures containing benzoic acid, and catalyst degradation was estimated to be 7-12% over a 2.5 h period. Note that the error incurred in neglecting catalyst degradation (i.e. ignoring the decrease in reaction that catalyst degradation will produce) will tend to compensate for any error incurred by assuming non-reactivity of Ru(OEP)(Et 2S)(Et250) toward 0 2 ; this will be discussed further in section 3.5.2.2. As mentioned, all of the assumptions inherent in figure 3.8 will be discussed again in section 3.5, after a rate law for the reaction has been derived. The next section deals with a quantitative study of the equilibria between Ru(OEP)(Et2S) 2 , Ru(OEP)(Et 2 S)(Et250) and Ru(OEP)(Et2 SO)2 , which were studied independently from the rest of the catalytic cycle using stopped-flow experiments.  113 3.4 Stopped-flow Analysis of Et 2 SO Substitution by Et 2S in Ru(OEP)(Et 2SO) 2 in Benzene Solution 3.4.1 Data Treatment and Results  The equilibria between Ru(OEP)(Et 2 S)2 , Ru(OEP)(Et 2 S)(Et 250), and Ru(OEP)(Et 2 SO) 2 were studied in isolation from the rest of the cycle outlined in figure 3.8, using stopped-flow techniques. The details of deriving the rate laws will be discussed fully in chapter 4,t but the likely probability that in solution Ru(OEP)(Et2SO) 2 exists as an equilibrium mixture of Ru(OEP)(Et 250) 2 and Ru(OEP)(Et 250)(Et2S0) (see section 2.3) is accounted for in the derivation. In practice, the system was studied by starting with a solution of Ru(OEP)(Et2 SO) 2 and excess Et 2SO, and adding an excess of Et 2 S to it, which is the reverse of the processes which take place during catalysis; for clarity, figure 3.12 shows the substitution steps in isolation. It turns out that substitution of the first sulfoxide in Ru(OEP)(Et 2 SO) 2 takes place on the 100 ms timescale, which is about 1000 times faster than that of the second. Thus the first equilibrium between Ru(OEP)(Et2 SO) 2 and Ru(OEP)(Et 2 S)(Et 250) is established before the second reaction has begun, which simplifies the rate laws considerably, since the two steps can be studied independently. In addition to occurring on very different timescales, the two substitution equilibria occur in sufficiently different Et 2 S/Et2 SO concentration regimes to allow some useful observations to be made by time-independent uv/vis spectroscopy. Thus figure 3.13a shows successive uv/vis spectra obtained for a solution, initially containing 3.4x10  -6  M Ru(OEP)(Et 2 SO) 2 and 0.19 M Et 2 SO, as it was titrated with neat Et 2 S. The band which It is possible to understand sections 3.4 and 3.5 in a qualitative way without going through the theory given in chapter 4; however, many readers will find it helpful to read chapter 4 concurrently with the next two sections of this chapter.  ^  114  First Substitution Equilibrium EN SO ^ Ru (OEP)(Et 250)2  ENS k-^ 1^ 2 Et? SO^Ru (0EP)(Et , SO)^Ru (0EP)(Et /S)(Et,S0) k, ENS Ru (0EP)(Et ,SOXEt2S0) k S() 1'  2  ,  Second Substitution Equilibrium ^EN  SO^ ENS jk^ Ru (0EP)(Et 2S) ^ k4Ru (OEP)(Et,S)2 Ru(OEP)(Et2S)(Et20)^ k^ k-4 EN SO^ ENS  2^  Figure 3.12. Scheme showing the proposed mechanisms for the sequential substitution of two Et2 SO ligands by Et 2S in Ru(OEP)(Et 2 S0) 2 . In solution, the bis-sulfoxide species is believed to exist as a mixture of the S- and 0-bound linkage isomers (see section 2.3).  ^  115  (a)  1.5  00  [Et2S](M) 0.0 0.018 0.037 0.056 0.096 0.14  0  A404  A 4 00 . 5  0.490 0.676 0.781 0.842 0.917 0.952  320  1.294 1.094 0.965 0.871 0.775 0.689  420  A,(nm)  (b) 0.5 [Et2S0](M)^A 409  A404  404.0  0.0^0.335^0.204 0.0095^0.305^0.273 0.019^0.282^0.323 0.028^0.265^0.359 0.038^0.251^0.388 0.047^0.240^0.409 0.057^0.231^0.425  0  ^  420 A,(nm) 350^ Figure 3.13. Uv/vis spectral changes observed as: (a) a benzene solution initially containing 3.4x10 M Ru(OEP)(Et2 SO) 2 and 0.19 M free Et2 SO is titrated with neat Et2 S; (b) a benzene solution initially containing 1.7x10' M Ru(OEP)(Et 2 S) 2 and 0.74 M free Et2 S is titrated with neat Et 2 SO. T = 35° C for both experiments.  116 grows in at 404.0 nm is attributed to Ru(OEP)(Et2 S)(Et 250). Similarly, figure 3.13b shows successive uv/vis spectra obtained for a solution, initially containing 1.7x10 5 M Ru(OEP)(Et 2 S) 2 and 0.74 M Et 2 S, as it was titrated with neat Et 2SO; again, the band appearing at 404 nm is attributed to Ru(OEP)(Et 2 S)(Et 2S0). The spectra in figures 3.13a and 3.13b both show at least three isosbestic points; isosbestics can result from a) a simple equilibrium between two absorbing species, or b) formation of a third absorbing species from a fixed ratio of two other species. The latter case applies to the first equilibrium in figure 3.12, where Ru(OEP)(Et 2S)(Et250) is formed from a fixed ratio of Ru(OEP)(Et 2S0) 2 and Ru(OEP)(Et2S0)(Et 2 SD), during the titration with Et2 S (in both substitution equilibria, the 5-coordinate intermediates are assumed to be present in negligible amounts). The equilibrium between Ru(OEP)(Et 2S0) 2 and Ru(OEP)(Et 250)(Et2 S0) is independent of either Et 2 SO or Et2 S concentrations:  K' = [1']/[1]^  3.3  where 1 =--. Ru(OEP)(Et2S0) 2 ; 1' -=-- Ru(OEP)(Et250)(Et2S0); and  K' --. Ic i lc_p/lc r lc_ i^3.4  The equilibrium ratio of Ru(OEP)(Et 250)2 to Ru(OEP)(Et 250)(Et2 S0) remains constant regardless of the free [Et 2 SO] (or [Et2 S]) ligand concentrations, and thus the BeerLambert expression for a solution containing Ru(OEP)(Et 250) 2 , Ru(OEP)(Et2a0)(Et2 S0) and Ru(OEP)(Et 2 S)(Et25.0), can be written as  117 A = (e l + e r IC)1[1] + € 21[2]^  3.5  where  2 =---- Ru(OEP)(Et 2 S)(Et zSO)  and A is the experimentally observed absorbance, e l , e l , and €2 are the extinction coefficients for Ru(OEP)(Et2S0) 2 , Ru(OEP)(Et2,80)(Et/ S0) and Ru(OEP)(Et2S)(Et2,50), respectively, and 1 is the absorbance path length. An isosbestic point will occur wherever (e l + € 1 1C) is equal to E2. ,  When the approach to the first equilibrium is followed by stopped-flow analysis at the isosbestic wavelength X = 402.8 nm, no change is detected in the absorbance at any time, showing that the equilibrium between Ru(OEP)(Et 250) 2 and Ru(OEP)(Et250)(Et 2S0) is not even transiently disturbed. The importance of this observation will become apparent below, and in section 4.2. In the stopped-flow experiments discussed in the remainder of this section, the two substitution equilibria were monitored at different wavelengths. The first was followed at X = 400.5 nm, which is the absorption maximum for Ru(OEP)(Et 2 SO) 2 solutions at 35° C (see figure 3.13a). During the second substitution, the equilibrium between the monoand bis-sulfoxide species must be considered and, as will be seen in section 4.2, it is simpler to follow the second substitution reaction at an isosbestic wavelength for a mixture of Ru(OEP)(Et 2 SO) 2 and Ru(OEP)(Et 2 S)(Et 2S0) species. The isosbestic wavelength chosen was X = 402.8 nm (see figure 3.13a).  118 Now, with the assumption that the changes in free [Et 2 S] and [Et 2 SO] are negligible over the whole reaction, and given that the equilibrium ratio between Ru(OEP)(Et 250) 2 and Ru(OEP)(Et 250)(Et2 S0) is not disturbed at any time, the absorbance changes as a function of time for X = 400.5nm over the first 100 ms, and for X = 402.8nm over 100 s, will both be described by a simple exponential decay equation (see section 4.2):  A = a + 13. e-61)^3.6  where  A =-,--- The absorbance at time t  a = A 0 - (3  ^  ^  3.7  3.8  (A 0 The absorbance at t = 0)  The parameter O'represents the total absorbance change observed for a given reaction, while y is the observed rate constant. All three parameters are themselves functions of the concentrations of the various reagents in solution; of course, the form of these functions is different for the first and second substitution reactions. Before discussing the functions, one other term should be defined, namely  119 v.^(dA/dt) 1 = 0 = - 7/3^3.9  where v o is the rate of change of the absorbance at the start of the reaction. For both the substitution steps, 13 and v o are the two most informative parameters. For the first substitution reaction, /3 and vo are given by (see section 4.2)  11 = -fRuL4cilEt2sl/(K, ApplEt2soi + [Et2S])^  vol = k1 A pp[Ru] 4ciUt2SVOCI[Et2S 0 ] + [Et2S])  ^  3.10  3.11  where  [Ru]. -= [1] + [1'] + [2]^  3.12  AE I ' -= (62 - (€1 + e 1 ,K')/(1 + K'))1 at X = 400.5 nm^3.13  K IApp ==..- K I /(1 + K')  ^  Ic iApp .. k,/(1 + K') + k 1 , /(1 + (IC) - )  ^  3.14  3.15  Kmi —= (k, + k_ v )/k2^3.16  K 1 -= k 1 k2/k_ 1 1( 2^3.17  120  K' was previously defined (equation 3.4), as were the three extinction coefficients c i ,  Er  and €2 , and the path length 1 of the absorbing species. Equations 3.10 and 3.11 (for variation of fl, and v 0 , with [Et2 S] at a fixed [Et 2 SO]) are the typical rectangular hyperbolas with zero intercept so commonly seen in kinetic analyses," and can be rearranged into linear form:  [Et2 S]/f, = c 1 + c 2 [Et2 S]^  3.18  [Et2 S]/v oi = c 3 + c4 [Et2 S]^  3.19  where  CI =-. [Et2SO]c2/K,A PP  c 2 =---  -  1/[RU]AE,  ^ '  C3 -=' [Et2S 0]C4 1(ml  C4 --"^ -. -C2/1C1App  ^  ^  ^  3.20  3.21  3.22  3.23  Two sets of experiments were carried out, one with [Et 2 SO] = 1.18+0.03 mM, the other with [Et2SO] = 17.7±0.2 mM. In each case, [Et 2 S] was varied from 0.119 mM to 0.464 M over several runs, and a,„8 1 ,7 1 were evaluated using the Levenberg-  121 Marquardt algorithm."' 6 These values were then used to generate the variables [Et 2 S]/fl 1 and [Et 2 S]/v ol , which were plotted against [Et 2 S]. Equations 3.18 and 3.19 could then be fitted to these plots using linear regression, ultimately yielding the desired equilibrium and rate constants. Figure 3.14 gives one typical fitted absorbance vs. time plot for X = 400.5 nm; the rest are all collected in appendix 2 (section A2.1), along with the tabulated values of a 1 ,(3 1 ,7 1 . Figures 3.15 and 3.16 show the fitted plots of equations 3.18 and 3.19 for the two sets of experiments. Finally, table 3.1 summarizes the obtained values of all the relevant parameters; their significance is discussed in section 3.4.3. For the second substitution reaction, the concentration functions of the parameters are somewhat more complicated in that linear functions of [Et 2 S] at constant [Et 2SO] and  Table 3.1 Fundamental Parameters Derived from Equations 3.18 and 3.19 [Et2 S0Jx103  AE4„,0.5ix10-5  (M)  (M-tcm-')  1.18±0.03  -(1.92±0.04)  2.8±0.1  17.7+0.2  -(2.03±0.05)  Average parameter values  -(1.97±0.05)  K.  k, (s')  135±2  0.85±0.03  41±2  2.58±0.06  131±3  0.74 ±0.02  37+2  2.7±0.1  133±2  0.79±0.06  39+2  KIA,„,  k,App  (s')  122  0.50 ^ 0.40 -  A = a l +^(710  0.30-  a l = —0.153  0.20 -  )3 1 =0.633 = 123.2 s 1  0.10 0.00—0.10 -  —0.20 I^ I , 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 Time (s)  0.003 ,1\10, op%Dik '1.  0.000 QP,6°°04,, P  oi^d  do cb.  —0.003  71 ,0, .,  Figure 3.14. A typical, fitted stopped-flow trace of the change in absorbance over 100 ms, at X = 400.5 nm, when Et 2 S is substituted for Et2 S0 in Ru(OEP)(Et2S0) 2 . [Et 2 S] = 9.27±0.09 mM; [Et2S0] = 1.18+0.03 mM; [Ru] o = (3.44+0.07)x10' M. The first four points likely are in the dead time of the instrument, and are neglected in the fit.  123 [Et 2 S]/19 1 = c i^c 2 [Et 2 S] 0.020  (a) c 1 = (6.36 ± 0.16)x10 -4 M c2 = 1.516 ± 0.016  X 0.005 -  2 = 12.5  Q = 0.41  0.000 0.000  0.002  0.004  0.006  0.008  0.010  0.012  0.010 0.000 -0.010 0.00 0.18  0.05  0.15  0.10  0.20  0.25  (b) c l = (9.85 ± 0.15)x10 -3 M c 2 = 1.436 ± 0.018  X2 = 14.4 Q = 0.16  0.00  "zz  0. 00 0.004 0.000  0  0.02  ^  0.04  ^  0.06  ^  0.08  0.10  ^  0.12  (N,^  -0.004 0.00  0.10  ^  [Et2s] (M)  ^  0.20  ^  0.30  Figure 3.15. Portions of the plots of [Et 2 S]/O I vs [Et2 S] for data collected at X = 400.5 nm over 100-ms time-frames. a) [Et 2 SO] = 1.18±0.03 mM; b) [Et 2 SO] = 17.7±0.2 mM. In each case [Ru]. = (3.44+0.07)x10 M. The residual plots show the full range of data collected; the main plots show only the region in which 0, increases (Q is the goodness of fit given the obtained x 2 value").  ^  124 [Et2S]/° o 1 = c 3 + c 4 [Et 2 S]  1.60E 4 (a)  c3 = (1.563 ± 0.032)x10 -5 M s  1.20E-4 -  c 4 = (1.122 ± 0.015)x10 -2 s 8.00E-5  -  x2 = 1.98 Q = 1.0  4.00E-5 -  0.00 0.000  ^1.5E  0.004  0.008  0.012  5^^  ai^0.0  ^  -1.5E-5 -^ 0.00  0.05  0.10  0.15  0.20  0.25  1.80E 3 (b) c 3 = (2.632 ± 0.042)x10 -4 M s 1.20E-3  c 4 = (1.096 ± 0.019)x10 -2 s  :3 ci) c.) M 6.00E-4 -  X  2 = 21.6  Q = 0.017  0.00 0.00  ^5.0E  5  0.02  0.04  0.06  0.08  0.10  0.12  ^  0.0 ^ -5.0E 5 ^ 0.00  0.10  0.20  [Et2S] Figure 3.16. Portions of the plots of [Et 2 S]ivol vs [Et 2S] for data collected at X = 400.5 nm over 100-ms time-frames. a) [Et 2 SO] = 1.18+0.03 mM; b) [Et 2 SO] = 17.7+0.2 mM. In each case, [Ru]. = (3.44±0.07)x10' M. The residual plots show the full range of data collected; the main plots show only the region in which v c, 1 increases.  0.30  125 [Ru] o cannot be obtained. Nevertheless, analysis analogous to that which yielded equations 3.18 and 3.19 (see section 4.2) gives the following quadratic functions:  [Et2 S] 2/(3 2 = d 1 [Et2 S] 2 + d 2 [Et2 S] + d 3^3.24  [Et2S]/V 02 = d4[Et2S] 2 + d5[Et2S] + d6^  3.25  where  d 1 -... aRuLAE27 1^3.26  d 2 .-=.- [Et2 SO]d 1 /K 2^3.27  d 3 =--= d2[Et2SO]/KIApp ^  3.28  d4 E--- d i /k3^3.29  d5 -=-- (Km2 + (KiApp) 4 )[Et2SOld4 ^  3.30  d 6 ---= 1C2[Et2SO] 2d4/Kmpp^  3.31  126 AE2' ==- (E3 - E2) 1 = (63 - (6 1 + e 1 -K')/(1 + K'))1  at the isosbestic wavelength X = 402.8 nm  [Ru].  K.2  K2  3.32  [1] + [1'] + [2] + [3]  3.33  k_3 /k4  3.34  3.35  k3k4/ 1c--3k4  Also, 3 represents Ru(OEP)(Et 2S) 2 , and E3 is its extinction coefficient. Functions 3.24 and 3.25 are linear in their dependence on the parameters d 1 -d 6 , and so it is still possible to do least-squares minimization without resorting to iterative methods. 5 a' 6 One set of experiments was carried out, with [Et 2 SO] = 1.18 + 0.03 mM, and a varying [Et 2 S]. Figure 3.17 shows a typical absorbance vs. time plot for X = 402.8 nm; again, the remaining plots are collected in appendix 2, along with the tabulated values of  a2 ,[32 ,7 2 .  Figure 3.18 shows the plots of equations 3.24 and 3.25, fitted to the data using the technique of singular value decomposition followed by back-substitution,* 5" to obtain the least-squares fit parameters. Table 3.2 summarizes the values of the equilibrium constant and the rate constants obtained from equations 3.24 and 3.25; their significance is discussed in section 3.4.3.  127  0.15 0 U  -  a 2 = —0.127  (Ts 0  (/)  A z- a 2 + , 2 e —(72t)  0.050 -  fl 2 = 0.289  .y 2 = 0.0706 s -1  0.) 725 —0.050 c4  —0.150 ^ ^ 0^20^40^60 80 Time (s)  100  0.003 72  0.000 0  4  —0.003  Figure 3.17. A typical, fitted stopped-flow trace of the change in absorbance over 100 s, at X = 402.8 nm, when Et 2S is substituted for Et 2 SO in Ru(OEP)(Et 2 S)(Et 250). [Et 2 S] = 18.6+0.2 mM; [Et 2SO] = 1.18+0.03 mM; [Rid, = (3.44+0.07)x10' M.  ^  128 0.030 (a)^, 2 a^A^ A /t, 2 =^[1.11.201^11.2[J,1.21-1]^ 2 +^d 3  0.025 -  d =  w^0' 020  d 2 = (3.264 ± 0.086)x10 -2 M  CCL.  N  1.662 ± 0.023  -  \ 0.015 d 3 = (1.81 ± 0.24)x10 -5 M 2 -" 0.010 41  X2 = 4.07 Q = 0.91  0.005 -  0.04  0.06  0.08  0.10  0.12  0.04  0.06  0.08  0.10  0.12  2.0E 4 0.0 -2.0E 4 ^ 0.00  0.02  0.60 (b) 0.50 -  N^  0  0.40  -  0.30 -  (nN 0.20 -  2  [Et 2 S] /v 02 = d 4 [Et 2 S] 2 + d 5 [Et 2 S] + d 6  d = 44 48 + 0 42 s d 5= (6.64 ± 0 68)x10 -2 M s d = (4.3 ± 1 4)x10 -5 M 2 s  X  2  = 14.8  Q = 0.097 0.10 0.00 0.00^0.02  0.04  0.06  0.08  0.10  0.12  1 ^ 1 ^1 0.02^0.04^0.06  0.08  0.10^0.12  1.7^3.0E 3 U  0  -3.0E 3 ^ 0.00  [Et2S1  Figure 3.18. Portions of the plots of: a) [Et 2 S] 2//32 vs [Et2 S], and b) [Et 2 S] 2 /v02 vs [Et 2 S], for data collected at X = 402.8 nm over 100-s time-frames. [Et2 SO] = 1.18+0.03 mM; [Ru]. = (3.44+0.07)x10 M. There is one off-scale point at [Et 2 S] = 0.232+0.002 M for each plot; all of the data are tabulated in appendix 2.  129 Table 3.2 Fundamental Parameters Derived from Equations 3.24 and 3.25 [Et2 SO]x10 3^De  .8 1 x10 -5^K2x102^lc3x102  (s1)^Km2^IC4 (s')  (M)^(M'cm') 1.18+0.03^-(1.75±0.04)  ^  6.0±0.2^3.74+0.06  ^  1.1+0.2^0.7±0.1  3.4.2 Error Analysis 3.4.2.1 Uncertainties in the Solution Concentrations Small amounts of the pure reagents were used to make up the initial stock solutions. Ru(OEP)(Et 2SO) 2 was weighed out in approximately 5 mg quantities on an analytical balance with a precision of a = 1.9x104 g (based on 38 weighings of the same object over a time period of 1.5 months). The liquid reagents were measured out using Unimetrics microliter syringes with stated precisions of 1 %. Once the stock solutions were made up, serial dilution using larger scale volumetric apparatus contributed little to increasing the uncertainties in the solution concentrations.  3.4.2.2 Instrumental Uncertainties Blank runs carried out with each series of experiments, both on the 100 ms and the 100 s timescales, showed that the baseline was not flat (see appendix 2). The raw data were therefore corrected by subtracting the blank from each individual run. No independent estimate of the measurement error in the absorbance was available, so a measure of the goodness of fit of the proposed exponential decay model to the data could not be obtained from the least squares analysis. 5 a Instead, an estimate of the measurement  130 error was calculated from the least squares analysis assuming that the exponential decay model (given by equation 3.6) accurately described the absorbance change with time, instead of testing this as a hypothesis. Qualitatively one can say, from inspection of figures 3.14 and 3.17, that there is a good fit of the theoretical curves to the data, both on the 100 ms and the 100 s timescales. A minor oscillatory deviation of the experimentally observed data points from the theoretical values is consistently observed in all of the absorbance vs. time plots obtained on the 100 ms timescale (see figure 3.12 and appendix 2). This is probably an artifact, and is small enough to be ignored.  3.4.2.2.1 Uncertainties on the Millisecond Timescale  Initially equations 3.18 and 3.19 were fitted to the data obtained by monitoring the 100 ms timescale, using the standard errors in  al ,  0 1 , and y i , calculated from fitting  equation 3.6, as weighting factors. The goodness of fit values (Q) that resulted from this procedure were unacceptably low (less than 10 -5), which could not be accounted for by one or two outlier points." Thus, either the model being used was wrong, or there were other sources of error beyond those already accounted for. sa Now if repeated stoppedflow experiments (5 run averages) were done without changing the concentration of any of the reagents, the variation in the calculated parameters a l , [s,, y, from run to run was found to be much higher than the standard errors calculated for any given run (figure 3.19). Moreover, in the case of parameter 0 1 , the variation was not entirely random, with 0 1 appearing to decrease slightly with with increasing number of runs. Two series of repeated runs were carried out, one at each end of the Et 2S concentration range used. In the case of parameter 0,, the relative error is approximately the same (2.4%) at both  131 [Et2S]/[Et2S0] = 0.100  0.095  (a)  1----.-  I^  131 0.090  1---,,f________----\\  ^I  ^  0.085  _TL-,__ i  ----  ---i  1^1^I^1^I^i^I^1^1^1  55.00 (b)  yi 50.00 — 45.00  I^ 1 0^1^2^3^4^5  1 ^ I^ i ^ 1 ^ 7^8^9^10 11 Experiment number  [Et2S]/[Et2S0] = 785  0.500  (c)  le 0.475 0.450  11111111111  134.00 — (d  1  1^  )  T^T  7 1 132.00 130.00  0  1  ^  2^3^4 5^6^7^8^9 10 11 12 13 14 Experiment number  Figure 3.19. Variation of the parameters 13 1 and -y 1 from experiment to experiment, when all reagent concentrations are held constant. The error bars represent the uncertainties estimated from fitting the raw stopped-flow data.  132 extremes, and this is considered to remain constant for experiments done at intermediate values of [Et 2 S]. Therefore, in the fitting of equation 3.18 a relative uncertainty of +2.4% was assumed for all 13 1 values. For parameter y 1 no such convenient trend exists, and a somewhat artificial convention was adopted by assigning a relative error of 2.5% to the points corresponding to the lowest three Et2 S concentrations, one of 0.87% to the three highest concentration points, and the average value of 1.7% to the remainder. This provides an educated guess as to the proper weighting. In figures 3.15 and 3.16, the error bars represent the combination of the instrumental uncertainties as calculated by the above procedures, and the uncertainty in the thioether concentration for the experimental point in question. The goodness of fit values (reported in figures 3.15 and 3.16) are now between 0.02 and 1.0, which is quite acceptable given the relatively small sample sizes.' A comparison of the two sets of equilibrium and rate constant values listed in table 3.1 shows them to agree within 10% or better. This suggests that the proposed model, together with the concomitant assumptions, adequately describe the system under study, and the obtained values closely approximate the true equilibrium and rate constants. In particular, within the context of this thesis, the key parameter is  KiA pp ,  whose value affects the determination of all of the parameters in the second substitution reaction, which is of fundamental importance in the catalytic oxidation cycle (see section 3.5.1). Knowing  K1APP  to within 10% accuracy is certainly adequate for estimating its  relatively minor effect on the second reaction. The difference between the equilibrium and rate constant values obtained in the two series of experiments is significantly greater than the uncertainties resulting from the least-squares fitting; however, since the instrumental errors are not entirely random, one must be careful in assigning too much  133 quantitative meaning to the uncertainties derived from this procedure. In fact, the main discrepancy between the two sets of results could well be due to a difference in the data collection method. For the experimental series which resulted in figures 3.15a and 3.16a, the data were collected sequentially starting at the lowest Et 2 S concentration, and ending with the highest. Probably as a result, the data points in these figures exhibit a slight underlying curvature relative to the theoretical lines. On the other hand, the series which resulted in figures 3.15b and 3.16b were collected in more random order, and the data points appear to be more randomly scattered about the theoretical line. As an indication that the uncertainties in the equilibrium and rate constant values are greater than suggested from the least squares analysis, the uncertainties reported with the average equilibrium and rate constants in table 3.1 are given as half the difference between the two sets of derived values. As to the most probable source of the abnormally high instrumental variation, it was likely due to the Xenon arc lamp being quite old and deteriorating significantly during the time that the experiments were being carried out. This was evidenced by the fact that the photomultiplier gain had to be turned up quite frequently to obtain constant absorbance readings. Normally this must be done over a period of months; during the course of the reported experiments, it was not unusual to have to adjust the gain twice in the same day. As the gain is turned up, one expects the output signal to become less stable.  134 3.4.2.2.2 Uncertainties in the One Hundred Second Timescale  The error bars in figure 3.18 combine the uncertainty in the Et 2 S concentration and the instrumental uncertainties affecting the parameters CY2, 02, and 72 , as calculated in the fitting of equation 3.6 to the data collected at X = 402.8 nm. The goodness of fit values (Q) derived from fitting data to equations 3.24 and 3.25 suggest reasonable fits assuming these uncertainties, and the data points appear to be fairly randomly scattered above and below the theoretical curves in figure 3.18. Apparently, some of the sources of error affecting the millisecond timescale were somehow compensated for over the longer time frame. Analysis of the intermediate results in the singular value decomposition solutions of equations 3.24 and 3.25 showed the parameters d i -d 6 to be determined uniquely. 5 a' b The experimental uncertainty calculated for parameter d 6 is high enough to make the value worthless for extracting rate constant data; nevertheless, both d 3 and d 6 are significantly different from zero, and the temptation to neglect them, which would allow equations 3.24 and 3.25 to be linearized, was resisted. For comparison with the values obtained over the 100 ms timescale, the value of K iApp was independently determined to be 2.1 ± 0.3, by inserting the data collected in the analysis of the second substitution reaction into the equation:  K iApp = d 2 [Et 2 S0]/d 3^3.36  Again, this value is significantly different statistically from the values calculated by studying the first substitution reactions directly, but is close enough to suggest that any  135 uncertainties or mechanistic factors unaccounted for so far are relatively minor. Finally, and of importance,  K2 was  also determined independently from 'H-nmr  experiments. Thus the 'H-nmr spectra of three solutions, initially containing 1-2 mM [Ru(OEP)(Et 2 S) 2], 0.45 M [Et 2 S], and 16, 40 and 79 mM [Et 2 SO], respectively, were collected using an aquisition time of 1.5 s, and a 7 s delay between pulses.  K2  was then  determined from the integral ratios of the meso signals (T, = 0.68 ±0.03 s) for Ru(OEP)(Et2 S) 2 and Ru(OEP)(Et 2 S)(Et2S0). These experiments were carried out at 20° C, rather than 35° C, but the average obtained value for  K2, 0.055  ± 0.005 is close to  that obtained in the stopped-flow experiments.  3.4.3 Discussion of the Parameter Values  The equilibrium constants obtained for the first  (KiA pp)  and second (K2 )  substitution reactions (tables 3.1 and 3.2) show that, in a solution containing equal amounts of free Et 2 S and free Et2 SO, Ru(OEP)(Et 2 S)(Et 250) is the predominant species in solution; i.e. it is the thermodynamically most stable of the four complexes which can possibly form. Kinetically, both substitution steps proceed via a dissociative mechanism; for both steps, the rate constants for binding to the five-coordinate intermediates (1( 4 , k_ 1 „k2 for the Ru(OEP)(Et 2S0) species, and 1( 3 and k4 for Ru(OEP)(Et 2 S)) are similar for Et2 S and Et 2 SO, as evidenced by Km values which are close to one. This means that the values of the equilibrium constants are essentially determined by the relative values of the dissociative rate constants for each reaction; i.e. Ic iApp/1( 2 for the first substitution, and k3 /k4 for the second. The observed values of K2, k3 and k 4 can be rationalized in terms of the  136 sulfoxide's ability to act as a better 7-electron acceptor from the metal center, relative to the sulfide (see section^The greater double-bond character of a Ru-(Et 250) bond would make it stronger, and hence more difficult to break, than a Ru-(Et 2 S) bond. Therefore it seems reasonable that Et 2 SO should dissociate more slowly than Et2 S (k3 < 1(4 ), and hence that the Ru(OEP)(Et 2 S)(Et 250) complex should be thermodynamically more stable than Ru(OEP)(Et 2 S)2 (K 2 < 1).t The large labilizing effect of a 7-accepting ligand on the ligand trans to it has been well documented in Ru(Porp) systems, 16 ' 17 and has been shown to be especially pronounced if the trans ligand is another 7-acceptor." This rationalizes why the Et 2 S is more labile in Ru(OEP)(Et 2 S)(Et250) than in Ru(OEP)(Et 2 S) 2 (k2 > 1(4 ), and leads to the prediction that Ru(OEP)(Et 2S)(Et 250) is more stable than Ru(OEP)(Et 2S0) 2 (K 1 > 1).t Without knowing what fraction of Ru(OEP)(Et 2 SO)2 is present as Ru(OEP)(Et 25.0)(Et 2 S0) in solution, the prediction cannot be verified directly; however, the solid-state it and electrochemical evidence from sections 2.3 and 2.4 suggest that Ru(OEP)(Et250)(Et2 S0) is a relatively minor species in solution. Furthermore, recall from section 1.2 that the most stable isomer of Ru(TMP)(Et 2SO) 2 is known to be the bis(S-bound) one.' If the fraction of Ru(OEP)(Et 2S0)(Et2 S0) is small (K' < < 1), then K1^KlApp (equation 3.14, p.119), and K IAPP is >1 (table 3.1). The so-called "trans effect" (labilization of a mutually trans ligand) has been studied extensively in square-planar Pt complexes, and a good qualitative theory has been established.' In the present case, in which the ligand responsible for the trans  t This reflects the relative concentrations of the two metal complexes when equal concentrations of free Et 2S and Et2 SO are present.  137  •  I  0  „  I  '"  Figure 3.20. Weakening of 7-bonds trans to a sulfoxide; a bonds trans to the sulfoxide will also be weakened, since the sulfoxide can transfer more a-electron density to the Ru cl z2 orbital than a comparable ligand incapable of 7-bonding (see text).  138 labilization is a 7-acceptor, the mechanism by which the phenomenon occurs can be visualized according to figure 3.20. When the sulfoxide accepts electron density from the ruthenium center via 7-7 * back-bonding, there will be less electron density left on the 7rbonding metal orbital for back-bonding to another 7-acceptor trans to the sulfoxide. Thus the bond of a sulfoxide trans to the first sulfoxide will be especially weak. At the same time, the back-bonding of the ruthenium to the sulfoxide has a synergistic effect on the Ru-S a bond; as more electron density is put on the sulfoxide via the 7-bond, more of that density can be fed from the sulfur back to the ruthenium via the a bond. This will mean that the (1,2 orbital of the ruthenium will also be monopolized by the sulfoxide, and less available for bonding with a trans ligand L. Therefore even a a bond trans to the sulfoxide will be weakened, but not as much as another 7-bond.  3.5 Catalytic Oxidation of Et 2S - Rate Dependence on [02] [PhCOOH] and [Ru(OEP)(Et 2 S) 2] 3.5.1 Data Treatment and Results  For carrying out a quantitative kinetic analysis of the catalytic oxidation, monitoring the oxygen uptake proved to be more convenient than following Et 2 SO production by gas chromatography. Although gc was useful in providing complementary information, it did not yield quantitatively reliable results consistently under conditions of higher PhCOOH ([PhC001-1] > 5 mM) or Ru(OEP) ([Ru] o > 0.5 mM) concentration. The presence of PhCOOH tends to broaden the Et 2 SO signals considerably when present in high concentrations. The effect of high concentrations of Ru(OEP) is more subtle; the appearance of the chromatograms remains unchanged by repeated injections of reaction  139 mixtures initially containing higher concentrations of Ru(OEP)(Et 2S) 2 , but standards run before and after monitoring the reactions show that the response factors for Et 2SO change appreciably during the period of the monitoring process. Based on the mechanism proposed in figure 3.8, a system of five differential equations can be derived (see section 4.3 for the derivations) to describe the rates of appearance and disappearance of the major species in solution:  d[2]/dt = klEt 2 S0][3]/[Et2S] 0 - k3 [Et 2 S][2]/[Et2 S] 0 ^ + kobs[Et2SO]PHEt2SL(Pl + 0[2]))  -43 .1/dt = d[2]/dt  ^  3.37  3.38  d[Et2 SO]/dt = kobs[3](2[Et2S]0 - [Et2SO])MEt2S] 0 ([3] + b[2])) + k3 [Et2S][2]/[Et2S] 0 - l 4 [Et2 S0][3]/[Et2 S] 0^3.39  -d[Et2S]/dt = d[Et 2SO]/dt  ^  -d[0 2 ]/dt = 0.5d[Et 2 S0]/dt  ^  3.40  3.41  where  Icobs =- vin (f[Ru] 0)[02 ][PhCOOH]/((K. 4 + [PhCOOH])(IC3 + [02]))^3.42  140 [Et2 S].^[Et2 S] + [Et 2S0]  3.43  and also  Vin^0.5Ci k7/(k6,  k7)  3.45  EE 1(5/14.6  Ka  E.3  3.44  144(74((6' + k7)1(8)  3.46  Again, 2^Ru(OEP)(Et 2 S)(Et 250), and 3 im Ru(OEP)(Et 2S) 2 . The constants c 1 and and the function f[Ru],, are all part of an empirical expression, the significance of which is discussed below. Note that at t = 0, [2] = 0, [3] = [Ru] o , [Et2 SO] = 0, and [Et 2S] = [Et 2 S].. Therefore:  (d[2]/d0 t = 0 = 0  ^  3.47  (d[Et 2 S0]/dt),= 0 = 21cobs^3.48  i.e. the initial rate of [Et2 S0] production is 21cobs . The forms of the initial rate equations 3.47 and 3.48 have an important theoretical significance, which is discussed in section 4.3.3.1.  141 Equations 3.37-3.41 were derived making all of the simplifying assumptions discussed in section 3.3: a) all species other than Ru(OEP)(Et 2 S) 2 and Ru(OEP)(Et 2 S)(Et2S0) are present in negligible, steady state concentrations; b) only Ru(OEP)(Et 2S) 2 reacts with 0 2 ; c) the photochemical effect is initiated by the  7- 7 *  transitions which give rise to the a,f3 bands in the uv/vis spectrum of Ru(OEP)(Et2 S) 2 ; d) no catalyst degradation takes place during reaction; e) reaction of Ru(OEP)(Et2 S) 2 with 02 via direct coordination of 0 2 to the metal center does not occur when excess thioether is present; f) rearrangement of Ru(OEP)(Et 2 S)(Et 2 S0) to Ru(OEP)(Et 2 S)(Et2_80) occurs only via the five-coordinate Ru(OEP)(Et 2 S) intermediate (i.e. the reaction pathway in figure 3.8 labelled "internal rearrangement" does not occur). In addition to these six assumptions, based on the results of the stopped-flow studies described in the previous section, two additional simplifying assumptions were made. First, the concentrations of Ru(OEP)(Et 25.0) 2 and Ru(OEP)(Et 2S0)(Et2SD) produced during the reaction were neglected. For the fastest reactions studied, the ratio [Et 2 SO]/[Et 2S] at the end of the typical time period monitored (1.7-2.5 h) was at most 0.1, which means that the [Ru(OEP)(Et2 S0) 2] would still be 30 times less than the [Ru(OEP)(Et2S)(Et250)], or 20 times less than the [Ru(OEP)(Et2S)2] (using the values of K iApp and K2 listed in tables 3.1 and 3.2). The second assumption was that K. 2 is essentially equal to one, as determined experimentally (1.1+0.2, see section 3.4 and table 3.2). The expression  c i (f[Ru] o)[3]/([3] + tk[2])^  3.49  142 is an empirical one meant to approximate Ia , the amount of light absorbed by Ru(OEP)(Et2S) 2 , for each turn of the catalytic cycle (I a^einsteins absorbed by Ru(OEP)(Et 2 S) 2 per liter per second). The true form of the function l a will be complicated, and the theoretical problem of approximating it by a reasonably simple function is treated in detail in section 4.3.2; for the moment, only a summary is provided. The approximate function consists of two distinguishable sub-functions, and the constant c l . The first sub-function is fiRuL, which is intended to reflect what fraction of the total incident light will be absorbed by all the contents of the reaction flask for a given [Rd,. As will be seen below, when the one-parameter function  f[Ru],, = 1 - exp(-10c 2 [Ru] o) + arctan(c2 [Ru] o)  ^  3.50  is used (where c 2 is the adjustable parameter), the resulting equation for k obs fits well all of the experimental data, although no doubt there are other suitable expressions for f[Ru] o (see section 4.3.2). The second sub-function of I. is defined by  f2^[M[3] + 0[2 ])  ^  3.51  Where  €3dX/ f €2dX^  3.52  143 Thus f2 represents what fraction of the total light absorbed by the solution is actually absorbed by Ru(OEP)(Et 2 S) 2 . Note that whereas c 1 and c 2 are empirical parameters whose value depends on the geometry of the experimental apparatus, the value of 1k is dictated by assumption (c) above; therefore b has chemical significance. Figure 3.21 illustrates the region of the spectrum over which the integrals in equation 3.52 were evaluated. The integral values were obtained as follows. First, the spectra of separate 0.0340 mM solutions of Ru(OEP)(Et 2S) 2 and Ru(OEP)(Et 2SO) 2 , containing 74.2 mM Et 2 S and 2.22 mM Et 2SO, respectively, were collected. The desired region in each spectrum was then cut out and weighed; these weights represented, in effect, the integrated "absorbance" (in units of g) of each species, over the region of interest. Thus an integrated "extinction coefficient" (in units of g  n'  cm - ') was calculated for each species. Next, the spectrum  of a solution initially containing 0.0340 mM Ru(OEP)(Et 2 S) 2 , 74.2 mM Et2 S and 44.9 mM Et2SO was obtained, and the desired region cut out and weighed. The equilibrium concentrations of Ru(OEP)(Et2 S) 2 , Ru(OEP)(Et2 S)(EtA0) and Ru(OEP)(Et2 SO) 2 were easily obtained from the known values of the equilibrium constants  K1APP  and K2 (see  section 3.4, and tables 3.1 and 3.2); thus, the integrated extinction coefficient for Ru(OEP)(Et 2 S)(Et250) (in units of g M A cm -1 ), being the only unknown value left, was obtained directly from the Beer-Lambert law. The unusual units of the integrated extinction coefficients do not pose a problem, because they cancel out when the desired ratio 0 is calculated. The value of b calculated using the above procedure was 0.86 ± 0.07.  144  1.0  0  420^  X(nm)  ^  700  Figure 3.21. Visible spectra of pure Ru(OEP)(Et2S)2 ( 3), a solution containing mostly Ru(OEP)(Et2 S)(Et250) (2, see text), and pure Ru(OEP)(Et 2 SO) 2 (1 and 1'). The dashed lines indicate the region of all three spectra over which the integrated extinction coefficients were calculated (see text for details).  145 The constant c l is conceptually important in that it reflects the maximum attainable value of I a . From equations 3.49 and 3.50, the maximum value of I a (when all of the light incident on the solution is absorbed) is given by  = 37rc 1 /2^  3.53  Note that c 1 is itself a function of I o (the intensity of the incident light, commonly given in einsteins dm -2 s'), the area of the cross-section of solution illuminated, and the solution volume (see section 4.3.2). Also, the area of the cross-section of solution illuminated is a function of various geometrical parameters such as flask size, lamp orientation and flask shaking speed. It was to keep c l constant over the whole series of experiments that all runs were carried out using the same solution volume, and great care was taken to keep every part of the apparatus, including the flask, bucket, shaking speed and illumination lamp orientation, the same from run to run. Some experiments were carried out in which either the volume or the shaking speed were deliberately varied; these will not be discussed further here, except to say that changing the shaking speed did not have a great effect on the observed results, but changing the volume did. The results of all the experiments in which either solution volume or shaking speed were varied are listed in appendix 3 (section A3.3). For the experiments discussed in this thesis, only v., rather than c o could be obtained (see equation 3.44); the relationship between c 1 and v m is further discussed at the end of section 3.5.2.2. With 1k calculated, and k 3 , k4 known from the stopped-flow experiments, all of the unknown parameters in the differential equations 3.37-3.41 fall within the expression for  146 kobs . Within any one experiment, [PhCOOH], [0 2 ] and [Rd, were held constant, and therefore kobs can be considered a pseudo rate constant, remaining unchanged for the duration of a single experiment. The initial conditions for the system of differential equations 3.37-3.41 are known experimentally, and so only k obs is needed to solve the system numerically for a given run. To find the best value of  kobs  for a given run, an  iterative algorithm, composed mainly of sub-programs from "Numerical Recipes", was devised. 5c,6 The complete program is listed in appendix 1, but essentially it works as follows. The program is supplied with a copy of an experimentally derived [Et2 SO] vs. time data set (where [Et2 SO] = 2[02labsothed, the initial conditions for the data set, and two initial guesses as to the best value of k obs . The first part of the program, a standard numerical integrator, uses these trial kobs values to generate two theoretical [Et 2SO] vs. time data sets. These data sets are individually compared with the experimental results in least-square fashion, and a x2 value is generated for each initially guessed  kobs  value. The  second part of the program then uses the first two (lcobs ,x2) pairs to generate new trial values of kobs according to a prescribed algorithm, and these are successively sent back to the integrator until the lowest possible value of x2 is obtained. Figure 3.9, seen in section 3.3, shows a typical [Et2 SO] vs. time plot, fitted using this x2 minimization routine; another is given in figure 3.22. A total of about 50 experiments were carried out, and the rest of the corresponding plots are collected in appendix 3. The experiments performed are divided into three categories; for any given category, one of [Ru] o , [PhCOOH] or [02] was varied, while the other two were held  147  0.020  0.015 -  cn 0.010 N w 0  0.005 -  0.000  0  2000^4000  6000  8000 t (s)  Figure 3.22. A plot of [Et2 SO] vs. time, fitted using the least squares procedure described in the text. For this experiment, the initial concentrations of the reagents are: [Ru(OEP)(Et 2 S) 2 ] = 0.202 mM; [PhCOOH] = 2.31 mM; [Et 2 S] = 0.742 M; p0 2 = 0.813 atm (corrected for benzene vapour pressure).  148 constant. Figure 3.23a shows a graph of k obs vs. [Ru] o for the data in which [Rd, was varied while keeping [0 2] and [PhCOOH] constant. Taking into account equations 3.42 and 3.50, the data were fitted to the equation  lcob. = P1( 1 - exp(-10c 2 [Ru] Q) + arctan(c2 [RuD^  3.54  using the Leavenberg-Marquardt algorithm. 5" It follows directly from equations 3.42 and 3.50 that  P1 =.-- v.[02][PhCOOH]/((Km4 + [PhCOOH])(K. + [02]))  ^  3.55  Figure 3.23b shows the graph of k obs vs. [PhCOOH] for the set of data in which [PhCOOH] was varied, while keeping [0 2] and [Ru] o constant. These data were fitted to a rectangular hyperbola with zero intercept, again using the Leavenberg-Marquardt algorithm. Thus  kb. = P 2 [PhCO0H]/(1C4 + [PhCOOH])^  3.56  where  P2 -''' Vm[ 02]( 1 - eXP( - 10C2[RUL) +  arctan(c2[Rulo)/( 1C3 + [ 0]2)  ^  3.57  149 1.0E 5  (a) kobs = P1(1 - exp(-10c2[Ru] o ) + arctan(c2[Ru] o ))  8.0E-6 -  I  I  6.0E-6  pl = (4.3 ± 0.2) x 10 -6 M/s  cn  4 0E-6 o^•  -1 c2^(1.1 ± 0.2) x 103 M  a= 2.8 x 10 -7 M/s  2.0E-6 -  0.0 0 0^4.0E-4^8.0E-4 [Ru] o (M)  1.2E-3  6.0E-6 - (b) k o b s = p2[PhCOOH]/(K m4 + [P h C 00H ]) 5.0E-6 4.0E-6 rn 3.0E-6 0  P2 =-- (7.5 ± 0.6) x 10 -6 M/s  2,0E-6 1.0E-6 -  0.0 0.000 7.0E 6  Km4 = (9 ± 2) x 10 -3 M  TT  a = 3.0 x 10 -7 M/s 0.005  0.010^0.015 [PhCOOH] (M)  0.020  0.025  6.0E-6 5.0E-6 4.0E-6  -  .2 3.0E-6 0  2.0E-6 1.0E-6 -  p3 = (1.5 ± 0.2) x 10 -5 M/s K m 3 = (1.4 ± 0 3) x 10 -2 M a  = 1.8 x 10 -7 M/s  0.0 ^ 0.000^0.002^0.004^0.006^0.008 [02] (M)  Figure 3.23. Plots of Ic b, vs.: (a) [Ru]., with [PhCOOH] and [02 ] held constant at 24.4 and 7.63 mM, respectively; (b) [PhCOOH], with [Ri]„ and [0 2] held constant at 0.408 and 7.63 mM, respectively; (c) [0 2] with [M. and [PhCOOH] held constant at 0.408 and 24.4 mM, respectively. The error bar magnitude in each case is given by  150 Finally, figure 3.23c illustrates the data obtained from experiments where [0 2] was varied, keeping [Rd :, and [PhCOOH] constant. These data were also fitted to a rectangular hyperbola with zero intercept,  L. = P3[0 2]/(Kn3 + [02])  ^  3.58  where  P3 -". Vm [PhCOOH](1 - eXP(-10C2[Ril]a) + arctan(c2[Ru]Y(Km4 + [PhCOOH]) 3.59  In addition to the data shown in figure 3.23, the experiments in which [PhCOOH] and [Ru], were varied were repeated several months after the first set of experiments, with the apparatus set up slightly differently (it was impossible to set it up in exactly the same way). The results of these experiments are shown graphically in figure 3.24. Note that, as expected, the parameters v m and c2 are different for these experiments, since the apparatus geometry was different (presumably it is the difference in the value of c i which makes the value of v m different). To avoid confusion, when referring to the second set of experiments, c 1 ,, c2 ,, p r , p2 , and v., are used instead of c l , c2 p i , p 2 and vm . Thus, for example, for the [Ru] o -dependence experiments, equations 3.54 and 3.55 become  'cobs = P( 1 - e xp(- 10 c2 fRup + arc tan(c 2TRul.)  ^  3.60  151  6.0E 6 -I  2 ,[Ru] 0 ) ( a ) kobs p i ,(1 - exp(-10c 2 ,[liu] 0 ) + arctan(c  5.0E-6 4.0E-6 -  n  3.0E-6  P1' = (2.3 ± 0.1) x 10 6 M/s  -  -  = (1.8 ± 0.3) x 10 3 M -1  0  2.0E-6 -  = 2.0 x 10 -7 M/s  4.0E-4  0 0  1.2E-3  8.0E-4 [Ru] o (M)  4.0E 6  (b) k obs = p 2 ,[PhC0 01-1 ]/(K m4 + [Ph C001-1]) 3.0E-6 -  2.0E-6 -  p 2 , = (3.6 ± 0.1) x 10  0  -6  M/s  K m4 = (5.4 ± 0.6) x 10 -3 M 1.0E-6 -  0. 0 0.00  a= 1.3 x 10  0.01  0.02^0.03 [PhCOOli] (M)  -7  M/s  0.04  0.05  Figure 3.24. Plots of kobs vs.: (a) [Ru]., with [PhCOOH] and [02 ] held constant at 24.4 and 7.63 mM, respectively; (b) [PhC001-1], with [Ru] o and [0 2] held constant at 0.202 and 7.63 mM, respectively. The error bar magnitude in each case is given by a.  152 where  P r -= ve [0 2][PhCOO H]/O K.4 + [PhCO OH])( IC3 + [02]) )  3.61  v., =--- 0.5c 1 , 1c7/(k_ 6 , + 1(2)  3.62  and  The values for K,3, K,4, v m and v., obtained in the two sets of experiments are tabulated in table 3.3.  TABLE 3.3 Fundamental Parameters Derived from the Plots of kobs vs. [Ru] , [PhCOOH] and [02] 0  Km3 (M)^K,4 (M)8^V, (M/s)b^V„, (M/ s) °  (1.4 ± 0.3)x10 -2^(5.4 + 0.6)x10 -3^(1.4 + 0.3)x10 -5^(8 + 2)x10 -6 a) Only the result obtained from figure 3.22 is considered. b) The reported value is the average of the values obtained from a consideration of Pi, P2 and P3. c) The reported value is the average of the values obtained from a consideration of p l , and p 2 ,.  153 3.5.2 Error Analysis and Discussion 3.5.2.1 Experimental Uncertainties The procedure used to weigh out reagents and prepare solutions was the same in the oxygen-uptake experiments as in the stopped-flow experiments, and so the uncertainties in the reagent concentrations are expected to be similar in both cases. The major source of experimental uncertainty for the gas uptake experiments is undoubtedly associated with the gas uptake measurements themselves. It was estimated that the oil manometer on the apparatus could be levelled with an accuracy of +1 mm, which translates to an uncertainty of ±0.1 mM in the measured uptake. This relationship holds, regardless of the pressure at which the reaction was carried out. As mentioned in section 3.2.4.2, the vapour pressures of [Et 2 S] and benzene caused a cyclic variation in the oil manometer levels as the temperature cycled between 34.85 ± 0.15° C, which was compensated for by always levelling the manometer at the temperature minimum. Now if the oil manometer were levelled either slightly before or after the minimum, the temperature in the reaction flask would be higher than required, which would cause the uptake to be underestimated over that time period. Thus uncertainties due to non-levelling of the manometer exactly at the minimum should always lead to an underestimation of the uptake volume, provided that the temperature never dropped below the average minimum. Experimentally, the temperature fluctuation was found not to be perfectly predictable, and sometimes the minimum would drop below the average value (34.70° C) while the manometer was being levelled. This can be attributed to the complicated mixing process which takes place in the reaction oil bath, due to both stirring by the mechanical stirrer, and the shaking of the reaction flask. It is difficult to get a good feeling for the combined  154 uncertainty due to the difficulties in always levelling the oil manometer at the same temperature. As an educated guess, the total uncertainty in the oxygen uptake measurement was estimated to be ±0.2 mM, twice the value suggested earlier for the levelling of the manometer in the absence of the temperature-induced pressure fluctuations. The error bars in figures 3.9 and 3.22 show an uncertainty in [Et 2 SO] of ±0.4 mM, which is twice the postulated [0 2] uncertainty.  3.5.2.2 Evaluation of the Kinetic Model The suitability of the proposed model can be evaluated at two distinct levels. At the first level, one wishes to asses how well the differential equations 3.37-3.41, as written, fit the raw data. At the second level, the question is how well does the proposed expression for kob , fit the replotted kobs vs. [Ru]a, [PhCOOH], and [0 2] data? Figure 3.25 shows plots of the goodness-of-fit parameter Q, vs. [Ru] o , [PhCOOH], and [0 2], obtained in the evaluation of K im for each uptake experiment. For the typical experiment performed, in which about 13-16 data points were collected, about 95% of the Q values should fall between .04 and .99, with an average around 0.4, assuming that the fitting model is correct, and the measurement errors are normally distributed  ^Most of the data points do indeed fall within this range, but there are  some notable exceptions. There are isolated data sets in figure 3.25 that have very low Q values (less than 10'; see also appendix 3). When these data sets are examined (appendix 3), they are found to have unusually high, but random scatter about the theoretical curve. Thus for these data sets, the low Q values are almost certainly due to the fact that the measurement  ^ ^  155 1.20 ^ 1.00 0.80 Q  0.60 0.40 0.20 0.00 -  - 0.20 ^ 00  4.0E-4  8.0E-4  1.2E-3  [Ru]o (M)  1.20 ^ 1.00 0.80 -  Q  0.60 0.40 0.20 0.00 -  - 0.20 ^ 00 ^1.20 ^  2.0E-2^3.0E-2 [PhCOOH] (M)  4.0E-2  4.0E-3^6.0E-3 [02] (M)  8.0E-3  ^  5.0E-2  1.00 0.80 Q  0.60 0.40 0.20 0.00 -  - 0.20 ^ 00  2.0E-3  1.0E-2  Figure 3.25. Plots of the goodness of fit parameter (Q) vs.: (a) [Ru].; (b) [PhCOOH]; (c) [02] for the fitting procedures illustrated in figures 3.23 and 3.24, and assuming that b = 0.85 (see text for details).  156 errors in the experiments were higher than normal, rather than to any flaw in the model. As mentioned in the previous section, the temperature cycle in the reaction vesssel was not entirely predictable, and sometimes the temperature minimum either went below that expected, or didn't quite reach the minimum. Generally the deviations from the typical cycle were not too bad, but occasionally the temperature minimum would be as much as 0.1° C off the average, sometimes for a few points in a row. What makes this phenomenon difficult to quantify is that the temperature cycle was clearly observed to be more chaotic in some experiments than in others. It is not obvious why this should be, but it does explain why the model fits some data sets more poorly than average. From a statistical point of view, the unpredicable temperature deviations represent a breakdown in the assumption that the measurement errors are normally distributed. Of greater concern than isolated "bad" data points, are identifiable regions in which several points in a row have low Q values. There are two such regions: the first data set in which [PhCOOH] was varied (figure 3.23b) shows many bad data points in a row, and all of the data collected at high [Ru] ° (figures 3.23a and 3.24a) have low Q values. The fact that very poor fits were obtained for the first data set in which [PhCOOH] was varied (figure 3.23b) was what prompted the repetition of all these experiments, to see if this was a reproducible trend. The second set of data, however (figure 3.24b), was of quality comparable to the data obtained generally for the [0 2 ] and [Ru] ° dependence experiments. A careful examination of the plots of [Et 2 SO] vs. t for the first data set in which [PhCOOH] was varied (see appendix 3) shows no obvious systematic deviations of the theoretical curves from the experimentally obtained data  157 points; however, the scatter of the data points is much greater in these plots than in other data sets. Moreover, the k ob, vs. [PhC001.1] plots also show considerable scatter relative to the other data sets. The high scatter is most likely attributable to the fact that this was the first set of data collected, and the technique required to obtain reproducible data had not yet been "perfected". The second set of k obs vs. [PhCOOH] data, collected several months after the first, has generally higher Q values for the raw data, and much less scatter in the replotted data. The cluster of low Q values observed at higher [Ru] o is of greater interest. In this case there is no obvious source of error which could account for the fact that in all of the experiments in which [Ru], > 0.5 mM, the [Et 2 SO] vs. t data (appendix 3) are poorly fitted by the proposed rate law. It appears that in these cases the low Q values may be indicating a real flaw in the proposed model, which becomes apparent at higher [Ru]. concentrations. Inspection of the complete set of graphs listed in appendix 3 shows that generally the theoretical curves arch over more than the experimental points. For experiments in which the total accumulation of Et 2 SO is small, the scatter due to experimental uncertainty tends to obscure this trend, but for experiments in which Et 2 SO accumulation over the course of the reaction is high (e.g. graphs A3.1.1.7-A3.1.1.10), the predicted curvature in the graphs is more pronounced, and the deviation of the experimental points from the predicted curve is clearly visible. In the case of experiments carried out at the highest [Ru] o , the arch in the theoretical curves is such that the curves are outside the error bars of a significant number of the experimental points. A smaller than predicted curvature in the experimental [Et 2 S] vs. t data means that the rate at which the reaction is slowing down with time is lower than predicted. Now  158 recall that accumulation of supposedly unreactive Ru(OEP)(Et 2 S)(Et250) as the reaction progresses is the only pathway included in the model by which Et2 SO production can slow down. Therefore one possible explanation for the smaller than predicted curvature in the experimental [Et 2 SO] vs. t data is that the mixed sulfide/sulfoxide complex perhaps reacts with 0 2 to some degree; as mentioned in section 3.3, the energy provided by yellow light is sufficient to allow this process to occur. If Ru ifi(OEP)(Et2 S)(Et250) + 02- is indeed produced, then the rate law expressed in equations 3.37-3.41 could be modified to include the reaction of Ru(OEP)(Et 2S)(Et250) with 0 2 , but there is a conceptually simple (and useful) way to correct for its effect, using the equations exactly as written. Combining equations 3.1 and 3.2 from section 3.3 gives the expression:  Ru m (OEP)(Et2 S)(Et250) + X - + Ru(OEP)(Et2S)2  -,  Ru ll (OEP)(Et2 S)(Et 2.5.0) + Ru ffi(OEP)(Et2 S) 2 + X - AG° = -39 kJ/mol 3.63  where X is either 02 or PhCOO. Therefore the one-electron transfer from Ru ll (OEP)(Et 2S) 2 to Ru m (OEP)(Et2 S)(Et 250) + X - is thermodynamically favoured. Furthermore, the electron exchange is likely to be fast, as transfer from Ru(OEP)(Et2S)2 to Ru(OEP)(Et 2 S) 2 + X - is fast (see section 2.5). According to equation 3.63, Ru ll (OEP)(Et2 S)(Et250) can be thought of as an "antenna", collecting the light energy required for electron transfer to occur, and eventually transferring it to Ru(OEP)(Et 2 S) 2 . Experimentally this energy transfer should have the effect of making lk lower than expected. Recall that is the ratio of the integral extinction coefficients of Ru(OEP)(Et 2 S)(Et250) and Ru(OEP)(Et 2 S) 2 ; if some of the light energy absorbed by  159 Ru(OEP)(Et 2S)(Et 250) eventually leads to the production of Ru(OEP)(Et 2 S) 2 + X - , it will appear as if Ru(OEP)(Et 2 S) 2 is absorbing more strongly, and Ru(OEP)(Et 2S)(Et 250) less strongly than expected, thus resulting in a lower 0 value. To test this hypothesis, all of the calculations were repeated, but this time 1// was left as an adjustable parameter, and a 2-dimensional X 2 minimization routine was used to simultaneously obtain the best values of 0 and  Icon,  (the program used for the  minimization is reported in appendix 1). This procedure yielded an average 1,b value of 0.6 ± 0.2. An important observation about the results of this analysis is that the variation in 0 was found to be independent of [Ru] 0 , [PhCOOH], or [0 2], while kobs increased with all three concentrations. According to the proposed model this is expected, since t,b is a true constant, while k obs is only constant while [Ru] o , [PhCOOH] and [02] are held constant. Unfortunately, the rather large scatter seen for the values of both 0 and k ths tends to obscure any trends which might be of interest. Therefore, instead of using these data for further analysis, the calculations were repeated again, this time fixing 0 at 0.6, and varying only kobs . Of course this means that the uncertainties obtained for the Ic bs values will be artificially low; however, the important question is whether choosing a 0 value other than 0.86 gives better fits of the experimental data overall. Figure 3.26 shows the Q vs. concentration plots, where Q is the goodness of fit parameter obtained by fitting equations 3.37-3.41 to the data, with 0 fixed at 0.6, and k b, adjusted to minimize x 2 . The Q values for the experiments carried out at high [Ru], are now quite good, and in fact the Q values overall are better and more randomly distributed than those obtained for ik = 0.86. Exceptions are the data obtained in the initial acid dependence studies but, as mentioned before, these data were probably perturbed by  ^  160 ^1.20  ^  o -o Data from figure 3.23  1.00 0.80 Q  0.60 0.40 0.20 0.00 -  - 0.20 ^ O0  4.0E-4  1.20 ^  8.0E-4 [Ru] o (M)  1.2E-3  1.00 0.80 0.60 Q  0.40 0.20 0.00 -  - 0.20 O0  2.0E-2^3.0E-2 [PhCOOH] (M)  ^  4.0E-2  ^  5.0E-2  1.20 ^ 1.00 0.800.80 Q  0.60 0.40 0.20 0.00 -  - 0.20 ^ O0  2.0E-3  4.0E-3^6.0E-3 [02] (M)  8.0E-3  1.0E-2  Figure 3.26. Plots of the goodness of fit parameter (Q) vs.: (a) [RuL; (b) [PhC0011]; (c) [02 ] for the fitting procedures illustrated in figures 3.21 and 3.22, and assuming that 1b = 0.6 (see text for details).  161 uncharacteristically high experimental errors. There is, of course, another possible explanation for why equations 3.37-3.41 fit the data better if 1G is set at 0.6 rather than 0.85, and that is that the photochemical effect could be initiated by a charge-transfer transition (or transitions) rather than by the 7r-7r" transitions which give rise to the «,(3 bands (i.e. assumption (c) from the begining of this section could be wrong). If there is in fact a band hidden under the a,(3 envelope originating from a metal-to porphyrin charge-transfer, it is impossible to directly evaluate 0 for this band. Therefore, if this charge transfer is responsible for initiating the photochemical reaction, lk would have to be treated as an adjustable parameter in a kinetic analysis, as described in the previous paragraphs. Further evidence that a chargetransfer transition is indeed responsible for the observed photochemistry is presented later in this section. Another simplification made in deriving the rate law was that no irreversible decomposition of the Ru(OEP)(Et2 S) 2 catalyst occurred (assumption (d)). Any such degradation would cause the experimentally observed rate of Et 2 SO production to decrease more rapidly than predicted. As mentioned above, the experimentally observed rate actually decreased less rapidly than predicted. This doesn't rule out catalyst degradation (indeed, slow degradation is observed experimentally by uv/vis spectroscopy; section 3.3), but it does mean that any effect on the 0 2 -uptake due to the degradation is experimentally undetectable, or masked. In conclusion, in order for the mechanism in figure 3.8 to explain the kinetic data, one or both of the assumptions (b) and (c), listed at the beginning of the section, must be relaxed. In so doing, the resultant modification in the rate law (i.e. empirically changing  162 the value of to fit the data) will automatically compensate for any effect which catalyst degradation might have upon the change in reaction rate with time. Note that the values of Kno , K„,4 and v., derived by plotting lc ob . vs. [Ru] o , [PhCOOH] and [0 2] (figures 3.23 and 3.24), are only marginally affected by using 1,t = 0.6 rather than b = 0.86. The conclusions from the above analysis may appear somewhat inexplicit; however, the fact that equations 3.37-3.41 can be made to fit the kinetic data is significant, even if this could only be done by adjusting arbitrarily. One important point is that even if equations 3.37-3.41 are considered to be completely empirical, they still give values of the initial rates (i.e. 21c obs) which are much better than could be obtained from estimating tangent lines at the origin. Another point worth mentioning is that not all of the mechanisms which could be reasonably proposed in the absence of a kinetic analysis will fit the experimental data. For example, figure 3.8 shows an alternate pathway (labelled "internal rearrangement"), by which Ru(OEP)(Et2 S)(Et2SQ) isomerizes directly to Ru(OEP)(Et2 S)(Et2S0), without the sulfoxide dissociating into the bulk of the solution. A rate law was derived allowing for internal sulfoxide rearrangement, and tested in the same way as the dissociative model described thus far (this represents a relaxation of assumption (f), listed at the begining of this section). The results of this analysis clearly show that the internal rearrangement cannot be an important pathway, assuming that the scheme proposed in figure 3.8 is otherwise a reasonable interpretation of the reaction mechanism. A detailed discussion of the analysis will not be included here (some theoretical elaboration is included in section 4.3.3.1), but the results can be easily understood by looking at one of the experiments in which the alternate model fails most noticeably. Consider the case in which internal  163 rearrangement is assumed to be the only pathway by which Ru(OEP)(Et 2 S)(Et 2 S0) can rearrange to Ru(OEP)(Et 2S)(Et 250) (i.e. k 14 = 0). If this were the situation, then the maximum rate for the oxidation reaction would be given by 2k 3 [Ru] o . This rate would be attained for a rate determining loss of Et 2 SO from the mixed thioether/sulfoxide species; i.e. kobs has to be sufficiently large, so that all of the Ru(OEP)(Et 2 S) 2 is rapidly converted to Ru(OEP)(Et 2S)(Et2.80). Figure 3.27 shows the results obtained for an experiment in which the reaction mixture initially contained 0.0255 mM [Ru(OEP)(Et2S)2], 24.4 mM [PhCOOH], and 0.742 M [Et 2 S], under 0.813 atm 02 . The solid curve in the figure represents the fit obtained from equations 3.37-3.41 (with 0 = 0.85), while the dashed line is the line obtained for  [Et2 SO] = 2k3 [Ru] at^  3.64  This line falls somewhat below the experimental data, meaning that the rate at which [Et2 SO] is produced exceeds that which is possible if k 3 is the rate limiting step. This in itself is significant, but not conclusive evidence that the internal rearrangement model does not work. After all, if the assumption that Ru(OEP)(Et 2S)(Et250) does not react with 0 2 is relaxed, then the theoretical line could be made to go through the experimental points. The main problem is that if the internal rearrangement route is assumed, modelling studies show that Ru(OEP)(Et 2S)(Et25,0) rapidly builds up to a near steady state in the first few seconds of reaction, after which the rate of Et 2 SO production should be much closer to linear than is observed experimentally. Note that relaxing the assumption that Ru(OEP)(Et 2 S)(Et25.0) does not react with 02 does not correct this  164  0.02  0  0.01  0.00  -  0^2000^4000^6000  8000  t (s)  Figure 3.27. A plot of [Et2 SO] vs. time, fitted using: (a) the least squares procedure described in the text; (b) the function [Et2 SO] = 2k3 [Ru] o t. For this experiment, the initial concentrations of all the reagents are: [Ru(OEP)(Et2 S) 2] = 0.0253 mM; [PhCOOH] = 24.4 mM; [0 2 ] = 7.63 mM; [Et 2 S] = 0.742 M.  165 problem; Ru(OEP)(Et 2S)(Et25.0) will still accumulate to a maximum value within a few seconds, after which the rate of Et 2 SO production will be essentially linear. If the internal rearrangement step is assumed to be significant, then it is necessary to invoke irreversible catalyst degradation (or some other, as yet unidentified mechanism) as a cause for the observed decrease in [Et 2 SO] production with time. Given that the rate law derived without invoking internal rearrangement fits the collected data quite well, there seems no reason to consider these possibilities. The next point of discussion is an analysis of the parameters obtained from fitting the plots of kobs vs. [Ri] ° , [PhCOOH], and [02]. Table 3.3 lists these parameters. No effort was made to estimate the uncertainty in the k obs values directly from the raw data; the error bars in figures 3.23 and 3.24 were calculated during the least-squares fitting procedures, assuming that the proposed models accurately described the data. This means that no independent statistical estimate of the goodness-of fit can be made for the replot analyses. Note, however, that the scatter of the experimental points about the theoretical lines is fairly random, which tends to suggest that any deviations of the experimental points from the theoretical curve are due to experimental errors, rather than to a failure of the model (the latter would generally lead to systematic over- or undershooting by the theoretical curve of several experimental points in a row). As previously mentioned, the first k ob, vs. [PhCOOH] data set obtained were of rather poor quality, and so only the parameters obtained from the analysis of the second data set are referred to in subsequent discussions. The calculated uncertainties in the parameters obtained from fitting the kb , vs. [0 2] plots are also quite large (14 % for p 3 and 20 % for IC3 ). In this case the large uncertainties do not arise from unusually high  166 scatter of the data, but rather from the fact that the [0 2] concentration range studied was fairly small; at the highest [0 2] studied, kas was only about 40% of its maximum value. In effect this means that the maximum value of K im is being estimated by a rather long extrapolation, and the degree of curvature in the plot (reflected by K,) is being estimated from the curvature in a comparatively straight segment of the total curve. Despite the uncertainty in the calculated value of K m3 , this value provides some interesting insights. Recall that K no is the ratio k_ 5 /k6 (equation 3.45), where 1( 5 is the first order rate constant for the decay of the RAOEP)*(Et 2 S) 2 species back to the ground state, and k6 is the second order rate constant governing the reaction of the excited species with 02 (see figures 3.5a and 3.8). The value obtained for K. (0.014 + 0.003 M) means that k6 is about 70 times greater than 1( 5 . As lc, is a second order rate constant, its magnitude cannot be greater than about 10 1°^which is the upper limit imposed by the rate at which two species in solution diffuse towards each other. 13b This in turn means that k 5 cannot be greater than about 10 8 s'; however, as the following analysis suggests, the assumption made so far, that the a, f3 absorbance bands for the porphyrin 7-7 *  transitions are responsible for the observed photochemistry, leads to the conclusion  that 1(5 should actually be > > 10 8 s -1 . The rate constant for the decay of a photoexcited state can be expressed as the sum of various more elementary rate constants; for k 5 one could write  k_5^kf  ^"other  ^  where kf is the rate constant for fluorescence emmission, and k  3.65  the  , is the rate constant for  167 deactivation via other processes, such as intersystem crossing/phosphorescence, and various radiationless processes.''''' There is a useful approximate relationship between the magnitude of k f and that of the extinction coefficient at the absorbance  peak: 22b  kf ,--.-- (104 e,nax ) s -1^3.66  For the a band at 525 nm, e n. is 2.5x104 1■4 -1 cm -1 (see section 2.2.4.2), and so k f should be about 2-3x10 8 s-1 . Experiments to investigate the optical emission properties of the synthesized Ru(OEP) complexes were not done, but previous studies by other groups have found that Ru(Porp) complexes in general show negligible fluorescence.' This implies that the rate constant for the decay of the photoexcited state by processes other than fluorescence must be several orders of magnitude > k f , i.e. the excited state is quenched via pathways alternative to fluorescence. This in turn suggests that k 5 should be > >10' s -1 , which is in contradiction with the conclusions drawn from the value of K. This analysis provides evidence that the observed photochemistry is not due to r*  T-  transitions (as suggested in figures 3.5a and 3.8), but rather to a weaker metal-to-  porphyrin charge-transfer transition, hidden under the a/A absorption manifold (as suggested in figure 3.5b, p. 98). A charge transfer transition such as the one pictured in figure 3.5b (k 5 step) would be symmetry forbidden (see figure 3.4); 8 accordingly, E max and therefore k 5 would be much smaller, and more reconcilable with the calculated K,, value. Furthermore, if a specific charge transfer band is responsible for the observed photochemistry, this provides a more logical explanation as to why it is specifically light above 480 nm which is necessary, even though the Soret band at 407 nm is both more  168 energetic and more intense (see section 3.3). Modifying the overall mechanism proposed in figure 3.8 with the photochemistry of figure 3.5b does not affect the form of the rate equations; however, the parameters K.4 , vm (and v.,) have new meanings (cf. section 4.3.3):  K.4 .=.- k_5 ,1(6 ,/(k7 (1c6 , + k 5 ,))^(cf. equation 3.46)^  v. ---= 0.5c i^(cf. equation 3.44)  ^  v., ==--- 0.5c l ,^(cf. equation 3.62)  ^  3.67  3.68  3.69  The fact that modifying the light dependence does not affect the form of the derived rate equations, given the data available, shows that it is unwise to attempt further interpretation of the data, without first doing more detailed experiments focussed on the photochemical phenomenon. However, it is worth considering one point, which could be of importance in designing future experiments. If the expressions obtained for v m and v.• in equations 3.68 and 3.69 are compared with those obtained for the mechanism of figure 3.8 (equations 3.44 and 3.62, respectively), an important difference is noted. In the case of the modified mechanism, v m and v., are simply equal to half of the geometrical parameters c i and c 1 ,, while in the original mechanism these parameters were each multiplied by a factor of 1c 7 /(k_6 , +14 Now, because the c l (or c 1 ) parameter is dependent only on the geometry of the apparatus and on the intensity of the light source, this parameter could be obtained  169 experimentally for a given apparatus setup by measuring the rate of a completely different photochemical reaction, for which the maximum rate was known to be dependent solely on the geometry of the apparatus. Then, the calculated value of v m could be checked to see if it was equal to 0.5c 1 , or whether it was significantly lower. In practice, this experiment would be much simpler if a monochromatic light source were utilized; however, in other respects, a crude apparatus such as the one used for this thesis work would be adequate.  170 NOTES AND REFERENCES FOR CHAPTER 3  1. This pressure was high enough to drive the syringes at the 35° C temperature reported in this work; studies not reported here showed that for higher temperatures the drive syringes become stiffer, and higher pressures are necessary. 2. See for example: Thorburn, I. S. M.Sc. Dissertation, The University of British Columbia, Vancouver, B. C., 1980. 3. a) The Handbook for Chemistry and Physics, 62nd ed., Weast, R. C.; Astle, M. J. Eds., Chemical Rubber Company, Boca Raton, Fla., 1981; p. D-192. The effect of diethylsulfide on the total solvent vapour pressure was neglected in this series of experiments. b) 1UPAC Solubility Data Series, Battino, R., Kertes, A. S., Eds., Pergamon Press, Elmsford, N. Y., 1981; Vol. 7, p. 250. 4. Bevington, Philip R. Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York, N. Y., 1969, Chapter 11. 5.Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes (the Art of Scientific Computing), Cambridge University Press, New York, N. Y., 1987. (a) Chapter 14; this chapter is an excellent treatise on data modelling. (b) Chapter 2 discusses singular value decomposition, and solution of linear equations in general. (c) Chapters 10 (function minimization) and 15 (solution of differential equations). 6. Reference (4) is for the main book, which contains extensive mathematical background for the relevant programs. It is available in three different versions, with the routines in Fortran, Pascal, or C. The Quick Basic versions are found in a separate book: Sprott, J. C. Numerical Recipes in Basic (Routines and Examples), Cambridge University Press: New York, N. Y., 1991. The latter does not contain a detailed mathematical background of the programs. All four books have the same chapters. 7. Gouterman, M. In The Porphyrins, Dolphin, D., Ed., Academic Press, New York, N. Y., 1978; Vol. III, Chapter 1. 8. Antipas, A.; Buehler, J. W.; Gouterman, M.; Smith, P. D. J. Am. Chem. Soc. 1978,  100, 3015.  9. (a) James, B. R.; Pacheco, A. A.; Rettig, S. J.; Ibers, J. A. Inorg. Chem. 1988, 27, 2414. (b) Barley, M.; Becker, J. Y.; Domazetis, G.; Dolphin, D.; James, B. R. Can. J. Chem. 1983, 61, 2389. 10. Brown, G. M.; Hopf, F. R.; Ferguson, J. A.; Meyer, T. J.; Whitten, D. G. J. Am. Chem. Soc. 1973, 95, 5939.  171 11. Barnard, D.; Bateman, L.; Cuneen, J. I. In Organic Sulfur Compounds, Kharasch, N., Ed., Pergamon Press, New York, N. Y., 1961; Vol. I, Chapter 21. 12. Pacheco, A. A. M. Sc. Dissertation, The University of British Columbia, Vancouver, B. C., 1986. 13. Laidler, K. J. Chemical Kinetics, 3rd ed, Harper and Row, New York, N. Y., 1987. a) e.g. Chapter 10; b) pp. 212-222. 14. For a full discussion on the meanings of x2 and Q, see reference 5a; however, the following summary may prove useful. Suppose we have a set of data points, each denoted by (yobs) 1 , and each with an associated measurement error a i . Now suppose that, according to a theoretical model, we calculate values (y ea, corresponding to each of the(y(vobs)11 .• Then, assuming that the measurement errors are random and normally distributed, a) x 2 =--E (((yobs ),-(ye ),) 2/0-); b) Q gives the probability (as a number between 0 and 1) of obtaining this x 2 value (or a higher one) if the model is assumed to be correct. Clearly, if Q is very low, then the model could be wrong. In practice, reference 5a suggests that the odd Q value as low as 10' may be tolerated if the distribution of the measurement errors is not perfectly normal. 15. Jaswal, J. S.; Rettig, S. J.; James, B. R. Can. J. Chem. 1990, 68, 1808. 16.Eaton, S. S.; Eaton, G. R.; Holm, R. H. J. Organometal. Chem. 1972, 39, 179. 17. Bonnet, J. J.; Eaton, S. S.; Eaton, G. R.; Holm, R. H.; Ibers, J. A. J. Am. Chem. Soc. 1973, 95, 2141. 18. Eaton, G. R.; Eaton, S. S. J. Am. Chem. Soc. 1975, 97, 235. 19. Buehler, J. W.; Kokisch, W.; Smith, P. D. Struct. Bonding 1978, 34, 79. 20. Rajapakse, N.; James, B. R.; Dolphin, D. Catal. Lett. 1989, 2, 219. 21. Huheey, J. E. Inorganic Chemistry, 2nd ed., Harper and Row, New York, N. Y., 1978; Chapter 11. N. J. Modern Molecular Photochemistry, University Science Books, Mill Valley, CA., 1991; a) p. 176; b) p. 90. 22. TUITO,  172 CHAPTER 4 RATE LAW DERIVATION FOR THE 02-OXIDATION OF DIETHYLSULFIDE CATALYZED BY Ru(OEP)(Et2 S)2  4.1 Introduction  In the last chapter a mechanism was suggested to account for the catalytic oxidation of Et2 S to Et2 SO by Ru(OEP)(Et 2 S) 2 , and a rate law based on this mechanism was shown to accurately describe the quantitative production of Et 2 SO under a variety of experimental conditions, at least over a time period of 2h. In addition, the equilibria between Ru(OEP)(Et 2 S) 2 , Ru(OEP)(Et 2 S)(Et250) and Ru(OEP)(Et 2 SO) 2 were studied independently, and rate laws for the net substitution processes verified experimentally. This chapter gives the mathematical derivation of the rate laws for both the overall catalytic cycle and the isolated equilibria. Most of the manipulations described are based on well established kinetic data treatments (see for example, reference 13 in the previous chapter). An exception is in the empirical treatment of the Et2 S oxidation rate dependence on light, so this topic is given special attention.  4.2 The Equilibria between Ru(OEP)(Et 2 S)2 , Ru(OEP)(Et2 S)(Et2 SO) and Ru(OEP)(Et 2 SO) 2 4.2.1 Rate Law Derivations  In the stopped-flow experiments described in the previous chapter, a solution containing Ru(OEP)(Et 2SO) 2 and Et 2SO was mixed with another containing Et 2 S. It was suggested that the ensuing pair of substitution reactions proceeded according the scheme  173 outlined in figure 3.12, and shown again in figure 4.1. Experimentally, the first substitution of a coordinated Et 2SO by Et 2 S was found to progress much faster than the second, so the assumption is made that Ru(OEP)(Et 2 SO) 2 and Ru(OEP)(Et 2 S)(Et 250) will achieve their equilibrium concentrations before the second substitution reaction has proceeded to any appreciable extent. This allows the rate laws for the two substitution processes to be derived independently, and the successful quantitative analysis of the kinetic data, described in section 3.4, substantiates this assumption. For the purpose of the derivations that follow, some shorthand notation will be used to make the equations less cumbersome. Thus:  Ru(OEP)(Et 250) 2 = 1; Ru(OEP)(Et250)(Et 2S0) = 1';  Ru(OEP)(Et 250) = 1 1 , first 5-coordinate intermediate;  Ru(OEP)(Et 2 S)(Et 250) - 2;  Ru(OEP)(Et 2S) ----- 12 , second 5-coordinate intermediate;  Ru(OEP)(Et2S)2 -- 3. --  ^  174  First Substitution Equilibrium k1  Ru (0EP)(Et SO)2  Et 2 SO  Et, S  1^k-  2  Et2S0  Ru (0EP)(Et 2a0)^Ru (0EP)(Et 2S)(Et 2 5.0) k-,  k  Ru (0EP)(Et S0XEt 2S 0)  1'  ^2  Et2S Et, SO  Second Substitution Equilibrium ^Et,  SO^ Et2 S j4 k k4 Ru (0EP)(Et ,S)(Et,S0)^ ^Ru (0EP)(Et S) Ru (0EP)(Et 2S)2 k 3^ k- 4  2^ Et 2 SO^a2)  Et,s  Figure 4.1. Mechanism proposed for the sequential substitution of two Et2 SO ligands by Et2 S, assuming that in solution the bis(sulfoxide) species exists as a mixture of the S- and 0-bound linkage isomers.  175 For the first substitution process, the rate of appearance of 2 is described by the differential equation  d[2]/dt = k 2 [I,J[Et2SJ - k 2 [2]^  4.1  Under conditions of high [Et 2 SO] and [Et2S], I, is not expected to accumulate to any appreciable extent, so the following steady state approximation is made:  d[I,]/d t = 0 = k 1 [1] + 1(1411 + k-2[2 ] - [Ii]((k_i + k_1-)[Et2S0] + k2[Et2S]))  ^  4.2  Thus the concentration of I, will be given by  II = (kiln + k i ln + k-2[2 ])/(((1 +k_1.)[Et2S0] +k2[Et2S])  ^  4.3  Using  k_ lApp ---E 1( 1 +1( 1 ,^  4.4  176 and combining 4.3 and 4.4, and then substituting for I I in 4.1 yields, after rearrangement,  d[2]/dt = k2[Et2S](ki[1] + ki , [11)/(k_ iApp[Et2S0] + k 2 [Et2 S]) - k- 1 Appk-2 [Et2S 0] [2]/ OC_ 1 App[Et2S 0] + k2[Et2S])  ^  4.5  Now, because the equilibrium between 1 and 1' is independent of [Et 2 S] and [Et 2 S0], and because the stopped-flow analysis of section 3.4 showed that the equilibrium is not disturbed, even transiently, during the substitution process, the following relation holds at all times during the first substitution (and of course also the second) reaction:  K' = [11/[1]^  4.6  where  K' ---.. ki k_ v /lci lc_ I^4.7  Equation 4.6 can be used to eliminate [1'] from 4.5. Straightforward algebra results in the expression  d[2]/dt = kik2k_lApp[Et2S][ 1 ]4-1(kiApp[Et2S0] + k 2 [Et2 S])) -  k_ m ppk 2 [Et2S 0 ] [2] / (k_ 1 A pp [E t2 S 0 ] + k2 [Et2S ] ) -  ^  4.8  177 For any given experiment, the concentrations of [Et 2 S] and [Et2 SO] remain essentially unchanged throughought; we therefore define two pseudo rate constants,  k if^k i k2k_ lApp [Et 2S]/(k_ 1 (k_ mpp [Et2 S0] + k2[Et2S]))  k_iAppk_2[Et2SO]/(k_IA Pp[Et2S0] + k2[Et2S])  ^  ^  4.9  4.10  On defining [Ru]. as  [Ru].^[1] + [1'] + [2] + [3]  ^  4.11  and remembering that before the first equilibrium is established, the concentration of [3] is assumed to be zero, the combination of 4.6 and 4.11 yields  [1] = ([Ru]. - [2])/(1 + K')^  4.12  Now equations 4.8, 4.9, 4.10 and 4.12 can be combined to give  d[2]/dt = k if[Ru]. /(1 + K') - [2](c 1i /(1 + K') + k ir)^ 4.13  [2] is the only variable on the right hand side of equation 4.13, so it is convenient to define two more parameters; let  178 0 1^lc if[Ru] o/(1 + K')^  4.14  0 2 ---= k 1 /(1 + K') + kb.^  4.15  d[2]/dt = 0 1 - 02 [2]^  4.16  so that  This equation is integrated to give the desired expression for [2] as a function of time:  [2] = (0 1 /0 2 )(1 - exp(-0 2t))^  4.17  Derivation of the rate law for the second substitution reaction begins by assuming that 1,1' and 2 are in equilibrium, and that the concentration of 3 equals zero at the start of this reaction. The rate of appearance of 3 is then described by the differential equation  d[3]/dt = 1(4[I2][Et2S] - k-4[3]  ^  4.18  A treatment analogous to that used for the first equilibrium allows us to rewrite equation 4.18 in the form  d[3]/dt = k2/2] - k2,[ 3]^  4.19  179 where  k2f =a k3 k4 [Et2 S]/(k_3 [Et 2S0] + k4 [Et2 S])^  4.20  ^ k2, =---- k_3k.4 [E t2 SO ]/ OC- 3 [Et2S 0] + k4 [Et2S] )  4.21  K 1 is defined as the equilibrium constant between 1 and 2, and therefore  K 1 = [2][Et2 S0]/[1][Et2S]^  4.22  Rearranging this expression and combining it with equations 4.6 and 4.11 gives  [Ru] o = [2][Et 2 SO](1 + K')/K 1 [Et2S] + [2] + [3]^  4.23  And on defining  KiA m  -=  r--  K1/(1 +  K')  ^  4.24  equation 4.23 becomes  [Ru]. = [2]([Et2 SO] + K lApp rEt2 SD/K IApp [Et2 S] + [3]^ 4.25  180 which gives, after solving for [2],  [2] = ([ 1( 1 ]0  -  [3])K1App[Et2S]/([Et2S0] + KiApp[Et2S])  ^  4.26  Let  A .--7-- K 1App [Et2 S]/aEt2 S0] + KiApprEt2S1)^  4.27  Thus equation 4.19 can be rewritten as  d[3]/dt = k2fA[Rul. - (k2fA + k20[3]  ^  4.28  This equation is identical in form to equation 4.13, and integrates to  [3] = (03/04)( 1 - exp( -04t))  ^  4.29  where  03 --= k2fA[Ru],,^  04 ....: k2fA  + k2 ^ 1  4.30  4.31  181 4.2.2 Correlation of Uv/Vis Absorbance Changes to the Derived Rate Laws 4.2.2.1 First Substitution Reaction  Experimentally, the reaction of Ru(OEP)(Et2 SO) 2 with Et 2 S was monitored by visible absorption spectroscopy. The first substitution was followed at 400.5 nm, which is the absorbance maximum for Ru(OEP)(Et 2 SO) 2 solutions at 35° C. From the BeerLambert law we can write  A = € 1 , 111 + f i ll] + 62 '[2] = (e l ' + € 1 , 1C)[1] + f 2 '[2] - = (El' + €1/KIRu])(1 + K') + [ 2](e2' - (e l ' + e 1 ,'K')/(1 + K'))  ^  4.32  The final form of equation 4.32 is obtained by substituting 4.6 for [1'], and then 4.12 for [1]. As defined, e n ' ---= €.1, where 1 is the path length of the solution whose absorbance is  being measured. If A. is defined as the absorbance at t = 0, and  nal.  are the initial  concentrations of 1 and 1', then  A. = € 1 11] 0 + 6 1 ,111 0^4.33  [Ru]. = M. + [11.^  Since 1 and 1' are in equilibrium, equations 4.33,4.34 can be rewritten as  4.34  182 A0 = (e l ' + El/V)[IL  4.35  [Ru] o = (1 + 1C)[ 1 ]0  4.36  Solving equation 4.36 for [1] 0 and substituting into equation 4.33 yields  A 0 = (E l ' + fr'KIRul o/(1 + K')  4.37  Let  flApp f..- (el l +  e r 'K')/(1 + K')  4.38  then  Ao =  e lApp f [ R U]0  4.39  The last two expressions can be used to simplify equation 4.32:  A = A0 +  (€2 1 -  E lApp ')[2]^  4.40  If we define  Afi =- €2 - cup;^  4.41  183 then equations 4.17, 4.40 and 4.41 can be combined to give the desired expression for the change in absorbance as a function of time:  A = 0 1 4E 1 V02 + A o - 0 I 4E 1 'exp(-02 0/02^4.42  This equation is equivalent to equation 3.6 (p. 118) if we define  a1  0 1 400 2 + A o^4.43  Si 7-: Ao - a 1 4.44  4.45  Equation 3.9 (p. 119), the expression for the initial rate of change of absorbance with time, also follows directly from equation 4.42:  Vol = - y1 R 1  = 014€1 '  ^  4.46  Rearranging equations 4.44 and 4.46 into the forms of equations 3.10 and 3.11 (p. 119) is straightforward, but somewhat tedious. The key steps are:  184 N1 = OA f 1 1 02 -  = -Ic If[Ru] 0LIEMIc if + kal + K')) = -[Ru] 0AE 1 '/(1 + (klr/klf)( 1 + K'))  ^  4.47  ki ral f = ( k- 1APP1C-2[Et2 S O]/(k_m pp [Et 2S 0] + k 2rEt2S1)) x(kik2k_iA pp[Et2 S]/(k-i(lc- 1app[Et 2S 0] + k2[E t2S])Y 1  = k_ 1 k_2 [Et2 S0]/k 1 lc2 [Et2 S]  = [Et2 SO]/K I [Et2 S]^  4.48  Substituting 4.48 into 4.47, and rearranging, gives the final desired expression for 13:  Si = - [Ru]AfilEt2SVOKIAppY l [Et2S0] + [Et2S])  ^  (3.10) 4.49  Similarly for v01 :  v oi = O i Ae l ' = k 1f[Ru],,A€ 1 1 /(1 + K') = (Ic i k2k_ i p pp [Et2S]/ (k_i(k_iA pp [Et2S 0] + k2[Et2S])))([Ru]0Ae1 '1(1 + K')) = (k_ 1App/(k_ 1 (1 + IC)))0c1[Et2S][Ru]aAEIRICI[Et2S0] + [Et2S])  ^  4.50  185 k l k_ mpp/k_ 1 (1 + K') = 101 + K') + k_pk i /(k_ i (1 + K')) = k,/(1 + K') + k v /(1 + (K') ') -  kiApp  ^  4.51  Therefore  v0 , = klApp[Ru]4ellEt2Sli(Knil[Et2S0] + [Et 2 S])  ^  (3.11) 4.52  The subscript App emphasizes an important feature of equations 4.49 and 4.52; the two equations have forms identical to those which would be obtained if Ru(OEP)(Et 2 SO) 2 were present as a single isomer; in this case, K lApp would be replaced simply by K,. In the same way, the parameter E mpp ' behaves like an extinction coefficient for a single species, Ru(OEP)(Et 2 SO) 2 , provided that all the experiments are being carried out at one temperature.  4.2.2.2 Second Substitution Reaction The second substitution reaction was followed at 402.8 nm, which is an isosbestic point for a mixture of Ru(OEP)(Et2 SO) 2 and Ru(OEP)(Et 2 S)(Et 2 SO) at a total fixed concentration. The Beer-Lambert expression at any wavelength will be  A = (e l ' +^+ E 2 12] + c 3 '[3]^  If equations 4.6 and 4.11 are used to eliminate [1] from equation 4.53, a little  4.53  186 rearranging simplifies the latter to  A = A. - e1App'([2] + [3]) + €212] + €313] ^  At the isosbestic point chosen, E2 ' - Empp f  =  4.54  0, and thus  A = A o + [3](e3 ' - e mpp )^  4.55  Now if Ae 2 ' is defined as  Aez ' =7 €3 ' E lApt:^ -  4.56  the desired expression for [3] as a function of absorbance is obtained:  [3 ] = (A - A o)/,A€ 2 '^  4.57  which, when combined with equation 4.29, gives the absorbance change as a function of time:  A = 03 ,6■6 2 '/84 + A o - (03 AE 2 'exp(- 040)/04^  4.58  187 Again this equation has the form of equation 3.6 (p. 118). For this particular system,  a2 = 03 0€ 2 '/04^A o^4.59  N2 = Ao a2  = -03AE2704  ^  4.60  'Y2 = 04^  4.61  vo2 =^= 03 ,6■62 '^  4.62  Also  Equations 4.60 and 4.62 need to be expanded to show the dependences of  02  and vo2 on  [Et2 S] and [Et2SO]; again, this is a long but straightforward process, and only a sketch of the procedure need be given. From equations 4.20, 4.21, 4.27 and 4.60,  02 = k2fAAE2 [RUMICHA k2r) k3k4[Et2S][R11].)AA€2'/(1(31(411[Et2S]  + k_3k4[Et2S0])  = [Et2S][RU]4E27([Et2S] + [Et2SO]A -1 K2 1 )  = K I AppK2 [R U ]oAE 2 [Et2S]2/ (KlAppl(2[Et2S]2 K iApp [Et2S] [Et2S 0] + [Et2S°])  ^  4.63  188 Similarly, from equations 4.20, 4.27, and 4.62,  v 02 = k2fA[Ru]4€2' (k3[Ru]0AE2'[Et2S]/(Km2[Et2S0]^[Et2S])) x(K lApp rEt2 S1/([Et2 S0] + KlApp[Et2S])) = k3[Ru]oziE2'[Et2S] 2/4K,.2[Et2S0] + [Et2S])((CIApp) 1 [Et2S0] + [Et 2S])  ^  4.64  In theory, all of the desired equilibrium and rate constants should be obtainable from equations 4.63 and 4.64 (the value of  KIAPP  could also be determined independently  from the study of the first substitution reaction). In practice, these equations prove to be very awkward to deal with numerically, but fortunately they are easily rearranged to the more tractable quadratic forms shown in equations 3.24 and 3.25 (p. 125):  [Et2S] 2/13 2 = d i [Et 2 SJ 2 + d 2 [Et2 S] + d 3^(3.24) 4.65  [Et2S] 2 /V02^d4rEt2S]2^d5[Et2S ]^d 6^  (3.25) 4.66  where the parameters d,-d 6 were previously defined in chapter 3 (p. 125). An analysis of the dependences of [Et 2 S] 2/13 2 and [Et2 S] 2/vo2 on [Et 2S] at constant [Et 2 SOJ yields the desired equilibrium and rate constants. Note, that if d 3 and d 6 are negligible relative to the other terms in equations 4.65 and 4.66, these equations simplify to the same linear form as equations 4.49 and 4.50.  189 4.3 Catalytic 0 2-Oxidation of Et 2S by Ru(OEP)(Et2 S) 2 4.3.1 General Rate Law Derivation  In section 3.3 a mechanism was proposed, by which Ru(OEP)(Et 2 S) 2 could catalyze 02 -oxidation of Et 2 S in acidic benzene. Throughout section 3.5, several modifications to this mechanism were suggested, in order to account for some of the experimentally derived results. In this section and the next, only the original mechanism, outlined in figure 3.8 and reproduced on the following page for convenience, is considered. Using the methodology provided, it is not difficult to derive rate laws for the modified mechanisms; a brief sketch of the procedures involved, together with some additional theoretical considerations, are given in section 4.3.3. According to the assumptions summarized in section 3.5.1 (pp. 140-141), the only Ru(OEP) species present in significant amounts during any given reaction are Ru(OEP)(Et 2S) 2 (3) and Ru(OEP)(Et2S)(Et25.0) (2); the Ru(OEP)(Et 2S0) 2 species (1 and 1')  are assumed to accumulate only negligibly over the time period monitored, and all  other Ru(OEP) species are assumed to remain in small, steady state concentrations. The rates of change in concentration of the two major Ru(OEP) species are governed by the differential equations:  d[2]/dt = k_ 3 [I2][Et 2S0] - k3 [2]^  -d[3]/dt = d[2]/dt^  4.67  (3.38) 4.68  (where 1 2 7-- Ru(OEP)(Et 2S) 2 ). Again some shorthand notation will be used to make the ,-  190 Et, SO II  ^Ru1l (OEP) ( Et,S0)2^II^Ruli( O EP) ( E t, SO X Et 2so)  ( 1' )  ^k  it  'k•^(1') ^— ^ 1 1• Re(oEp)(Et2a0) (i i )  Et 2 S -  k, -  (2) Ru 1i(oEp)(Ei„s)(Et,s0) ^-^Internal Et2 S  Rearrangement , &14 ,  k Et, SO Ru iT (OEP)(Et ,S) k  ( 3 ) /--rc-4 (12) ; 0, coordination  2Ru IT (OEP)(Et 2S )2 hv  Ru(OEP)(Et2S)(02  )  Ru li (OEP)(Et ,S)(Et,S0)  2RII II (OEP)'(Et,S ) 2 02  (  (I8) \ti3  (I3)  2[Ru I I(OEP)(Et 2 S) 2 ]0, k k  (Li)  2TRU M (OEP)(Et 2 S )2 r02  Et, S  0=Ru iv (OEP)(Et ,S) 21'^ PhCOOH 6 12 [Ralv(OEP)(Et ,S)(PhC00)1+0HPhCOOH H,0 [Ru iv (OEP)(Et ,S)(PICOO)r - PhC00-  (Is)  PhCOOH  k to Ru m (OEP)(Et ,S)(PhC00) 2[Ru ill (OEP)(Et ,S) 2 rPhC00 (T 6)^----k9  2H0, kd  (17) Et ,S  0,  kOX  Et ,S0 H,0  Figure 4.2. Mechanism proposed for the 0 2 -oxidation of Et2 S to Et2 SO, catalyzed by Ru(OEP)(Et 2 S) 2 and PhCOOH (dotted pathways imply that these processes can be neglected, or do not occur, under catalytic conditions; see the assumptions on pp. 140141).  191 equations less cumbersome. Thus:  1 3^Rull(OEP)*(Et 2 S) 2  14 =4 Ru ll (OEP)+ . (Et2 S) 2 02 -  15^Ru m (OEP)(Et2S)2 + 02  16 = Ru m (OEP)(Et2 S) 2 + PhC00 -  Ru m (OEP)(Et 2 S)(PhCOO)  1 8^Ru ll (OEP)(Et 2S)(Et 2S0)  The steady state equation for [1 2 ] will be:  k 14 [1 8 ] + 1(3 [2] + k.4 [3] = [I 2](k_3[Et2 S0] + k4 [Et2S])^4.69  All of the reactions between k 10 and k 14 are unbranched, and are assumed to be irreversible; therefore, k 14 [1 8 ] = 1c 10[I6 ][12]. Upon substituting for k 14 [18 ] and rearranging, equation 4.69 becomes  [I2] = (k 10[1 6][17}^k3[2]^1(4[3])/(k_3[Et2S0]  ^k4[Et2S])  ^  4.70  192 Substituting for [I 2 ] in equation 4.67 yields  d[2]/dt = k_3[Et2S0](klofi6][I7] + k3[2] + 1(43])/(k_3[Et2S0] + k 4 [Et2 S]) - k3 [2] 4.71  Rearranging 4.71 and using K m2 --.- (k_3/14) gives  d[2]/dt = k i jEt2 S0][I6 ][I7]/aEt2 S01 + (1(.2) 4 [Et2S]) + 1(4[3 ][Et2SO]/([Et2S 0] + (1C2) - '[Et2 S]) ^ - k3[Et2S][2 ]/( 1C2[Et2S0] + [Et 2 S])  4.72  Recalling that Km2 was found experimentally to be very close to 1 (table 3.2, p. 129), equation 4.72 can be simplified to  d[2]/dt = kio[Et2S0][4][Idi[Et2S], + k4[Et2S0][ 3 ]/[Et2S]o -k3 [Et2 S][2]/[Et 2 S] 0,^  4.73  where [Et2 S] o =--- [Et2 S] + [Et 2 SO]. The steady state relationships for [I 3]-[I7] are given by the following equations:  [1'3] = I./(k_ s +k6[02])  ^  4.74  (where I. is the amount of light absorbed by Ru(OEP)(Et 2 S) 2 for each turn of the catalytic cycle; I, ---- einsteins absorbed per liter per second).  k6[0 2][ 13] +  kAI5] — [14](k_6, + 1(7)  1c7 [14] = [I 5 ](k..7 + kaPhCOOHD  193 ^  ^  k8[PhCOOH][ 151 = [I6](k9 + k10[17])  k9[I6] = k1o[I 6M7]  4.75  4.76  ^  4.77  ^  4.78  Combining equations 4.77 and 4.78 gives  k8 [PhC00}1][4] = 21(10[16][17]  ^  4.79  At the same time, combining equations 4.74, 4.75 and 4.76 gives  ^ 4.80 1C6[°2]Ial(k-5 + k6[ 02]) + k-7[15] = [I5li k7 + k8[P h COO H])(k. 6, + k7)/k7  A series of algebraic manipulations converts this last expression to  [Is] -= k61(7[02]iaNk-A7 + (k_-6, k8 + k71(8)[PhCOOHDOc..5 + k6[02]))  which, when combined with expression 4.79, yields  ^  4.81  194 k10 [I6][I7 ] = 0.5k6 k7 k8 [PhCOOM[O 2]la +((k-6 1-7 + k8(k-6 , + k7 )[PhC001-1])(k_ s + k6 [02}))  ^  4.82  Now we can substitute for k 10 [I6][I7] in equation 4.73:  d[2]/dt =-- 0.51c6k7k8[PhC001-1][02][Et2SOlia ÷aEt2Sl ak-6 k-7 + k8 (k_6 + k7)[ PhC OOH])( k_ 5 + k6 [ 02])) ,  ,  +klEt2 S0][3]/[Et2 SJ 0 - k3 [Et2 S]pit[Et2S] o^4.83  Upon defining  Kno^1(5/ 1(6  ^  k_6 ,1(7/0•6 , + 10 1(8  v.^0.51c7 /(k_6 , + k7)  ^  ^  4.84  4.85  4.86  equation 4.83 can be rewritten in a somewhat more compact form:  d[2]/dt = v.[PhC00 11][02][Et2SO]ia +ffEt2Slo(Km3 + [ 02])(Km4 + [PhCOOH])) +k_4 [Et2 S0][3]/[Et2 S], - k3[Et2S]Pl/[Et2S]o ^ 4.87  195 Expressions for the rate of change in [Et2 SO], [Et 2 S] and [0 2] are now required. For [Et 2S0]:  d[Et 2 S0]/dt = icox[Et2S][14202] + k14[18] - k_ 3 [0,2 S0][I2] + k3 [2] = Ic s [PhCOOH][I 5] - d[2]/dt^  4.88  Substituting expression 4.81 for [I i ] in equation 4.88, and taking into account the definitions 4.84-4.86, we can write:  d[Et2 S0]/dt = 2v.[PhCOOH][0 2]IMIC3 + [ 02])(1C4 + [PhCOOH])) -d[2]/dt^  4.89  Finally, combining equations 4.87 and 4.89 gives, after rearrangement:  drEt 2S0Vdt = v max [PhCOOH][0 2]I)(1C3 + [0 2])(Km4 + [PhCOOH]) x(2[Et2 S],, - [Et2SO])/[Et2S1. -  k_4 [Et2 S 0][3]/[Et2 S] o + k3 [Et2 S][2 ]/[Et2S].^4.90  For [Et 2S] and [0 2 ],  -d[Et2 S]/dt = d[Et 2 SO]/dt  ^  -d[02 ]/dt = 0.5d[Et 2 S0]/dt  ^  (3.40) 4.91  (3.41) 4.92  196 Equations 4.68, 4.87 and 4.90-4.92 are very close to the desired expressions, given in equations 3.37-3.41 (p.139); however, one problem remains: that of finding a suitable expression to describe  4.3.2 An Approximate Expression for I.  In the system of interest, a solution contained in a spherical vessel was irradiated by polychromatic light. The vessel was shaken at a fixed rate, and the light source was mounted at an angle to the solution surface. In such a system, any function describing the amount of light (Ia) absorbed by a solution species is expected to have a complicated form. Nevertheless, empirical funtions to approximate I. can be suggested, based on the form which Ia would have if a more simple apparatus had been used. Suppose, for instance, that a quiescent solution of Ru(OEP)(Et 2 S) 2 and Ru(OEP)(Et 2 S)(Et2 SO) was contained in a rectangular reaction vessel, and illuminated by monochromatic light striking the vessel normal to a wall. From the exponential form of the Beer-Lambert law,  = Lexp(-2.303(e 2 1 [2] + e3' [3])^  4.93  where I is the intensity of the incident light, I is the intensity of the transmitted light, ,  and €2 ' and 63 ' are the extinction coefficients of each species, multiplied by the path length 1. The typical units for both these quantities are (einsteins dm -2 s - '); i.e. moles of photons transmitted per unit area, per unit time. It follows directly from equation 4.93 that the intensity of light absorbed by the solution is simply  197 Iabs = Io (1 - exp(-2.30302 1 [2} + E3 1 [3 ]))  ^  4.94  In studies of homogeneous reactions, it is customary to deal with units of mol t'; we therefore define:  'abs' -.. . Iabs(A/V)^  4.95  where A is the surface area being irradiated ( in dm), and V is the volume of the solution being irradiated (in dm 3 , or 1). It is important to emphasize this point: I ts ,, unlike 'abs' is  not in units of intensity. 'abs' represents  the total amount of light that would be absorbed by a solution  containing Ru(OEP)(Et 2 S) 2 and Ru(OEP)(Et 2 S)(Et 250); the required variable is the amount of light absorbed only by Ru(OEP)(Et2 S) 2 , in a solution containing both species. Consider an infinitessimally small cross-section, perpendicular to the incident radiation, located somewhere in the irradiated solution. Let I be the intensity of the light incident on this plane. The following relationship will hold:  -dI/d1 = -(dI 2/dl + dI 3/dl)^  4.96  -dI2 /d1 --.== € 2 1[2]^  4.97  where  198 -d13 /d1^€ 3 1[3]^  4.98  Equation 4.96 is simply the differential form of the Beer-Lambert law, which requires that the exponential decrease in light intensity, as it passes through a unit length of a solution containing several absorbing species, depends on how much the light intensity decreases exponentially due to each indivival species. The fractional contribution to the decrease in light intensity by Ru(OEP)(Et 2 S) 2 , which is equivalent to the fraction of the total light absorbed by Ru(OEP)(Et 2S) 2 , will be given by  X3^C3[3]/(62[21^E3[3])  ^  4.99  and the total amount of light a absorbed by Ru(OEP)(Et2 S) 2 (in units of einsteins will be given by  Ie = X 3 4 8 , ^  4.100  Upon defining the constants  €2/€3  ^  4.101  c 1^I,A/V (constant only for any one particular apparatus) ^4.102  equation 4.100 can be written in the desired form:  199 Ia = ciPl( 1 - exp(-2.303(c2 1 [2] + €3'[3 ]))/([3 ] + 0[2 ])  ^  4.103  Now in the experiments described in section 3.5.1 it was seen that E 2 and e3 (actually the integrated forms of these parameters over the absorption region of interest; see below) differ only by a factor of around 0.6-0.8; furthermore, in all of the experiments described, a substantial proportion of the incident light was absorbed (e.g. for the most dilute reaction solution studied, [Ru(OEP)(Et2 S) 2 ] = 2.55x10 -5M and A525 n,  ",=*-  0.6 for a 1  cm cell; in this situation, 75% of the 525nm incident light would be absorbed). Under these conditions, the total amount of light absorbed by the solution will not change very much provided that [Ru] o remains constant. Therefore equation 4.103 should be well approximated by  Ia --z--  ci[3 ]( 1 - exPec2[Ru]o))/([3 ] + 0[2])  ^  4.104  where  c 2^2 .303f.;  ^  4.105  and  E ar =  (E2 t^E 3 ')12^  Equation 4.104 describes the amount of monochromatic light which would be  4.106  200 absorbed by Ru(OEP)(Et 2 S) 2 , in a solution containing both Ru(OEP)(Et 2 S) 2 and Ru(OEP)(Et 2S)(Et250), if the solution were in a rectangular reaction vessel, with the incident light striking the vessel normal to a wall. We now consider the real apparatus  setup, shown in figure 3.1 (p. 89), and consider qualitatively what changes need to be made to equation 4.104 as the experimental setup is made more complicated. The discussion considers the effects of each change in the apparatus on I abs , (equations 4.94 and 4.95) and X3 (equation 4.99) separately (see equation 4.100). Making the light source polychromatic will not affect the form of either  lab s ,  or X3,  but the molar extinction coefficients for 2 and 3 must be replaced by their equivalent forms integrated over all of the absorbing wavelengths, as was done in the data analysis of section 3.5.1 (equation 3.52, p. 142). Neither shaking the solution nor switching from a rectangular to a spherical vessel will affect X3, but both these changes will have effects on Ith .,. Switching to a spherical vessel means that the path length is no longer constant over the reaction solution; shaking the solution makes the determination of the solution surface area exposed to the light very difficult or impossible, and means that scattering effects due to the bubbles produced by the shaking of the solution will have to be contended with. Despite the expected complicated nature of l abs , in the real experimental system, one thing is certain: regardless of the experimental setup, any equation proposed to describe I abs , must behave the same under limiting conditions as the equation derived for the rectangular system; that is, it must drop to zero as either [Ri]. or 1 drops to zero (i.e. when no solution is present, the transmittance must be 100%), and it must approach a maximum value as either [Ru] o or 1 becomes very large (i.e. when the solution becomes  201 infinitely concentrated, the transmittance must be 0%). The latter means that c 1 still reflects the maximum attainable value of I., and although A is no longer a parameter which can be directly obtained, c 1 will still be a linear function of I,A/V. To summarize, in the real system I. should still be describable by a function of the form  It, = c 1 f[Ru] o [3]/([3] + tk[2])^  4. 107  where c 1 is a constant dependent only on the geometry of the experimental setup, the solution stirring rate, and on the intensity of the incident light, 1,G is the ratio of the molar absorption coefficients of Ru(OEP)(Et 2 S) 2 and Ru(OEP)(Et 2S)(Et 250) integrated over all absorbing wavelengths, and 4124, is a function of [Ru] o , which has a value of zero when [Ri], = 0, and approaches a constant value asymptotically as [Ru] o becomes very large. The equation given in section 3.5.1 (p. 142)  1 - exp(-10c 2 [Ru] o) + arctan(c2[Ru] o)^  (3.50) 4.108  was arrived at through trial and error; it has the disadvantage that its range is from 0 to 1 + (7/2) which makes the expression for the maximum value of I. somewhat cumbersome (=3irc 1 /2, instead of c 1 which would be more convenient); however, the equation proved easy to work with, and has only one adjustable parameter. Now, upon defining  V m =," Vmaxel  ^  4.109  202 and  kb. --..- vARti ] o) [02][PhC OOH]/OKno + [ 02] ) (Kin4 + [Ph C O OH]))  ^  4.110  equations 4.87 and 4.90 can be written in the form of equations 3.37 and 3.39 (p.139), respectively:  d[2]/dt = klEt 2 S0][3]/[Et2S]. - k3[Et2S]Pli[Et2S]o + kobs[Et2SO][3]NEt2S1([3] + 0[ 2 ]))^(3.37) 4.111  d[Et2 SO]/dt = kobs[3 ](2 [Et2SL - [Et2SO])MEt2SL([3] + 0[ 2 ])) -k4 (Et2 SON3V[Et2 S] o + k3 [Et2 S][2]/[Et2S] O^(3.39) 4.112  4.3.3. Modifications to the Proposed Mechanism  In sections 3.3 and 3.5.2.2, two possible modifications to the mechanism discussed so far (for the 0 2 -oxidation of Et2S catalyzed by Ru(OEP)(Et 2 S) 2) were proposed. In one of the modifications it was postulated that Ru(OEP)(Et 2 S)(Et2 S0) could be rearranging to the Ru(OEP)(Et 2 S)(Et250) isomer without dissociation of Et 2 SO into the bulk of the solution (this "internal rearrangement" is labelled k 14 , in figure 4.2, p.190). In the other modification it was postulated that perhaps the initial photoactivation step (k 5 in figure 4.2) involved a direct, light-induced metal-to-porphyrin d-ir . charge transfer, rather than a porphyrin 7-7 * transition, as implied in figure 4.2. The procedures used to derive rate laws for the alternative mechanisms parallel those described in detail in sections  203 4.3.1 and 4.3.2, so only a summary is provided here. In addition, some important features of the derived rate laws are considered.  4.3.3.1 Internal Rearrangement  If Ru(OEP)(Et 2 S)(Et2 SO) were isomerizing directly to Ru(OEP)(Et2S)(Et250), without intermediate dissociation of Et 2 SO into the bulk solution, then the rate of change in Ru(OEP)(Et2 S)(Et 250) would be governed by the differential equation:  d[2]/dt = k14.[ 1 8] + k_3 [Et2 S0][I 2 ] - k3 [2] k10 [4][17] + k_3 [Et2 S0][I 2 ] - k3 [2]  ^  4.113  The steady-state expression for [I 2 ] would be  [12] = ( k3 [2] + k4 [3]) /(k 3[Et2SO ] + 1(4[Et2s] )  ^  4.114  Substituting equation 4.114 into 4.113 yields, after several steps (cf. steps 4.70-4.73):  d[2]/dt = k ic,[4][I7] + k4Et 2 S0][3]/[Et2 S]. - k3 fEt2 SJ[2]/fEt2 S1,^4.115  Substituting expression 4.82 for k lo [I6 ][I7], and keeping in mind the definition of kobs (cf. equation 4.110), yields the counterpart to equation 4.111:  421/dt = klEt 2 SOPP[Et2S]. - k3[Et2S][2]/[Et2S].^kobs[3 ]/([3 ] + b[2])^4.116  204 For the alternative mechanism, the differential equation governing the appearance of Et 2 SO would be:  d[Et2SO]/dt = 0.5k 8 [PhC001-1]U 5l + k3[2] - k_3[Et2S0][I2]  ^  4.117  A series of substitutions analogous to those used for the previous derivations yield the expression:  d[Et2 SO]/dt = lcobs[3]/([3] + 0[2]) +k3 [Et2S][2]/[Et2 S] a - k4 [Et2 S0][3]/[Et 2S] o^4.118  which is the counterpart of equation 4.112. Equations 4.116 and 4.118 may appear somewhat similar to equations 4.111 and 4.112, but they are fundamentally different. The difference is best seen by considering the initial values of the differentials d[2]/dt and d[Et 2 S0]/dt for each of the mechanisms. For the dissociative mechanism,  (421/dt),. 0 = 0  ^  4.119  (d[Et2SO]/dt),. 0 = Robs^4.120  For the internal rearrangement mechanism,  205 (42}/d0t=o = kobs  ^  4.121  (d[Et2 S0]/dt),= 0 = 'cobs^  4.122  The important difference between the first and second set of initial rate equations is that the internal rearrangement mechanism predicts that [2] should begin to build up immediately, and independently from [Et2SO]. Because of this, the appearance of the integrated [Et 2 SO] vs. time curves are very different for the two models. Experimentally, the original mechanism (i.e. isomerization of Ru(OEP)(Et 2 S)(Et2S0) to Ru(OEP)(Et2 S)(Et250) via a five-coordinate intermediate) is found to fit the data much better (see also the discussion in section 3.5.2.2).  4.3.3.2 Photoactivation Via Metal to Porphyrin Charge Transfer -  -  The alternative mechanism proposed in section 4.3.3.1 affected the shape of the theoretical [Et2 SO] vs. time plots, but not the form of k obs . The alternative photoactivation mechanism, first illustrated in figure 3.5b, and reproduced in figure 4.3 for easy reference, affects only k obs . This allows a convenient shortcut to be employed in deriving the form of kobs . From equation 4.120 and figure 4.3,  (d[Et2 S0]/dt) t . 0 = 2kobs = k2 [PhCOOH][I 5 ]  therefore,  ^  4.123  206  R u ii (OE P) (Et S), (3)  Ru ii (OEP) .1"(Et ,S)')02 (I4)  (I4') Ru ni(OEP)*(Et 2 S),  k6.  [Ru m  ('5) (OEP)(Et 2S)2] + 02 PhCOOH  k7^  ^ HO )  kd  V [Ru III (OEP)(Et S)21 + PhC00 (I6)  0.5 02  0.5 H 2 0 2  r  kox  )11.  0.5 H 2 O  0.5 Et2 S 0.5 Et 2 SO  Figure 4.3. Alternative mechanism for the photochemical stage of the 02 -oxidation of Et 2 S catalyzed by Ru(OEP)(Et 2 S) 2 ; see text for details.  207 kobs = 0.5k4PhCOOHRI 5.1^  4.124  The steady-state conditions for [I 4], [4], and [I 5 ] are (recall that at t=0, [3] = [Ru].):  [14](k..5 , + 1c6 , ) = k_61I51  ^  4.125  Rvlik_s + k6 [0 2] = c i f[Ru] a^4.126  [I5 ](k_6 , + 1c7 [PhCOOH]) = 1c6[ 0 2][ 14] + k_6 114.1  ^  4.127  where f[Ru] 0 is the light absorption function (see equation 4.108). Combining expressions 4.125-4.127 yields, after rearrangement,  [IS ] = ci[02]f[Ru]j(k7(1C3 + [02])( 1C4 + [PhCOOH]))  4.128  where K no is still k_5/1c6 (equation 4.84), but K in4 is now defined as:  k_5 ,1(-6 , /(k7(k_5 , + kg))  4.129  Finally, substituting 4.128 into 4.124 yields:  Icobs = v m [PhCOOH][O2]f[Ru]iaK m3 + [ 02])(Km4 + [PhCOOH])) where v„, is now defined as 0.5c 1 .  4.130  208 CHAPTER 5 GENERAL CONCLUSIONS AND SUGGESTIONS FOR FURTHER STUDIES  Exposure to 0 2 or air of a benzene, toluene or methylene chloride solution containing PhCOOH and Ru(OEP)(RR'S) 2 (where R = methyl, ethyl or decyl, and R' = methyl or ethyl) results in selective oxidation of the axial ligands to the corresponding sulfoxides. A 1 11-nmr study of this reaction in CD 2 C1 2 for the case where RR'S = dms, indicated the presence of reaction intermediates. Attempts to identify these intermediates led to the synthesis and characterization, by 1 H-nmr, uv/vis and it spectroscopy, and CV, of a variety of Ru 11(OEP) and Ru m (OEP) complexes; of these, Ru(0EP)(dms)(dm5o), Ru(OEP)(dms) 2 + and Ru(OEP)(dms)(PhCOO) are found to be present during the 02 oxidation of Ru(OEP)(dms) 2 to Ru(OEP)(dmso)2. Based on the identities and properties of the reaction intermediates, a mechanism is proposed for the 0 2 -oxidation of Ru(OEP)(RR'S) 2 complexes, which can be broken down into three stages. In the first stage, 02 coordinates to the Ru ii (OEP)(dms) intermediate formed by dissociation of a dms ligand from Ru(OEP)(dms) 2 . This is followed by electron transfer from the metal to 02 ; the 02 - so formed is protonated by PhCOOH, yielding Ru m (OEP)(dms)(PhC00) and H0 2 . The protonated superoxoxide disproportionates to give 0.5 equivalents each of 0 2 and H 20 2 , and the latter oxidizes 0.5 equivalents of Et 2 S to Et2 SO. This first stage results in the oxidation of one mole of thioether for every two moles of Ru(OEP)(dms) 2 initially oxidized. In the second stage, a Ru m (OEP) species (possibly Ru m (OEP)(dms)(PhCOO)), which has had its oxidation  209 potential lowered by coordination of an anionic ligand, is oxidized to Ru"(OEP) by another species (possibly Re(OEP)(dms) 2 + PhC00 -), which has two neutral axial ligands. During the third stage, the Ru N (OEP) species is eventually converted to 0=Ru N (OEP)(dms), which then reacts with one equivalent of dms to produce Ru n (OEP)(dms)(dmso). One mole of 0=Ru iv (OEP)(dms) is produced for every two moles of Ru(OEP)(dms) 2 initially oxidized. The net reaction results in two moles of dms being oxidized to dmso for every mole of 02 consumed, with no net consumption of PhCOOH. The basic mechanism appears to be the same for the oxidation of coordinated Et2 S or decMS, regardless of whether the reaction is performed in CH 2 C1 2 , benzene or toluene; however, differences in detail are observed between systems. In the presence of excess thioether, solutions of Ru(OEP)(RR'S) 2 and PhCOOH, in CH2 C1 2 , benzene or toluene, catalyze the 0 2 -oxidation of free thioether to sulfoxide; however, under these conditions, light of wavelength above 480 nm is required for the reaction to proceed. The catalysis is quite efficient, with initial turnovers of up to 350 If' being observed under favourable circumstances (i.e. high [0 2 ] and [PhCOOH], but low [Ru]., so that a greater fraction of the metalloporphyrin molecules in the reaction vessel are exposed to the light). The catalytic system was studied in detail for the case in which RR'S = Et 2 S; again, the basic mechanism appears to be the same whether RR'S = dms, Et2 S or decMS. The stoichiometry of two moles of sulfoxide produced for every mole of 0 2 used was verified by monitoring a reaction simultaneously by gc and by oxygenuptake experiments. The light dependence observed under catalytic conditions is believed to arise from the fact that 02 coordination to the metal is inhibited by the presence of excess thioether; light is then required to provide energy for an otherwise highly  210 unfavourable outer-sphere electron transfer from the metal to 0 2 . After the initial electron transfer, the reaction is believed to follow the same course in both the stoichiometric and catalytic oxidations. A detailed kinetic analysis of the gas uptake data shows that, under the experimental conditions used, a maximum value for the initial rate is approached at [Ru]. > 2 mM, [02 ] > 0.14 M, and [PhC001-1] > 54 mM, respectively. The limit to the value of the initial rate appears to be imposed by the complete absorption by the reaction solution of the incident light by the metalloporphyrin species. The results of the kinetic analysis also suggest two other conclusions. The first conclusion is that whichever electronic transition is responsible for the observed photochemistry, it cannot have a lifetime lower than about 10 4 s (corresponding to a decay rate constant of 10 8 s'), in the absence of 02 . According to a qualitative molecular orbital picture, this suggests that the photochemical reaction is initiated by a metal-to-porphyrin charge-transfer transition (rather than a 7-7r* ring-centered transition), which is followed by transfer of the excited electron from the porphyrin ring to 0 2 . The second conclusion is that Ru(OEP)(Et2 S)(Et250), although seen to accumulate as Et2 S0 builds up with time, is outside of the catalytic cycle (i.e. it is not an intermediate in the reaction pathway). To our knowledge, photoactivated electron transfer has not been reported previously for ruthenium porphyrin systems; however, a neglected, possible light dependence probably explains the irreproducibility encountered in studies of the 0 2 oxidation of PPh 3 catalyzed by Ru(OEP)(PPh 3 ) 2 .' A light dependence could also explain the irreproducibility encountered in the apparently unrelated investigations of aldehyde decarbonylation catalyzed by Ru(Porp) complexes, although some data suggested that the  211 catalysis was a purely thermal process; 2 of note, Ru(OEP)(CO)L complexes (L = a neutral axial ligand) appear to be minor side products in both the stoichiometric and catalytic oxidations described in this thesis. When successfully initiated, the catalytic decarbonylation reactions were reported to be quite efficient, 2 and it may be worth reinvestigating these reactions to see if they behave more consistently under steady illumination. The possible commercial value of a catalyst which could selectively oxidize thioethers to sulfoxides was a consideration in the initial decision to investigate the reactivity of Ru(OEP)(RR'S) 2 complexes with 0 2 . Two general commercial applications can be envisioned for a catalyst which oxidizes thioethers to sulfoxides. The first is to oxidize simple thioethers such as dms, which are often waste products in industrial processes,' to the more valuable sulfoxides. The second commercial application would be to convert prochiral thioethers into chiral sulfoxides, which could then be used as chiral synthetic reagents in organic synthesis.' For the oxidation of simple thioethers, the system described in this thesis could probably be reasonably effective if efforts were made to optimize the geometry of the reaction apparatus for light absorption; however,the eventual decomposition of the catalyst would always be a problem. Furthermore, the cerium-based system of Riley et al. (see section 1.3) currently appears to show more promise, despite requiring high temperatures (100° C) and 0 2 pressures (14 bar). 3 As a model system for future developement of a chiral oxidant, the Ru(OEP)(RR'S) 2 /PhCOOH system is fundamentally flawed in that half of the thioether is oxidized by the achiral H2 0 2 . For chiral oxidation of thioethers, a chiral Ru(Porp) system based on the Ru(OCP)(0) 2 system previously studied in our laboratories (see section  212 1.2) 5 could be investigated. For such a system, care would have to be taken to avoid side reaction via the mechanism reported in this thesis. An especially intriguing direction for future study of the reaction of Ru(OEP)(RR'S) 2 complexes (and possibly other Ru ( (Porp) complexes) with 0 2 , in acidic media, would be to use the reaction as a probe, as part of a detailed investigation of the electronic structure of these complexes. In particular, it would be interesting to combine an investigation of the photochemistry described in this thesis with photophysical experiments, such as those recently reported by Holten et al., in which the photophysical properties of a variety of Ru(Porp) complexes were investigated by picosecond laser techniques.'  REFERENCES FOR CHAPTER 5 1. James, B. R.; Mikkelsen, S. R.; Leung, T. W.; Wiliams, G. M.; Wong, R. Inorg. Chim. Acta 1984, 85, 209. 2.a) Domazetis, G.; James, B. R.; Tarpey, B.; Dolphin, D. ACS Symp. Ser., 1981, 152, 243. b) Domazetis, G.; Tarpey, B.; Dolphin, D.; James, B. R. J. Chem. Soc., Chem. Commun. 1980, 939. c) Tarpey, B. M.Sc. Dissertation, The University of British Columbia, Vancouver, B. C., 1982. 3. Riley, D. P.; Smith, M. R.; Correa, P. E. J. Am. Chem. Soc. 1988, 110,177. 4. a) Pitchen, P.; Dunak, E.; Deshmukh, M. N.; Kagan, H. B. J. Am. Chem. Soc. 1984, 106, 8188. b) Mikolajcyk, M.; Drabowicz, J. Top. Stereochem. 1982, 13, 333. 5. a) James, B. R. Chem. Ind. 1992, 47, 245. b) Rajapakse, N. Ph.D. Dissertation, The University of British Columbia, Vancouver, B. C., 1990. 6. a) Tait, C. D.; Holten, D.; Barley, M. H.; Dolphin, D.; James, B. R. J. Am. Chem. Soc. 1985, 107, 1930. b) Levine, L. M. A.; Holten, D. J. Phys. Chem. 1988, 92, 714.  213 APPENDIX 1 QUICK BASIC PROGRAMS  This appendix lists all of the Quick Basic programs that were used for the data analyses discussed in chapter 3 of this thesis. In all cases the programs consist of one or more modules which were specifically written for the tasks performed in the thesis, and several generic modules obtained from "Numerical Recipes In Basic" (reference 6 in chapter 3). Only the parts of the programs tailored specifically for this thesis are included here. A complete list of the modules taken from Numerical Recipes, along with the chapter in which the modules can be found, is included after each program.  A1.1 UNFIT  This is a program for fitting an experimentally derived data set (x, y,  oy ) -  (where  ay is the uncertainty in y) to a straight line, y = a + bx. The program returns the best values of a and b, the value of x 2 given these values, and the goodness of fit parameter Q. In addition, the theoretical line and the experimental data points can be displayed graphically on the screen, and the theoretical points can be saved for future inclusion in a graphical print-out.  DECLARE SUB FIT (X!(), Y!(), NDATA!, SIG!(), MWT!, A!, B!, SIGA!, SIGB!, CHI2!, Q!) DECLARE SUB PLOT (XDATO, YDATO, XP(), YPO, NPT, NTHEOR, SIGO) 'Driver for routine FIT CLS LINE INPUT "Filename:", dum$  214 OPEN dum$ FOR INPUT AS #1 LINE INPUT #1, dum$ INPUT #1, NPT DIM X(NPT), Y(NPT), SIG(NPT) LINE INPUT #1, dum$ LINE INPUT #1, dum$ FOR I = 1 TO NPT INPUT #1, X(I), Y(I), SIG(I) NEXT I PRINT "If you wish to leave the first m data points out of the least squares" PRINT "calculation, input m at this point (m =0 to include all points):" INPUT M NDAT = NPT - M DIM XDEL(NDAT), YDEL(NDAT), SIGDEL(NDAT) NDEL = M + 1 FOR J = NDEL TO NPT XDEL(J - M) = X(J) YDEL(J - M) = Y(J) SIGDEL(J - M) = SIG(J) NEXT J FOR MWT = 0 TO 1 CALL FIT(XDELO, YDELO, NDAT, SIGDELO, MWT, A, B, SIGA, SIGB, CHI2, Q) IF MWT = 0 THEN PRINT "Ignoring standard deviation" ELSE PRINT "Including standard deviation" END IF PRINT " A = "; PRINT USING "#.#####—"; A; PRINT "^Uncertainty: "; PRINT USING "#.#####"'"; SIGA PRINT " B = "; PRINT USING "#.#####'""; B; PRINT "^Uncertainty: "; PRINT USING "#.#####"'"; SIGB PRINT " Chi-squared: "; PRINT USING "#.#####'"; CHI2 PRINT " Goodness-of-fit: "; PRINT USING "#.##'""; Q PRINT PRINT NEXT MWT PRINT "Do you want to see a plot of the data (y/n)" INPUT dum$  215 IF dum$ = "n" THEN END NTHEOR = 2 DIM XP(NTHEOR), YP(NTHEOR) XP(1) = 0 YP(1) = A PRINT XP(1); YP(1) XP(NTHEOR) = 2 * X(NPT) YP(NTHEOR) = A + B * XP(NTHEOR) PRINT XP(NTHEOR); YP(NTHEOR) INPUT "Press return to continue", dum$ CALL PLOT(X(), Y(), XP(), YP(), NPT, NTHEOR, SIG()) END  SUB PLOT (XDAT(), YDAT(), X(), YO, NDATA, NTHEOR, SIG()) DO SCREEN 2 CLS 2 VIEW PRINT 1 TO 4 LOCATE 1, 1 PRINT "Enter X1,X2 (X1=X2 to stop)" INPUT Xl, X2 IF X1 = X2 THEN EXIT SUB PRINT "Enter Y1,Y2" INPUT Yl, Y2 CLS VIEW (50, 35)-(550, 180) WINDOW (0, 0)-(500, 145) LINE (0, 0)-(500, 145), B DX = (X2 - X1) / 500 'X Units per pixel DY = (Y2 - Y1) / 145 'Y Units per pixel FOR K = 1 TO NDATA SX = INT((XDAT(K) - Xl) / DX) SY = INT((YDAT(K) - Y1) / DY) ERRY = INT(SIG(K) / DY) CIRCLE (SX, SY), 1 LINE (SX, SY + ERRY)-(SX, SY - ERRY) NEXT K FOR L = 1 TO NTHEOR ClX = INT((X(L) - X1) / DX) C1Y = INT((Y(L) - Y1) / DY) IF L < > 1 THEN LINE (C2X, C2Y)-(C1X, ClY) C2X = C1X C2Y = C1Y  216 NEXT L LOOP END SUB The following modules were incorporated, directly and without any modification, from "Numerical Recipes In Basic" into the program:  FIT (Chapter 14); GAMMLN, GAMMQ, GCF, GSER (Chapter 6).  The (x, y, ay) experimental data file should be in the ASCII format given by the following example:  NPT= 14 X,Y,SIG(Y) 5.934E-5,.0007805,2.90E-5 .00011868,.00083401,3.10E-5 .00029669,.0010711,2.98E-5 .0005934,.0015153,4.22E-5 .0007417,.001709,4.76E-5 .0014835,.0028049,7.81E-5 .0018543,.0033231,9.26E-5 .0037086,.0061133,1.70E-4 .0092715,.014638,4.08E-4 .01855,.029296,8.16E-4 .0371,.058381,1.63E-3 .05563,.086382,2.41E-3 .11126,0.17426,4.85E-3 .23179,.36055,1.00E-2 'DATA FOR K1 DETERMINATION; [Et2S]/P(1) vs [Et2S]  217 A1.2 POLFIT  This is a program for fitting an experimentally derived data set (x, y, a y) (where o y is the uncertainty in y) to a polynomial, using the method of singular value -  decomposition. The program first returns the diagonal values of the W matrix (see chapters 2 and 14 of numerical recipes), and prompts the user for the maximum tolerated value of the condition number. If this value is exceeded, the appropriate w i values are set to zero; in either case, the program then returns the best values of a, b, c... in y = a + bx +cx 2 +..., the value of x 2 given these values, and the goodness of fit parameter Q. In addition, the theoretical curve and the experimental data points can be displayed graphically on the screen, and the theoretical points can be saved for future inclusion in a graphical print-out.  DECLARE SUB SVDVAR (V!(), MA!, NP!, W!(), CVM!O, NCVM!) DECLARE SUB SVDFIT (X!(), Y!(), SIG!(), NDATA!, A!(), MA!, U!(), V!(), W!(), MP!, NP!, CHISQ!, FUNCS$, Q!) DECLARE SUB PLOT (XDATO, YDATO, X(), YO, NDATA, SIGO) 'Driver for routine SVDFIT CLS LINE INPUT "Filename?:", dum$ OPEN dum$ FOR INPUT AS #1 LINE INPUT #1, dum$ INPUT #1, NPT LINE INPUT #1, dum$ LINE INPUT #1, dum$ INPUT #1, NPOL DIM X(NPT), Y(NPT), SIG(NPT), A(NPOL), CVM(NPOL, NPOL) DIM U(NPT, NPOL), V(NPOL, NPOL), W(NPOL) LINE INPUT #1, dum$ LINE INPUT #1, dum$ FOR I = 1 TO NPT INPUT #1, X(I), Y(I), SIG(I) NEXT I  218 CALL SVDFIT(XO, Y(), SIG(), NPT, AO, NPOL, U(), V(), W(), MP, NP, CHISQ, "FPOLY", Q) CALL SVDVAR(VO, NPOL, NP, WO, CVMO, NPOL) PRINT "Polynomial fit:" FOR I = 1 TO NPOL PRINT "A("; I; ") ="; PRINT USING "#.#####"'"; A(I); PRINT " +-"; PRINT USING "#.#####'""; SQR(CVM(I, I)) NEXT I PRINT "Chi-squared"; PRINT USING "#.#####""; CHISQ PRINT "Goodness of fit"; PRINT USING "#.##"'", Q PRINT PRINT "Do you want to see a plot of the data (y/n)" INPUT dum$ IF dum$ = "y" THEN DIM XP(NPT), YP(NPT) FOR J = 1 TO NPT XP(J) = X(J) YP(J) = A(1) + X(J) * (A(2) + X(J) * A(3)) NEXT J CALL PLOT(XO, YO, XP(), YPO, NPT, SIG()) END IF PRINT "Do you want to save the theoretical points (y/n)?" INPUT dum$ IF dum$ = "y" THEN INPUT "Filename?", filename$ OPEN filename$ FOR OUTPUT AS #2 FOR I = 1 TO NPT WRITE #2, X(I), Y(I), SIG(I), XP(I), YP(I) NEXT I END IF END  SUB SVDFIT (X(), YO, SIG(), NDATA, AO, MA, U(), V(), W(), MP, NP, CHISQ, FUNCS$, Q) DIM B(NDATA), AFUNC(MA) FOR I = 1 TO NDATA IF FUNCS$ = "FPOLY" THEN CALL FPOLY(X(I), AFUNC(), MA) TMP = 1! / SIG(I) FOR J = 1 TO MA  219 U(I, J) = AFUNC(J) * TMP NEXT J B(I) = Y(I) * TMP NEXT I CALL SVDCMP(UO, NDATA, MA, MP, NP, W(), V()) PRINT "DIAGONAL OF MATRIX W" FOR K = 1 TO MA "; W(K) PRINT USING "#.##### NEXT K INPUT "HOW SMALL A FRACTION OF WMAX WILL YOU ACCEPT?", TOL WMAX = 0! FOR J = 1 TO MA IF W(J) > WMAX THEN WMAX = W(J) NEXT J THRESH = TOL * WMAX FOR J = 1 TO MA IF W(J) < THRESH THEN W(J) = 0! IF W(J) = 0! THEN PRINT "Resetting W(J)="; J; "equal to zero" NEXT J CALL SVBKSB(U(), W(), V(), NDATA, MA, MP, NP, BO, AO) CHISQ = 0! FOR I = 1 TO NDATA IF FUNCS$ = "FPOLY" THEN CALL FPOLY(X(I), AFUNCO, MA) SUM = 0! FOR J = 1 TO MA SUM = SUM + A(J) * AFUNC(J) NEXT J CHISQ = CHISQ + ((Y(I) - SUM) / SIG(I)) 2 NEXT I Q = GAMMQ(.5 * (NDATA - NPOL), .5 * CHISQ) ERASE AFUNC, B END SUB AAAA  A  The supprogram SVDFIT listed above was taken directly from "Numerical Recipes" with only minor modifications.  The subprogram PLOT was the same one used in the program UNFIT described earlier.  220 The following modules were incorporated, directly and without any modification, from "Numerical Recipes In Basic" into the program:  SVDVAR (Chapter 14); GAMMLN, GAMMQ, GCF, GSER (Chapter 6); SVDCMP, SVDVAR (Chapter 2).  The (x, y, cry ) experimental data file should be in the ASCII format given by the following example:  NPT= 9 NPOL= 3 X,Y,SIG(Y) .0005934,.0000393,3.72E-6 .0018543,.000085194,1.92E-6 .0037086,.00015811,2.89E-6 .0092715,.00047466,8.48E-6 .01855,.0011898,2.10E-5 .0371,.0035157,6.22E-5 .05563,.0070143,1.24E-4 .11126,.024116,4.27E-4 .23179,.096683,1.71E-3 DATA FOR FITTING [Et2S]"2/P(1) vs [Et2S]  221 A 1.3 ONEDMIN  This is the iterative program which was used to find the best value for Ica,„ in section 3.5.1 of the thesis. The user provides: 1) a set of experimentally derived data points (t, [Et 2SO], ffia,s01 ) (where aras01 is the uncertainty in [Et2SO] produced); 2) a set of initial conditions [Ru(OEP)(Et2 S)(Et250)] o = [A] (INIT), [Ru(OEP)(Et 2S) 2] 0 = [B] (INIT), [Et 2SO]" = [Et2SO] (INIT), [Et 2S] o = [Et2S] (INIT), t o = Xl; 3) a final time X2 to stop the integrator, and an estimate of an appropriate step size for the integrator; 4) a value for the integrated extinction coefficient ratio 0; 5) two initial guesses as to the value of Ic ob ,. Along with the best value of kobs , the program also returns the value of x2min •  DECLARE FUNCTION BRENT! (XDAT!O, YDAT!O, SIG!O, NPT!, YSTART!O, NVAR!, Xl!, X2!, AX!, BX!, CX!, DUM!, TOL!, XMIN!, H1) DECLARE SUB MNBRAK (XDAT!O, YDAT!O, SIG!(), NPT!, YSTART!O, NVAR!, Xl!, X2!, AX!, BX!, CX!, DUM!, H1) DECLARE SUB HUNT (XX!O, N!, X!, JLO!) DECLARE SUB ODEINT (YSTART!O, NVAR!, Xl!, X2!, EPS!, Hl!, HMIN!, NOK!, NBAD!, DUM1!, DUM2!) DECLARE SUB RATINT (XPO, YTHEORO, KOUNT, X, Y, DY) DECLARE FUNCTION RKCHI2 (W, XDATO, YDATO, SIG(), NPT, YSTARTO, NVAR, Xl, X2, HD COMMON SHARED KMAX, KOUNT, DXSAV, XP(), YP() COMMON SHARED KOBS, PSI, Et2S CIS NVAR = 4 DIM YSTART(NVAR), XP(200), YP(10, 200) INPUT "What is the initial time in seconds?", X1 INPUT "What is the final time in seconds?", X2 INPUT "[A] (INIT)?", YSTART(1) INPUT "[B] (INIT)?", YSTART(2) INPUT "[Et2SO] (INIT)?", YSTART(3) INPUT "[Et2S] (INIT)?", YSTART(4)  222 Et2S = YSTART(4) INPUT "Estimate PSI", PSI INPUT "Estimate the required stepsize for the integration sequence", H1 PRINT "Input a filename containing raw data for comparison" INPUT DUM$ OPEN DUM$ FOR INPUT AS #1 LINE INPUT #1, DUM$ INPUT #1, NPT DIM XDAT(NPT), YDAT(NPT), SIG(NPT) LINE INPUT #1, DUM$ LINE INPUT #1, DUM$ FOR I = 1 TO NPT INPUT #1, XDAT(I), YDAT(I), SIG(I) NEXT I PRINT "Input two trial values for kobs: a,b" INPUT AX, BX CALL MNBRAK(XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2, AX, BX, CX, DUM, H1) B = BRENT(XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2, AX, BX, CX, DUM, TOL, XMIN, H1) PRINT "Chi2 Min ="; B PRINT "kobs="; XMIN END FUNCTION BRENT (XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2, AX, BX, CX, DUM, TOL, XMIN, H1) ITMAX = 100 CGOLD = .381966# ZEPS = 1E-10 A =AX IF CX < AX THEN A =CX B = AX IF CX > AX THEN B =CX V = BX W=V X=V E = 0! FX = RKCHI2(X, XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2, H1) FV = FX FW = FX FOR ITER = 1 TO ITMAX PRINT ITER XM = .5 * (A + B) TOL1 = TOL * ABS(X) + ZEPS TOL2 = 2! * TOL1  223 IF ABS(X - XM) < = TOL2 - .5 * (B - A) THEN EXIT FOR DONE% = -1 IF ABS(E) > TOL1 THEN R = (X - W) * (FX - FV) Q = (X - V) * (FX - FW) P = (X - V) * Q - (X - W) * R Q = 2! * (Q - R) IF Q > 0! THEN P = -P Q = ABS(Q) ETEMP = E E=D DUM = ABS(.5 * Q * ETEMP) IF ABS(P) < DUM AND P > Q * (A X) AND P < Q * (B - X) THEN D=P/Q U=X+D IF U - A < TOL2 OR B - U < TOL2 THEN D = ABS(TOL1) * SGN(XM - X) DONE% = 0 END IF END IF IF DONE% THEN IF X > = XM THEN E=A-X ELSE E=B-X END IF D = CGOLD * E END IF IF ABS(D) > = TOL1 THEN U=X+D ELSE U = X + ABS(TOL1) * SGN(D) END IF FU = RKCHI2(U, XDATO, YDATO, SIG(), NPT, YSTARTO, NVAR, Xl, X2, H1) IF FU < = FX THEN IF U > = X THEN A =X ELSE B=X END IF V=W FV = FW W=X FW = FX X=U FX = FU  224 ELSE IF U < X THEN A=U ELSE B=U END IF IF FU < = FW OR W = X THEN V=W FV = FW W=U FW = FU ELSEIF FU < = FV OR V = X OR V = W THEN V=U FV =FU END IF END IF NEXT ITER IF ITER > ITMAX THEN PRINT "Brent exceed maximum iterations:: END XMIN = X BRENT = FX END FUNCTION  SUB DERIVS (X, YO, DYDXO) DYDX(1) = .7 * Y(3) * Y(2) / Et2S - .0374 * Y(4) * Y(1) / Et2S + KOBS * (Y(2) / (Y(2) + PSI * Y(1))) * (Y(3) / Et2S) DYDX(2) = -DYDX(1) DYDX(3) = KOBS * (2 - Y(3) / Et2S) * (Y(2) / (Y(2) + PSI * Y(1))) + .0374 * Y(4) * Y(1) / Et2S - .7 * Y(3) * Y(2) / Et2S DYDX(4) = -DYDX(3) END SUB  SUB HUNT (XXO, N, X, JLO) ASCND% = XX(N) > XX(1) IF JLO < = 0 OR JLO > N THEN JLO =0 JHI = N + 1 ELSE INC = 1 IF X > = XX(JLO) EQV ASCND% THEN  225 1 JHI = JLO + INC IF JHI > N THEN JHI = N + 1 ELSEIF X > = XX(JHI) EQV ASCND% THEN JLO = JHI INC = INC + INC GOTO 1 END IF ELSE JHI = JLO 2 JLO = JHI - INC IF JLO < 1 THEN JLO =0 ELSEIF X < XX(JLO) EQV ASCND% THEN JHI = JLO INC = INC + INC GOTO 2 END IF END IF END IF DO IF JHI - JLO = 1 THEN EXIT SUB JM = INT((JHI + JLO) / 2) IF X > XX(JM) EQV ASCND% THEN JLO = JM ELSE JHI = JM END IF LOOP END SUB  SUB MNBRAK (XDATO, YDATO, SIG(), NPT, YSTARTO, NVAR, Xl, X2, AX, BX, CX, DUM, H1) GOLD = 1.618034 GLIMIT = 100! TINY = 1E-20 FA = RKCHI2(AX, XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2, H1) FB = RKCHI2(BX, XDATO, YDATO, SIG(), NPT, YSTARTO, NVAR, Xl, X2, H1) IF FB > FA THEN DUM = AX AX = BX BX = DUM DUM = FB  226 FB = FA FA = DUM END IF CX = BX + GOLD * (BX - AX) FC = RKCHI2(CX, XDATO, YDAT(), SIGO, NPT, YSTART(), NVAR, Xl, X2, H1) DO IF FB < FC THEN EXIT DO DONE% = -1 R = (BX - AX) * (FB - FC) Q = (BX - CX) * (FB - FA) DUM = Q - R IF ABS(DUM) < TINY THEN DUM = TINY U = BX - ((BX - CX) * Q - (BX - AX) * R) / (2! * DUM) ULIM = BX + GLIMIT * (CX - BX) IF (BX - U) * (U - CX) > 0! THEN FU = RKCHI2(U, XDATO, YDATO, SIG(), NPT, YSTARTO, NVAR, Xl, X2, H1) IF FU < FC THEN AX = BX FA = FB BX = U FB = FU EXIT SUB ELSEIF FU > FB THEN CX = U FC = FU EXIT SUB END IF U = CX + GOLD * (CX - BX) FU = RKCHI2(U, XDATO, YDATO, SIG(), NPT, YSTARTO, NVAR, Xl, X2, H1 ELSEIF (CX - U) * (U - ULIM) > 0! THEN FU = RKCHI2(U, XDATO, YDATO, SIG(), NPT, YSTARTO, NVAR, Xl, X2, H1) IF FU < FC THEN BX = CX CX = U U = CX + GOLD * (CX - BX) FB = FC FC = FU FU = RKCHI2(U, XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2, H1) END IF ELSEIF (U - ULIM) * (ULIM - CX) > = 0! THEN U = ULIM )  227 FU = RKCHI2(U, XDATO, YDATO, SIG(), NPT, YSTARTO, NVAR, Xl, X2, H1) ELSE U = CX + GOLD * (CX - BX) FU = RKCHI2(U, XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2, H1) END IF IF DONE% THEN AX = BX BX = CX CX = U FA = FB FB = FC FC = FU ELSE DONE% = 0 END IF LOOP WHILE NOT DONE% END SUB  FUNCTION RKCHI2 (W, XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2, H1) KOBS = W DIM YCOPY(NVAR) FOR K = 1 TO NVAR YCOPY(K) = YSTART(K) NEXT K EPS = .0001 KMAX = 200 HMIN = 0 DXSAV = 1 CALL ODEINT(YSTARTO, NVAR, Xl, X2, EPS, H1, HMIN, NOK, NBAD, DUM, RKQC) FOR K = 1 TO NVAR YSTART(K) = YCOPY(K) NEXT K DIM YINT(NPT), YTHEOR(KOUNT), XTHEOR(KOUNT), XTABL(4), YTABL(4) FOR I = 1 TO KOUNT YTHEOR(I) = YP(3, I) XTHEOR(I) = XP(I) NEXT I JLO = 0 KPASS = KOUNT  228 FOR I = 1 TO NPT CALL HUNT(XTHEORO, KPASS, XDAT(I), JLO) FOR K = 1 TO 4 IF JLO < = KOUNT - 2 THEN XTABL(K) = XP(JLO - 2 + K) YTABL(K) = YTHEOR(JLO - 2 + K) ELSE XTABL(K) = XP(JLO - 3 + K) YTABL(K) = YTHEOR(JLO - 3 + K) END IF NEXT K CALL RATINT(XTABLO, YTABL(), 4, XDAT(I), Y, DY) YINT(I) = Y JLO = INT(JLO + KOUNT / NPT) NEXT I CHI2 = 0 FOR J = 1 TO NPT CHI2 = CHI2 + ((YDAT(J) - YINT(J)) / SIG(J)) 2 NEXT J RKCHI2 = CHI2 ERASE YINT, YTHEOR, YTABL, XTHEOR, XTABL END FUNCTION A  Of the subprograms and functions listed above, the following were taken directly from "Numerical Recipes" with only minor modifications:  BRENT, MNBRAK, (Chapter 10); HUNT (Chapter 3).  229 The following modules were incorporated, directly and without any modification, from "Numerical Recipes In Basic" into the program:  ODEINT, RKQC, RK4 (Chapter 15); RATINT (Chapter 3).  The (t, [Et2S0l, a[F_Azsoi) experimental data file should be in the ASCII format illustrated by the following example:  NPT= 12 X^Y^SIG (Y) 821,.0030894,.0004 1200,.0042814,.0004 1615,.0056192,.0004 2031,.0067806,.0004 2516,.0083214,.0004 2972,.0094714,.0004 3436,.010583,.0004 3835,.011614,.0004 4229,.0124036,.0004 5000,.0142396,.0004 5790,.015424,.0004 6261,.016413,.0004  A1.4 TWODMIN  This program is exactly analogous to ONEDMIN, but in this case tk is treated as an adjustable parameter, and the program iteratively seeks the values of both k ob , and 1,t/ for which X 2 is a minimum. Three initial guesses as to the value of the set (k ob „lk) are fed  230 into the program, and three (k ot,„1//) values for which x2 differs by less than 1% are returned.  DECLARE SUB HUNT (XX!0, N!, X!, JLO!) DECLARE FUNCTION AMOEB! (X(), NP, XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2, H1) DECLARE SUB ODEINT (YSTART!0, NVAR!, Xl!, X2!, EPS!, Hl!, HMIN!, NOK!, NBAD!, DUM1!, DUM2!) DECLARE SUB RATINT (XA!0, YA!O, N!, X!, Y!, DY!) DECLARE FUNCTION RKCHI2! (W, Z, XDAT!0, YDAT!0, SIG!(), NPT!, YSTART!O, NVAR!, Xl!, X2!, H1!) DECLARE SUB AMOEBA (P0, Y(), MP, NP, NDIM, FTOL, DUM, ITER, XDATO, YDATO, SIG(), NPT, YSTARTO, NVAR, Xl, X2, H1) COMMON SHARED KMAX, KOUNT, DXSAV, XP(), YPO COMMON SHARED KOBS, PSI, Et2S CLS NVAR = 4 NP = 2 MP = 3 FTOL = .0001 DIM YSTART(NVAR), XP(200), YP(10, 200), P(MP, NP), X(NP), Y(MP) INPUT "What is the initial time in seconds?", X1 INPUT "What is the final time in seconds?", X2 INPUT "[A] (INIT)?", YSTART(1) INPUT "[B] (INIT)?", YSTART(2) INPUT "[Et2SO] (INIT)?", YSTART(3) INPUT "[Et2S] (INIT)?", YSTART(4) Et2S = YSTART(4) INPUT "First guess at kobs,PSI?", P(1, 1), P(1, 2) INPUT "Second guess at kobs,PSI?", P(2, 1), P(2, 2) INPUT "Third guess at kobs,PSI?", P(3, 1), P(3, 2) INPUT "Estimate the required stepsize for the integration sequences", Hi NDIM = NP PRINT "Input a filename containing raw data for comparison" INPUT DUM$ OPEN DUM$ FOR INPUT AS #1 LINE INPUT #1, DUM$ INPUT #1, NPT DIM XDAT(NPT), YDAT(NPT), SIG(NPT) LINE INPUT #1, DUM$  231 LINE INPUT #1, DUM$ FOR I = 1 TO NPT INPUT #1, XDAT(I), YDAT(I), SIG(I) NEXT I FOR I = 1 TO MP FOR J = 1 TO NP X(J) = P(I, J) NEXT J Y(I) = AMOEB(XO, NP, XDATO, YDATO, SIG(), NPT, YSTARTO, NVAR, Xl, X2, H1) PRINT Y(I) NEXT I CALL AMOEBA(PO, Y(), MP, NP, NDIM, FTOL, DUM, ITER, XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2, H1) PRINT "Iterations:"; ITER PRINT PRINT "Vertices of final 2-D simplex and" PRINT "function values at the vertices:" PRINT PRINT " I X(I) Y(I) CHISQUARE" PRINT FOR I = 1 TO MP PRINT USING "###"; I; FOR J = 1 TO NP PRINT USING "##.#####""; P(I, J); NEXT J PRINT USING "##.#####''"; Y(I) NEXT I PRINT END  FUNCTION AMOEB (X(), NP, XDATO, YDATO, SIG(), NPT, YSTARTO, NVAR, Xl, X2, H1) IF X(1) < = 0 OR X(2) < = .1 OR X(2) > 1 THEN AMOEB = 10000 ELSE AMOEB = RKCHI2(X(1), X(2), XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2, H1) END IF END FUNCTION  232 SUB AMOEBA (P0, Y0, MP, NP, NDIM, FTOL, DUM, ITER, XDATO, YDATO, SIG(), NPT, YSTART(), NVAR, Xl, X2, H1) ALPHA = 1! BETA = .5 GAMMA = 2! ITMAX = 500 DIM PR(NDIM), PRR(NDIM), PBAR(NDIM) MPTS = NDIM + 1 ITER = 0 DO ILO = 1 IF Y(1) > Y(2) THEN IHI = 1 INHI = 2 ELSE IHI = 2 INHI = 1 END IF FOR I = 1 TO MPTS IF Y(I) < Y(ILO) THEN ILO = I IF Y(I) > Y(IHI) THEN INHI = IHI IHI = I ELSEIF Y(I) > Y(INHI) THEN IF I < > IHI THEN INHI = I END IF NEXT I RTOL = 2! * ABS(Y(IHI) - Y(ILO)) / (ABS(Y(IHI)) + ABS(Y(ILO))) IF RTOL < FTOL THEN ERASE PBAR, PRR, PR: EXIT SUB IF ITER = ITMAX THEN PRINT "Amoeba exceeding maximum iterations.": EXIT SUB ITER = ITER + 1 FOR J = 1 TO NDIM PBAR(J) = 0! NEXT J FOR I = 1 TO MPTS IF I < > IHI THEN FOR J = 1 TO NDIM PBAR(J) = PBAR(J) + P(I, J) NEXT J END IF NEXT I FOR J = 1 TO NDIM PBAR(J) = PBAR(J) / NDIM PR(J) = (1! + ALPHA) * PBAR(J) - ALPHA * P(IHI, J)  233 NEXT J YPR = AMOEB(PRO, NDIM, XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2, H1) PRINT "YPR= ", YPR IF YPR < = Y(ILO) THEN FOR J = 1 TO NDIM PRR(J) = GAMMA * PR(J) + (1! - GAMMA) * PBAR(J) NEXT J YPRR = AMOEB(PRRO, NDIM, XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2, H1) PRINT "YPRR= ", YPRR IF YPRR < Y(ILO) THEN FOR J = 1 TO NDIM P(IHI, J) = PRR(J) NEXT J Y(IHI) = YPRR ELSE FOR J = 1 TO NDIM P(IHI, J) = PR(J) NEXT J Y(IHI) = YPR END IF ELSEIF YPR > = Y(INHI) THEN IF YPR < Y(IHI) THEN FOR J = 1 TO NDIM P(IHI, J) = PR(J) NEXT J Y(IHI) = YPR END IF FOR J = 1 TO NDIM PRR(J) = BETA * P(IHI, J) + (1! - BETA) * PBAR(J) NEXT J YPRR = AMOEB(PRRO, NDIM, XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2, H1) PRINT "YPRR= ", YPRR IF YPRR < Y(IHI) THEN FOR J = 1 TO NDIM P(IHI, J) = PRR(J) NEXT J Y(IHI) = YPRR ELSE FOR I = 1 TO MPTS IF I < > ILO THEN FOR J = 1 TO NDIM PR(J) = .5 * (13 (I, J) + P(ILO, J))  234 P(I, J) = PR(J) NEXT J Y(I) = AMOEB(PRO, NDIM, XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2, H1) PRINT "Y("; I; ")=", Y(I) END IF NEXT I END IF ELSE FOR J = 1 TO NDIM P(IHI, J) = PR(J) NEXT J Y(IHI) = YPR END IF PRINT ITER LOOP END SUB  SUB DERIVS (X, Y(), DYDXO) DYDX(1) = .7 * Y(3) * Y(2) / Et2S - .0374 * Y(4) * Y(1) / Et2S + KOBS * (Y(2) / (Y(2) + PSI * Y(1))) * (Y(3) / Et2S) DYDX(2) = -DYDX(1) DYDX(3) = KOBS * (2 - Y(3) / Et2S) * (Y(2) / (Y(2) + PSI * Y(1))) + .0374 * Y(4) * Y(1) / Et2S - .7 * Y(3) * Y(2) / Et2S DYDX(4) = -DYDX(3) END SUB  SUB HUNT (XXO, N, X, JLO) ASCND% = XX(N) > XX(1) IF JLO < = 0 OR JLO > N THEN JLO =0 JHI = N + 1 ELSE INC = 1 IF X > = XX(JLO) EQV ASCND% THEN 1 JHI = JLO + INC IF JHI > N THEN JHI = N + 1 ELSEIF X > = XX(JHI) EQV ASCND% THEN JLO = JHI INC = INC + INC  235 GOTO 1 END IF ELSE JHI = JLO 2 JLO = JHI -INC IF JLO < 1 THEN JLO = 0 ELSEIF X < XX(JLO) EQV ASCND% THEN JHI = JLO INC = INC + INC GOTO 2 END IF END IF END IF DO IF JHI - JLO = 1 THEN EXIT SUB JM = INT((JHI + JLO) / 2) IF X > XX(JM) EQV ASCND% THEN JLO = JM ELSE JHI = JM END IF LOOP END SUB  FUNCTION RKCHI2 (W, Z, XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2, H1) KOBS = W PSI = Z DIM YCOPY(NVAR) FOR K = 1 TO NVAR YCOPY(K) = YSTART(K) NEXT K EPS = .0001 KMAX = 200 HMIN = 0 DXSAV = 1 CALL ODEINT(YSTARTO, NVAR, Xl, X2, EPS, H1, HMIN, NOK, NBAD, DUM, RKQC) FOR K = 1 TO NVAR YSTART(K) = YCOPY(K) NEXT K DIM YINT(NPT), YTHEOR(KOUNT), XTHEOR(KOUNT), XTABL(4), YTABL(4)  236 FOR I = 1 TO KOUNT YTHEOR(I) = YP(3, I) XTHEOR(I) = XP(I) NEXT I JLO = 0 KPASS = KOUNT FOR I = 1 TO NPT CALL HUNT(XTHEOR(), KPASS, XDAT(I), JLO) FOR K = 1 TO 4 IF JLO < = KOUNT - 2 THEN XTABL(K) = XP(JLO - 2 + K) YTABL(K) = YTHEOR(JLO - 2 + K) ELSE XTABL(K) = XP(JLO - 3 + K) YTABL(K) = YTHEOR(JLO - 3 + K) END IF NEXT K CALL RATINT(XTABLO, YTABLO, 4, XDAT(I), Y, DY) YINT(I) = Y JLO = INT(JLO + KOUNT / NPT) NEXT I CHI2 = 0 FOR J = 1 TO NPT CHI2 = CHI2 + ((YDAT(J) - YINT(J)) / SIG(J)) 2 NEXT J RKCHI2 = CHI2 ERASE YINT, YTHEOR, YTABL, XTHEOR, XTABL END FUNCTION A  Of the subprograms and functions listed above, the following were taken directly from "Numerical Recipes" with only minor modifications:  AMOEBA (Chapter 10); HUNT (Chapter 3).  237 The following modules were incorporated, directly and without any modification, from "Numerical Recipes In Basic" into the program:  ODEINT, RKQC, RK4 (Chapter 15) RATINT (Chapter 3)  The (t, [Et2 SO], arEbsol) experimental data file should be in the same format as that required by the ONEDMIN program.  A1.5 ODEGRPH  This is a program which can be used to display graphically the results of a numerical integration of the equations 3.37-3.40 (see section 3.5.1). The user provides: 1) a set of experimentally derived data points (t, [Et 2 SO], 0- rEt2s0); 2) a set of initial -  conditions [Ru(OEP)(Et2S)(Et250)]. = [A] (INIT), [Ru(OEP)(Et 2 S) 2]. = [B] (INIT), [Et2 SO] a = [Et2SO] (INIT), [Et2S]. = [Et2S] (INIT), t o = Xl; 3) a final time X2 to stop the integrator, and an estimate of an appropriate step size for the integrator; 4) a value for the integrated extinction coefficient ratio ik; 5) a value for k obs . Note that this program does not find the best values of kob , as do the previous two; this program simply integrates equations 3.37-3.40 once, using the kob , and b values provided. However, the program allows any one of the generated concentration vs. time data pairs to be displayed graphically on the screen; in the case of [Et2 SO] vs. t, the experimentally derived data set  238 will be displayed along with the theoretical curve. Also, the program provides the opportunity of saving the theoretical [Et 2 SO] vs. t data set, for later inclusion in a graphical print-out.  DECLARE SUB RKPLOT (YSTART!O, YCOPY!O, Xl!, X2!, XDAT!O, YDAT!O, SIG!(), NPT, NVAR!) DECLARE SUB PLOT (XDAT!(), YDAT!(), X!(), Y!(), NDATA!, NTHEOR!, SIG!()) DECLARE SUB ODEINT (YSTART!O, NVAR!, Xl!, X2!, EPS!, Hl!, HMIN!, NOK!, NBAD! , DUM1 ! , DUM2 !) COMMON SHARED KMAX, KOUNT, DXSAV, XP(), YPO COMMON SHARED KOBS, PSI, Et2S DO CLS DIM XP(200), YP(10, 200) NVAR = 4 DIM YSTART(NVAR) DIM YCOPY(NVAR) INPUT "What is the initial time in seconds?", X1 INPUT "What is the final time in seconds?", X2 INPUT "[A] (INIT)?", YSTART(1) INPUT "[B] (INIT)?", YSTART(2) INPUT "[Et2SO] (INIT)?", YSTART(3) INPUT "[Et2S] (INIT)?", YSTART(4) FOR K = 1 TO NVAR YCOPY(K) = YSTART(K) NEXT K PRINT "Input a filename containing raw data for comparison" INPUT DUM$ OPEN DUM$ FOR INPUT AS #1 LINE INPUT #1, DUM$ INPUT #1, NPT DIM XDAT(NPT), YDAT(NPT), SIG(NPT) LINE INPUT #1, DUM$ LINE INPUT #1, DUM$ FOR I = 1 TO NPT INPUT #1, XDAT(I), YDAT(I), SIG(I) NEXT I DO CALL RKPLOT(YSTARTO, YCOPYO, Xl, X2, XDATO, YDATO, SIG(), NPT,  239 NVAR) PRINT "Do you want to do further analysis on this data set (y/n)?" INPUT DUM$ IF DUM$ = "n" THEN EXIT DO LOOP PRINT "Any other data you wish to analyse (y/n)?" INPUT DUM$ IF DUM$ = "n" THEN END ERASE XP, YP, XDAT, YDAT, SIG, YSTART, YCOPY CLOSE #1 LOOP END  SUB DERIVS (X, Y(), DYDXO) DYDX(1) = .7 * Y(3) * Y(2) / Et2S - .0374 * Y(4) * Y(1) / Et2S + KOBS * (Y(2) / (Y(2) + PSI * Y(1))) * (Y(3) / Et2S) DYDX(2) = -DYDX(1) DYDX(3) = KOBS * (2 - Y(3) / Et2S) * (Y(2) / (Y(2) + PSI * Y(1))) + .0374 * Y(4) * Y(1) / Et2S - .7 * Y(3) * Y(2) / Et2S DYDX(4) = -DYDX(3) END SUB SUB RKPLOT (YSTARTO, YCOPYO, Xl, X2, XDATO, YDATO, SIGO, NPT, NVAR) DO DO INPUT "Estimate kobs", KOBS INPUT "Estimate PSI", PSI Et2S = YSTART(4) EPS = .0001 INPUT "Estimate the required stepsize", H1 HMIN = 0! KMAX = 200 DXSAV = (X2 - Xl) / (X2 - X1) CALL ODEINT(YSTARTO, NVAR, Xl, X2, EPS, H1, HMIN, NOK, NBAD, DUM, RKQC) PRINT "Successful steps:^"; NOK PRINT "Bad steps:^"; NBAD PRINT "Stored intermediate values:"; KOUNT PRINT "Press return to continue" INPUT DUM$ PRINT "^t^[A]^[B]^[Et2S0]^[Et2S]^,, FOR I = 1 TO KOUNT  240 PRINT USING "####.# "; XP(I); PRINT USING "#.####"' "; YP(1, I); YP(2, I); YP(3, I); YP(4, I) NEXT I FOR K = 1 TO NVAR YSTART(K) = YCOPY(K) NEXT K PRINT "Do you wish to try another value of kobs (y/n)?" INPUT FLAG$ IF FLAG$ = "n" THEN EXIT DO LOOP PRINT "Do you wish to see a plot of the data (y/n)?" INPUT FLAG$ DO IF FLAG$ = "n" THEN EXIT DO PRINT "Which variable? (Input as a number 1-4)" INPUT VAR# DIM YTHEOR(KOUNT) FOR I = 1 TO KOUNT YTHEOR(I) = YP(VAR#, I) NEXT I CALL PLOT(XDATO, YDATO, XP(), YTHEOR(), NPT, KOUNT, SIG()) SCREEN 0 PRINT "Do you wish to save the calculated data set (y/n)?" INPUT FLAG$ IF FLAG$ = "y" THEN INPUT "Document to be saved:", DUM$ OPEN DUM$ FOR OUTPUT AS #2 FOR I = 1 TO KOUNT WRITE #2, XP(I), YTHEOR(I) NEXT I CLOSE #2 END IF PRINT "Do you wish to try another variable? (y/n)" INPUT FLAG$ ERASE YTHEOR LOOP PRINT "Do you wish to plot another value of kobs (y/n)?" INPUT FLAG$ IF FLAG$ = "n" THEN EXIT DO LOOP END SUB  The subprogram PLOT was the same one used in the program UNFIT described  241 earlier.  The following modules were incorporated, directly and without any modification, from "Numerical Recipes In Basic" into the program:  ODEINT, RKQC, RK4 (Chapter 15).  The (t, [Et 2 SO], cr[Ekso) experimental data file should be in the same format as that required by the ONEDMIN program.  242 APPENDIX 2 RESULTS OF STOPPED-FLOW EXPERIMENTS A2.1 Experiments Carried Out Using Light of 400.5 nm Wavelength  The two tables that follow give the numerical values of the parameters a t , (3 1 'y i , used to obtain the data points in figures 3.15 and 3.16. Following each table are the relative absorbance vs. time raw data plots (corrected for a non-level baseline; see section A2.3) to which the equation  A  =  al + flie-(yit)  was fitted, to obtain each set of a t , fi t , 7 1 values. For each experiment, the relative absorbance change was monitored over a period of 100 ms; the first four points of every experiment appear to be within the dead time of the instrument, and were neglected in the fit. The initial concentration of Ru(OEP)(Et 2 SO) 2 in each case was (3.44 + 0.07)x10' M (note: all of the concentrations reported in this appendix take into account the 50% dilution in the stopped-flow reaction chamber).  243 A2.1.1 Experiments Carried Out Using a Constant [Et 2 SO] of 1.18 ± 0.03 mM  Relative uncertainty in [Et 2S] for each experiment .--- 1-2%. 200 Data points were collected in the 0-200 ms time range.  Graph #^[Et2S] (M)  ^  al  ^  a,^71 (s  -1  A2.1.1.1  5.93x10-5  -0.009  0.076  48.2  A2.1.1.2  1.19x10  -0.050  0.142  48.3  A2.1.1.3  2.97x10-4  -0.024  0.277  55.0  A2.1.1.4  5.93x104  -0.152  0.392  67.4  A2.1.1.5  7.42x10  -0.123  0.434  72.6  A2.1.1.6  1.48x10-3  -0.171  0.529  88.1  A2.1.1.7  1.85x10-3  -0.154  0.558  92.3  A2.1.1.8  3.71x10-3  -0.148  0.607  108  A2.1.1.9  9.27x10-3  -0.153  0.633  123  A2.1.1.10  1.85x10-2  -0.169  0.633  130  A2.1.1.11  3.71x10-2  -0.174  0.636  134  A2.1.1.12  5.56x102  -0.179  0.644  133  A2.1.1.13  0.111  -0.176  0.639  137  A2.1.1.14  0.231  -0.176  0.643  139  )  2 44  0.07  2..), 0.05 z 0  ,2 0.03 0  -  cI) 0.01 —0.01 0.00  ■  0.01  0.02  0.03  0.04^0.05^ Time (s)  0.01^0.02  0.03^0.04^0.05  0.06  0.06  0.07  0.08  0.09  0.10  0.07  0.08  0.09  0.10  (s) Time (s)  A2.1.1.3  0.08 Time (s)  0.09  0 10 .  245  0.20 0.16 A2A.1.4  G 0.12 L.,  0.08 -  ,n  0.04 -  0  ¢  0.00 45.-0.04 a) -0.08 -0.12 -0A6 ^ 0.00  0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08^0.09^0.10 Time (s)  0.28 0.22 A2.1.1.5  V  g 0  .0  0.16 -  2 0.10  A  -  0.04 -  0.02  -0.08 -0.14 ^ 0.00  0.01^0.02^0.03^0.04  ■^1^1^1^1 0.05^0.06^0.07^0.08^0.09  0.10  Time (s)  0.28 A2.1.1.6  c 0.20 c.., v)  0.12  -  0.04 -0.12 -0.20 ^ 0.00  0.01^0.02^0.03  ^  I^I^I^I^r^r  0.04^0.05^0.06^0.07^0.08^0.09 Time (s)  0.10  246  0.38 0.30 cu 0.22 -  to .o c.  u) 0.14 -  0.06 Z-0.02 -  0.10  -  -0.18 ^ 0.00^0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08  0.09^0.10  Time (s) 0.38 0.30 -  0)  2 0  A2A.L8  0.22 0.14-  V > 0.06 .7:5' 17) -0.02 -0.10 -0.18 ^ 0.00  0.01^0.02^0.03  ^  7  0.04^0.05^0.06^0.07^0.08^0.09  0.10  Time (s)  A2.1.1.9  i.1)) 0.28 0 0) L. 0  0.20-  rn  0.12 a) co  0.04 -  cd-0.04 -0.12 -0.20 ^ ^ ^ 0.00 0.01^0.02 0.03^0.04^0.05^0.06^0.07^0.08^0.09 0.10 Time (s)  247 0 44 0.36-m 0.28 -^  A2.1.1.10  0.20 0  4D  ¢ 0.12 -  -0.12 -0.20 ^ 0.00 ^0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08^0.09  0.10  Time (s) 0.44 0.36 ,c), 0.28 -  A2.1.1.11  .  cis L., 0 (,)  0.20 0.12 -  a)  0.04  air 713  -0.12 -0.20 -0.00  0.01^0.02  0.03^0.04^0.05^0.06^0.07^0.08^0.09  0.10  Time (s) 0.44 0.36  z)) 0.28 -  A2.1.1.12  0  as -a  0.20 -  0  0.12 ar  0.04  Tu c4-0.04 -0.12 -0.20 0.00  I^ I^ I^  I^ I^ I  0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08^0.09 Time (s)  0.10  248 0.44 0.36 -1. 41) ,  0.28 -  A2.1.1.13  a. 0.200 42  0.12  0.04 m Tu co-0.04 -0.12 -0.20 ,^I^I^I^I^I^i^I 0.00^0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08  0.09^0.10  Time (s) 0.44 0.36 4) 0  0.28 -^  A2.1.1.14  0.20 0  -at 0.12 a) 0.04  -  co-0.04 -0.12 -0.20 ,^1^,^I^I^I^I^I^I ^ 0.00^0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08^0.09 0.10 Time (s)  249 A2.1.2 Experiments Carried Out Using a Constant [Et 2SO] of 17.7 ± 0.2 mM  Relative uncertainty in [Et 2 S] for each experiment ....-- 1-2%. 400 data points were collected in the 0-100 ms time range.  Graph #  [Et2S] (M)  cri  01  71 (s 4 )  A2.1.2.1  5.93x104  -0.034  0.057  39.2  A2.1.2.2  7.42x10  -0.023  0.069  38.3  A2.1.2.3  1.48x10-3  -0.049  0.121  42.3  A2.1.2.4  1.85x10-3  -0.079  0.143  43.1  A2.1.2.5  3.71x10-3  -0.097  0.232  51.6  A2.1.2.6  9.27x10-3  -0.128  0.403  64.7  A2.1.2.7  1.86x10-2  -0.088  0.539  82.7  A2.1.2.8  3.71x10-2  -0.188  0.597  93.6  A2.1.2.9  5.57x10-2  -0.176  0.617  103  A2.1.2.10  0.111  -0.179  0.654  113  A2.1.2.11  0.232  -0.198  0.677  122  A2.1.2.12  0.464  -0.178  0.662  126  250  0  F. 0 COI  0 .01 0.00 -  -0.01  d  -  -0.03 -  0.01  0.02  0.03  0.04^0.05^0.06  0.07  0.08  0.09  0.10  0.07  0.08  0.09  0.10  0.07  0.08  0.09  0.10  Time (s) 0.05 ^ 0.04 0.03 tQ A  0.02-  0  0.01 cis  0.00  7.) s:4-0.01 -0.02 -0.03 0.00  0.01  0.02  0.03  0.04^0.05^0.06 Time (s)  0.07 0.05 0  A 0.03 0  0.01 -  a) -0.03 -0.05 0.00  0.01^0.02^0.03^0.04^0.05^0.06 Time (s)  251  4.) U  0.02 -  ct i.  2 0.00 " -0.02 )  -0.04 -  -0.08 ^ 0.00^0.01^0.02^0.03^0.04^0.05^0.06  0.07^0.08^0.09  0.10  0.07  0.10  Time (s)  C.) 16  tel  0.06 0.02 -  -0.06 -0.10 ^ 0.00^0.01^0.02^0.03^0.04^0.05^0.06  0.08  0.09  Time (s) 0.26 0.20 U ca  A2.1.2.6 0.14 0.08  a) 0.02 a)-0.04  --  -0.10 -0.16 ,^I^I^I^I 0.00^0.01^0.02^0.03^0.04^0.05^0.06 Time (s)  0.07  0.08  0.09  0.10  252 0.44 0.38 a) 0.32 0 C 0.26 -  A2.1.2.7  A  0.20 A a) 0.14 ccs 0.08 T.) C4 0.02 -0.04 4~••■•■■•^  -0.10^ 0.00^0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08^0.09  0.10  Time (s) 0.40 0.30 A2.1.2.8  0  0.20 L  0  0.10 a) 0.00 -0.10 -0.20 ^ 0.00  I^I^I^I^I^  I^I  0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08^0.09^0.10 Time (s)  0.40 0.30 -  A2.1.2.9  0  0  0.20 0  a)  0.10 -  z 0.00 -0.10 Inwp■mmi...1111.10.^  -0.20 ^1^, 1^ ,^,^, 0.00^0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08^0.09 Time (s)  0.10  •  253  0.40 A2.1.2.10  0.30 -  0.20 0.10 0.00 - 0.10 - 0.20 0.00  0.01  0.02^0.03^0.04^0.05^0.06  0.07  0.08  0.09  0.10  Time (s) 0.44 0.34 a) U C 0.24 ms  c.  cn  A2.1.2.11  0.14 -  a) 0.04 > es 17)-0.06 -  es  - 0.16 - 0.26 ^ ^ 0.10 0.00^0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08^0.09 Time (s)  0.38 a.) c) as  0.28 -  • m  0.18 -  A2.1.2.12  a) 0.08 73-0.02  rx  -0.12 - 0.22 0.00^0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08^0.09^0.10 Time (s)  254 A2.2 Experiments Carried Out Using Light of 402.8 nm Wavelength  The table that follows gives the numerical values of the parameters a 2 , 02 7 2 , used to obtain the data points in figure 3.18. Following the table are the relative absorbance vs. time raw data plots (corrected for a non-level baseline; see section A2.3) to which the equation  A = a2 + 132e-(72t)  was fitted, to obtain each set of a2 , 13 2 , 72 values. For each experiment, the relative absorbance change was monitored over a period of 100 s. The initial concentration of Ru(OEP)(Et 2 SO) 2 in each case was (3.44 + 0.07)x10 -6 M.  255 A2.2.1 Experiments Carried Out Using a Constant [Et 2SO] of 1.18 ± 0.03 mM Relative uncertainty in [Et2 S] for each experiment ..-- 1-2%. 400 data points were collected in the 0-100 s time range.  Graph #  [Et2s ] (M)  a2  o2  72 (5-1  A2.2.1.1  5.93x104  0.0344  0.0090a  0.47a  A2.2.1.2  1.85x10'  0.0073  0.0404  0.251  A2.2.1.3  3.71x10-3  -0.059  0.0870  0.183  A2.2.1.4  9.27x10-3  -0.093  0.181  0.104  A2.2.1.5  1.86x10-2  -0.127  0.289  0.0706  A2.2.1.6  3.71x10-2  -0.086  0.391  0.0549  A2.2.1.7  5.56x10-2  -0.139  0.441  0.0489  A2.2.1.8  0.111  -0.180  0.513  0.0432  A2.2.1.9  0.231  -0.185  0.556  0.0414  a) The calculated uncertainites in these values are about 10%; for the remaining 02 and 'Y2 values, the calculated uncertainties were about 1 %.  )  •^  ^  256  A2.2.1.1 0.04  0^ab^0  08  °6 6 8 00^ O  0  o  00,^o°  ^0c  0 % o o^  V • 6"---51  :a.  00 °^a? 276 ^ B$ 4,^a, .00 0 6,  O.^  %0 00  o TO^ 059 %o tr.%^0.,0  0 ,L"--°----U , 0°^'0^  0  °^  00  0  o * OS 9^*('  ^?moo 0 o °°<,^op. .° CO^ ^° ' 4 ^:ofto^0  0.03 ^ ^ ^ ^ 0.00 20.00 40.00 60.00^80.00 100.00 Time (s)  0.00  ^  40.00^60.00  ^  100.00  Time (s)  0.01 a) ro  -  O  .0 -ra —0.03 -  ro  —0.05 -  - 0.07 0.00  60.00 Time (s)  ^  100.00  • 257  0.08 0  g 0.03  -  0  4:1  d  -0.02  -  Tu c4 -0.07 -  -0.12 0.00  20.00  40.00^60.00  80.00  100.00  Time (s) 0.15 0.10 co  0.05  A  c.  A2.2.1.5  -  0 • 0  a  0.00  -  -a)  0.05 -  -0.10 16.1■4•11amelowileMINIIIMMONERONWIMINO)10  -0.15 ^ ^ ^ ^ 0.00 20.00 40.00^60.00 80.00 100.00 Time (s) 0.30 0.25 a) o 0.20 aro 0.15 o) -  N  0.10 -  •  0.05  C4  0.00 -  a  A2.2.1.6  -  -0.05 -0.10 ^ 0.00  •11  20.00  40.00^60.00 Time (s)  80.00  100.00  •  258 0.30 0.25 0.20 -  U  A2.2.1.7  0.15 s.  0.10  C/  -tt •  -  0.05 0.00 -  73  -.05-0.10 - 0.15 ^ 0.00  20.00  ^  40.00  ^  60.00  ^  80.00  ^  100.00  Time (s)  40.00^60.00  80.00  100.00  80.00  100.00  Time (s)  0.30 a) 0.20 -  m 0 ce) .G1  0.10 -  a) co  0.00 -  V rx - 0.10 - 0.20 0.00  20.00  40.00^60.00 Time (s)  259 A2.3 Blank Experiments 0.04  Blank 2.1.1  0.03 -  A  0.02 431bOIS.t. Ob  0%.lb 6f/t45 6% ,  C'Z'D  gbc.001%  0.01 -  0.00 -  -0.01 0.00  0.01  0.02  0.03  0.04^0.05^0.06  0.07^0.08^0.09  0.10  Time (s) 0.02  Blank 2.1.2  0.01 -  0.00  -  -0.01 -  44,444SN49310 e^°^ 40t9 40^° s  •^ 7094: s..^  te<4et9°- 4e,  '^ ° %o Ake1111%°,84'9  toi  -0.02 0.00  0.01^0.02^0.03  0.04^0.05^0.06 Time (s)  0. 07  0. 08  0.09  0.10  260 APPENDIX 3 RESULTS OF OXYGEN UPTAKE EXPERIMENTS A3.1 First Data Set  The three tables that follow give the numerical values of the data points shown in figures 3.23 and 3.25. Following each table are the [Et 2 SO] vs. time raw data plots which gave rise to each data point in figures 3.23 and 3.25.  261 A3.1.1 [Ru], Dependence Studies [PhCOOH] = 24.4 + 0.1 mM [02 ] = 7.63 ± 0.07 mM [Et2 S] = 0.742 + 0.006 M Shaking rate = 164 + 10 cycles/min Solution volume = 10.0 + 0.1 mL Relative uncertainty in [Ru] o -.-- 1% Graph #^[Ru]. (M)^kobsx106^x 2^  Q  A3.1.1.1  2.55x105  1.26  8.0  0.34  A3.1.1.2  5.10x10-5  2.26  19  0.071  A3.1.1.3  1.02x10-4  3.41  17  0.11  A3.1.1.4  2.04x10-4  4.48  6.2  0.90  A3.1.1.5  2.43x10-4  4.68  11  0.29  A3.1.1.6  4.08x104  5.72  10  0.30  A3.1.1.7  6.15x10  6.42  36  2x104  A3.1.1.8  8.37x104  7.91  25  0.014  A3.1.1.9  1.04x10-3  8.14  34  3x104  A3.1.1.10  1.21x10-3  8.38  33  9x10  262  0.00 0  6000  0.04 ^  0.03 —  F, 0.02 —  c\t ..., 43 ,_.  0.01 —  0.00 0  2000  6000 t (s)  263  t (s)  t (s)  264  0 07 0.06 -  m  0.05 -  -E 0.04 E';'^0.03 0.02 0.01 0.00 0  2000^ t (s)  4000^  6000  0.07 ^ 0.06 0.05 -  A3.1.1.9  0.04C."  cn  j'2 0.03  -  C4  0.02 0.01 0.00 2000^  4000^ t (s)  6000  265 0.07 0.06 0.05 i'  --  0 cn \'7  w  0.04 0.03 0.02 0.01 0.00  0  2000  4000 t (s)  6000  266 A3.1.2 [PhCOOH] Dependence Studies [Ru]. = 0.408 + 0.004 mM [0 2] = 7.63 ± 0.07 mM  [Et2 S] = 0.742 + 0.006 M Shaking rate = 164 + 10 cycles/min Solution volume = 10.0 + 0.1 mL Relative uncertainty in [PhCOOH] = 0.5-1 % Graph #^[PhCOOH] (M)  ^  kobsx 106  ^  x  2  ^  Q  A3.1.2.1  8.35x104  1.24  14  0.30  A3.1.2.2  1.25x10-3  1.25  16  0.15  A3.1.2.3  2.09x10-3  1.55  25  0.020  A3.1.2.4  4.09x10-3  2.11  29  2.1x10'  A3.1.2.5  7.42x10-3  3.41  56  1.4x10'  A3.1.2.6  9.86x10'  3.46  39  3.5x104  A3.1.2.7  1.75x10-2  4.98  30  1.8x10'  A3.1.2.8  2.11x10-2  5.16  2.2  1.0  A3.1.2.9  2.44x10-2  5.72  9.5  0.30  267  268  t (s)  0.04  0.03 -  0.01 -  0.00 ^ 0^  2000  4000 t (s)  6000  269  t (s)  t (s) 0.05  0.04 -  i 0.03 0 U)  N  41 0.02 -1-J  0.01 -  0.00 ^ 0^  ■ 2000  4000 t (s)  6000  270 A3.1.3 [0 2] Dependence Studies [Ru]. = 0.408 ± 0.004 mM [PhCOOH] = 24.4 + 0.1 mM [Et2 S] = 0.742 + 0.006 M Shaking rate = 164 + 10 cycles/min Solution volume = 10.0 + 0.1 mL Relative uncertainty in [0 2 ] --. 1% 2  Graph #  [02] (M)  kthsx 1 0 6  x  A3.1.3.1  1.76x10-3  1.72  3.5  0.98  A3.1.3.2  2.18x10-3  1.71  2.2  0.99  A3.1.3.3  2.65x10-3  2.69  3.6  0.96  A3.1.3.4  3.64x10-3  3.26  15  0.17  A3.1.3.5  4.90x10-3  4.05  7.2  0.78  A3.1.3.6  5.13x10-3  4.10  6.1  0.87  A3.1.3.7  6.32x10-3  4.82  9.9  0.45  A3.1.3.8  7.63x 10 3  5.16  9.5  0.30  A3.1.3.9  8.44x10-3  5.93  16  0.19  Q  271 0.02  cn 0 0 1 0  C\  0.00  t (s)  t (s) 0.03  0  2000  4000 t (s)  6000  272  0.04 -  0.03 -  0.00  0  ^  2000^ t (s)  4000^  6000  273  0 04 -  0.03 7:7 0.02  -  0.01 -  0.00 0  2000  4000  6000  t (s) 0.05 ^  0.04 -  0.01 -  0.00 0  2000  4000 t (s)  6000  274 A3.2 Second Data Set The two tables that follow give the numerical values of the data points shown in figures 3.24 and 3.25. Following each table are the [Et2 S0] vs. time raw data plots which gave rise to each data point in figures 3.24 and 3.25.  A3.2.1 [Ru]. Dependence Studies [PhCOOH] = 24.4 + 0.1 mM [0 2] = 7.63 + 0.07 mM  [Et2 S] = 0.742 + 0.006 M Shaking rate = 164 + 10 cycles/min Solution volume = 10.0 + 0.1 mL Relative uncertainty in [Ru] o .--- 1% Graph #  [Ru]a (M)  k03x106  X2  Q  A3.2.1.1  2.53x10-5  1.23  9.7  0.72  A3.2.1.2  5.06x10'  1.71  8.2  0.88  A3.2.1.3  1.01x10  1.86  14  0.18  A3.2.1.4  1.01x10  2.29  15  0.45  A3.2.1.5  2.02x10"  3.23  7.9  0.95  A3.2.1.6  2.28x104  3.18  29  0.023  A3.2.1.7  4.05x104  3.79  6.6  0.95  A3.2.1.8  1.18x10-3  4.80  125  0  275  276  0.05  0.04 -  0.01 -  0.00 0  1^ 1 2000^4000^6000 t (s)  8000  277  0.05 -  0.04 -  0.01 -  0.00 0^  I^ r^ i 2000^ 4000^ 6000 t (s)  8000  278 A3.2.2 [PhCOOH] Dependence Studies [Ru] o = 0.202 + 0.002 mM  [02 ] = 7.63 + 0.07 mM [Et2S] = 0.742 + 0.006 M Shaking rate = 164 + 10 cycles/min Solution volume = 10.0 + 0.1 mL Relative uncertainty in [PhCOOH] ...-- 0.5-1 % Graph #  [PhCOOH] (M)  kob sx1 06  x2  Q  A3.2.2.1  1.21x10-3  0.786  2.9  0.99  A3.2.2.2  2.31x10-3  1.18  9.6  0.39  A3.2.2.3  4.59x10-3  1.71  6.7  0.88  A3.2.2.4  4.99x10-3  1.58  40  1.6x104  A3.2.2.5  1.03x10-2  2.38  4.2  0.95  A3.2.2.6  1.50x10-2  2.55  0.89  1.0  A3.2.2.7  2.44x10-2  3.23  7.9  0.95  A3.2.2.8  4.79x10-2  3.20  21  0.10  279  1^ i 4000^6000 t (s)  0  2000  4000 t (s)  ^  1E4  6000  280  CID  N  t(s) 0 03  0.02  -  N  0.01 -  0.00  0  ^  2000^ t (s)  4000^  6000  281  0.04 ^  0.03 —  c:7 0.02 — cv i;.1 0.01  0.00 0  2000^ 4000^ 6000 t (s)  8000  282 A3.3 Additional Data Sets  The two tables that follow give the numerical values of the data points for some experiments not discussed in the body of the thesis. The first gives the results of a series of experiments in which the reaction vessel shaking rate was varied from one experiment to the next. The second table lists the results of a series of experiments in which the volume of the reaction solution was varied from one experiment to the next. Following each table are the [Et2 SO] vs. time raw data plots which gave rise to each k ths value in the table.  A3.3.1 Dependence of the Reaction Rates on the Reaction Vessel Shaking Speed [Ru] o = 0.202 + 0.002 mM  [02] = 7.63 + 0.07 mM [PhCOOH] = 24.4 + 0.1 mM [Et2 S] = 0.742 + 0.006 M Solution volume = 10.0 + 0.1 mL Relative uncertainty in the shaking rate = 5-8% Graph #  Shaking Rate  kthsx106  x  A3.3.1.1  133  3.04x10'  11.8  0.62  A3.3.1.2  164  3.23x10-6  7.9  0.95  A3.3.1.3  186  2.61x10'  22  0.10  2  Q  283 0.04 ^  0.03  -  5.) 0.02 )  N  0.01 -  0.00 0  2000  ^  4000  ^  6000  t (s) 0.04  A3.3.1.2 0.03  -  0.02 N  0.01 -  0.00 0  2000  4000 t (s)  6000  0.04 ^  A3.3.1.3 0.03 -  o 0.02 m N  0.01 -  0.00 0  2000  4000 t (s)  6000  284 A3.3.2 Dependence of the Reaction Rates on the Volume of the Reaction Mixture [Ru],, = 0.408 ± 0.004 mM [0 2] = 7.63 ± 0.07 mM  [PhCOOH] = 24.4 ± 0.1 mM [Et2 S] = 0.742 ± 0.006 M Shaking rate = 164 ± 10 cycles/min Relative uncertainty in the solution volume .-- 0.5-2% Graph #^Solution Volume (mL)  ^  kobsx10°  ^  x2  ^  Q  A3.3.2.1  10.0  8.14  34  3.5x104  A3.3.2.2  5.00  8.64  3.8  0.97  A3.3.2.3  2.00  13.3  14  0.33  285 0.07 ^ 0.06 0.05  0 U)  c.4  -  0.04 0.03 0.02 0.01 0.00 0  ^  2000  ^  ^ 4000 t (s)  6000  0.06 A3.3.2.2  ' 0.04 0  V) N  al j  0.02 -  0.00 0  2000  4000  6000  t (s)  0.08 -  0.02  0.00 0  ^  2000^ t (s)  4000  6000  

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