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

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THE REACTION OF BIS(THIOETHER) COMPLEXES OF(OCTAETHYLPORPHYRINATO)RUTHENIUM(II) WITH DIOXYGEN,AND THE CATALYZED 02-OXIDATIONOF THIOETHERSbyARSENIO ANDREW PACHECO-OLIVELLAB.Sc., The University of British Columbia, 1982M.Sc., The University of British Columbia, 1986A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESTHE DEPARTMENT OF CHEMISTRYWe accept this thesis as conformingto the required standardTHE UNIVER ITY OF BRITISH COLUMBIASeptember 1992Arsenio Andrew Pacheco-Olivella, 1992In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.Department of ^C ke^r), The University of British ColumbiaVancouver, CanadaDate^becet4er(Signature) DE-6 (2/88)11ABSTRACTThis thesis describes a detailed study of the reactivity of Ru(OEP)(RR'S) 2complexes (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 02 , in various solvents.Exposure to 02 (or air) of a benzene, toluene or methylene chloride solutioncontaining PhCOOH and Ru(OEP)(RR'S)2 at ambient conditions, results in the selectiveoxidation of the axial ligand(s) on the metalloporphyrin complex to the correspondingsulfoxide(s). For a CD2C12 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)2over 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 andRu(OEP)(dms)(PhC00).To identify the products and intermediates of oxidation, the complexes in theseries 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/visspectroscopy, cyclic voltammetry, and elemental analysis; the x-ray crystal stucture ofRu(OEP)(decMS)2 +13F4 was obtained. The Ru(OEP)(dmso) 2 complex exists as the bis(S-bound) isomer in the solid state, although variable temperature uv/vis studies suggest thatisomerization to 0-bound species occurs in solution.The Ru(OEP)(RR'S)(RR'SO) complexes could not be isolated pure, but they werecharacterized in solution by 'H-nmr, CV, and uv/vis studies. For solutions containingiiiRu(OEP)(Et2SO)2 , Ru(OEP)(Et2S)(Et250), Ru(OEP)(Et2S)2 , and varying concentrations ofEt2S and Et2SO, the equilibrium and rate constants governing the relative solutionconcentrations of the three species were determined from stopped-flow experiments.The Ru(OEP)(RR'S)(PhCOO) complexes could not be isolated in pure formeither, but solutions containing 1:1 mixtures of Ru(OEP)(dms) 2 +13F4 andMe4N+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) 2in acidic organic media. For example, for the bis(dms) system, in the "first stage", 02coordinates to Ru"(OEP)(dms) formed by dissociation of a dms ligand. This is followedby electron transfer from the metal to 02 ; the 02 formed is protonated by PhCOOH toyield HO2 , while Rum(OEP)(dms)(PhC00) is also formed. The HO 2 disproportionates to02 and H202 , and the latter oxidizes Et2S to Et2SO. In the "second stage", a Rum species,probably Rum(OEP)(dms)(PhCOO), is oxidized to Re by another Ru m species, probablyRum(OEP)(dms)2 +1311C00 - (i.e. 2Rum --> 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 toproduce Ru ll(OEP)(dms)(dmso). The overall process results in two moles of dms beingoxidized to dmso per mole of 02 consumed. The basic mechanism appears to be the samefor the oxidation of dialkylsulfides in CH2C12 , benzene or toluene, but with somedifferences 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 tosulfoxide, but light above 480 nm is required. It is believed that, under catalyticivconditions, 02-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 outer-sphere electron transfer from the metal to 0 2 . After the initial electron transfer, thereaction would follow the same course as in the stoichiometric oxidation. The catalyticsystem was studied for the case in which RR'S = Et 2S. The stoichiometry: 2Et2S + 02 -->2Et2SO was verified by gas chromatography and by oxygen-uptake experiments.A kinetic analysis of the gas uptake data showed that, under the experimentalconditions 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 completeabsorption of the incident light by the reaction solution. The results of a kinetic modellinganalysis suggest that the photoexcited state that gives rise to the observed photochemistryhas a minimum lifetime of 10-8 s (in the absence of 02), and that Ru(OEP)(Et 2S)(Et2S0),which accumulates as the concentration of Et2SO builds up, is outside of the catalyticcycle.VTABLE OF CONTENTSABSTRACT ^  iiTABLE OF CONTENTS ^  vLIST OF TABLES ^ xLIST OF FIGURES^  xiLIST OF ABBREVIATIONS AND SYMBOLS ^ xviiiACKNOWLEDGEMENTS ^ xxCHAPTER 1 INTRODUCTION ^  11.1 General Introduction  11.2 Reactivity of Ruthenium Porphyrins with Dioxygen ^ 51.3 Reactivity of Dialkylsulfides with Dioxygen ^  141.4 Outline of this Thesis ^  19NOTES AND REFERENCES FOR CHAPTER 1 ^  20CHAPTER 2 REACTION OF Ru(OEP)(RR'S) 2 COMPLEXES WITHDIOXYGEN IN ACIDIC MEDIA ^  232.1 Introduction ^  232.2 Experimental  242.2.1 General Reagents, Gases and Solvents ^  242.2.2 Tetramethylammonium Benzoate (Me 4N+PhC00-) ^ 252.2.3 Tetra-n-butylammonium Tetrafluoroborate (n-Bu4N+BF4)^262.2.4 Ruthenium Porphyrin Complexes ^ Ru(OEP)(dins)2 ^  27vi2.2.4.2 Ru(OEP)(Et2S)2 ^ Ru(OEP)(dmso) 2 and the dmso-d6 Analogue ^ Ru(OEP)(Et25.0)2 ^ Ru(OEP)(decMS0)2 Ru(OEP)(dms) 2+BF4  302.2.4.7 Ru(OEP)(Et2S)2 +BF4 ^  312.2.4.8 Ru(OEP)(decMS)2 +BF4  312.2.4.9 Me4N +Ru(OEP)(PhC00)2 ^  322.2.5 Instrumentation ^  322.2.5.1 Ultraviolet/Visible Absorption Spectroscopy ^ 322.2.5.2 Infrared Spectroscopy ^  332.2.5.3 Proton Nuclear Magnetic Resonance Spectroscopy^332.2.5.4 Conductivity ^  332.2.5.5 Cyclic Voltammetry  332.2.5.6 Elemental Analysis  362.3 Characterization of Ru(OEP)(RR'S0)2 Complexes ^ 362.4 Characterization of Ru m(OEP) Complexes  402.5 Reaction of Ru(OEP)(dms)2 With Dioxygen and Benzoic Acid inMethylene Chloride ^  492.6 Reaction of Ru(OEP)(RR'S) 2 Complexes with Dioxygen and BenzoicAcid in Hydrocarbon Solvents ^  71REFERENCES AND NOTES FOR CHAPTER 2 ^  81CHAPTER 3 A MECHANISTIC STUDY OF THE 02-OXIDATION OFDIETHYLSULFIDE CATALYZED BY Ru(OEP)(Et2S)2 ^  843.1 Introduction ^  843.2 Experimental  853.2.1 Materials ^  853.2.2 Stopped-Flow Experiments ^  853.2.2.1 Sample Handling  85vii3.2.2.2 Instrumentation ^  863.2.3 Gas Chromatography  863.2.3.1 Sample Handling ^  863.2.3.1 Instrumentation  873.2.4 Oxygen Uptake Experiments ^  873.2.4.1 Sample Handling  873.2.4.2 Apparatus Setup ^  883.2.5 Data Treatment ^  923.3 Ru(OEP)(Et2S)2-Catalyzed 02-Oxidation of Et2S in Benzene Solution -General Observations ^  923.4 Stopped-Flow Analysis of Et2SO Substitution by Et2S inRu(OEP)(Et2SO)2 in Benzene Solution ^  1133.4.1 Data Treatment and Results  1133.4.2 Error Analysis ^  1293.4.2.1 Uncertainties in the Solution Concentrations ^ 1293.4.2.2 Instrumental Uncertainties ^  1293. Uncertainties on the Millisecond Timescale^1303. Uncertainties in the One Hundred SecondTimescale ^  1343.4.3 Discussion of the Parameter Values ^  1353.5 Catalytic Oxidation of Et2S - Rate Dependence on [02] [PhCOOH] and[Ru(OEP)(Et2S)2] ^  1383.5.1 Data Treatment and Results ^  1383.5.2 Error Analysis and Discussion  1533.5.2.1 Experimental Uncertainties ^  1533.5.2.2 Evaluation of the Kinetic Model  154NOTES AND REFERENCES FOR CHAPTER 3 ^  170CHAPTER 4 RATE LAW DERIVATION FOR THE 0 2-OXIDATION OFDIETHYLSULFIDE CATALYZED BY Ru(OEP)(Et2S)2 ^ 172viii4.1 Introduction ^  1724.2 The Equilibria between Ru(OEP)(Et2S) 2 , Ru(OEP)(Et2S)(Et2SO) andRu(OEP)(Et2SO)2 ^  1724.2.1 Rate Law Derivations ^  1724.2.2 Correlation of Uv/Vis Absorbance Changes to the DerivedRate Laws ^  1814.2.2.1 First Substitution Reaction ^  1814.2.2.2 Second Substitution Reaction  1854.3 Catalytic 02-Oxidation of Et2S by Ru(OEP)(Et2S)2 ^ 1894.3.1 General Rate Law Derivation ^  1894.3.2 An Approximate Expression for I.  1964.3.3. Modifications to the Proposed Mechanism ^ 2024.3.3.1 Internal Rearrangement ^  2034.3.3.2 Photoactivation Via Metal-to-Porphyrin ChargeTransfer ^  205CHAPTER 5 GENERAL CONCLUSIONS AND SUGGESTIONS FORFURTHER STUDIES ^  209REFERENCES FOR CHAPTER 5 ^  213APPENDIX 1 QUICK BASIC PROGRAMS^  213A1.1 LINFIT ^  213A1.2 POLFIT  217A1.3 ONEDMIN ^  221A1.4 TWODMIN 229A1.5 ODEGRPH ^ 237APPENDIX 2 RESULTS OF STOPPED-FLOW EXPERIMENTS ^ 242A2.1 Experiments Carried Out Using Light of 400.5 nm Wavelength ^ 242A2.1.1 Experiments Carried Out Using a Constant [Et2SO] ofix1.18 ± 0.03 mM ^  243A2.1.2 Experiments Carried Out Using a Constant [Et2SO] of17.7 + 0.2 mM ^  249A2.2 Experiments Carried Out Using Light of 402.8 nm Wavelength ^ 254A2.2.1 Experiments Carried Out Using a Constant [Et2SO] of1.18 + 0.03 mM ^  255A2.3 Blank Experiments  259APPENDIX 3 RESULTS OF OXYGEN UPTAKE EXPERIMENTS ^ 260A3.1 First Data Set ^  260A3.1.1 [Ru]. Dependence Studies ^  261A3.1.2 [PhCOOH] Dependence Studies  266A3.1.3 [0 2] Dependence Studies ^  270A3.2 Second Data Set ^  274A3.2.1 [Ru]. Dependence Studies ^  274A3.2.2 [PhCOOH] Dependence Studies  278A3.3 Additional Data Sets ^  282A3.3.1 Dependence of the Reaction Rates on the Reaction VesselShaking Speed ^  282A3.3.2 Dependence of the Reaction Rates on the Volume of theReaction Mixture ^  284xLIST OF TABLESTable 2.1 Summary of the 'H-nmr Peak Positions in CD 2C12 for the Ru(OEP)Complexes Discussed in Section 2.5 ^  52Table 2.2 Positions of the 11-I-nmr Signals (Sobs), Assigned to Ru11(OEP)(dms)2 +Rum(OEP)(dms) 2 +PhC00- in the Experiment Illustrated in Figure 2.7, andthe Calculated Remaining Mole Fraction of Ru(OEP)(dms) 2 (NI) ^ 57Table 2.3 Selected Bond Distances (A) and Bond Angles (deg) forRu(OEP)(decMS) 2 and Ru(OEP)(decMS)2 ÷BF4 ^  60Table 2.4 Summary of the 11-1-nmr Peak Positions in C 6D6 for the dms- and dmso-Containing Ru(OEP) Complexes Discussed in Section 2.6 ^ 73Table 2.5 Summary of the 1 1.1-nmr Peak Positions in C 6D6 for the Et2S- andEt2SO-Containing Ru(OEP) Complexes Discussed in Section 2.6 ^ 76Table 3.1 Fundamental Parameters Derived from Equations 3.18 and 3.19 ^ 121Table 3.2 Fundamental Parameters Derived from Equations 3.24 and 3.25 ^ 129TABLE 3.3 Fundamental Parameters Derived from the Plots of k obs vs. [Ru]o ,[PhCOOH] and [02] ^  152xiLIST OF FIGURESFigure 1.1. Structure of the porphyrin ring skeleton ^  2Figure 1.2. Sample structures of Ru(OEP)L2 and Ru(TMP)L2 complexes.a) Ru(OEP)(Ph 2S)2 (taken from reference 19); b) Ru(TMP)(THF)(N2) (taken fromreference 8b). ^  9Figure 1.3. Proposed catalytic cycle for the epoxidation of olefins catalyzed byRu(TMP)(0)2 (taken from reference 11) ^  11Figure 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) samplepreparation flask. ^  35Figure 2.2. Changes in the visible spectrum of a CH 2C12 solution containing 0.039mM Ru(OEP)(Et2SO)2 , and 4.72 mM free Et2SO, as the temperature isincreased in 10° intervals, from 20-50° C. ^  38Figure 2.3. Uv/vis spectra in CH2C12 of (a) Ru(OEP)(dms)2 andRu(OEP)(dms) 2 +13F4, and (b) Me4N+Ru(OEP)(PhC00)2. ^ 41Figure 2.4. Cyclic voltammograms in CH2C12/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 sulfoxidecomplexes are virtually indistinguishable from those of the dms and dmsocomplexes illustrated. Also, a CV identical to (a) was obtained forRu(OEP)(dms)2 +BF4. ^  43Figure 2.5. (a) Visible spectrum of a 1:1 mixture of Ru(OEP)(Et 2SO)2 and AgBF4in CH2C12 ; (b) 1 1-I-nmr spectrum of a CD2C12 solution initially containing[Ru(OEP)] 2(BF4)2 and free dmso in approximately 1:8 ratio; S^solvent,T = 20° C ^  44Figure 2.6. 'H-nmr spectrum of Ru(OEP)(decMS)2 +13F4 in CD2C12 , taken at 20.0°C; S^solvent. ^  48xiiFigure 2.7. 'H-nmr spectral changes over time after an acidic CD2C12 solution ofRu(OEP)(dms) 2 is exposed to 1 atm of 02 at room temperature(approximately 20° C). The peak assignments for each species aresummarized in table 2.2. ^  50Figure 2.8. 'H-nmr spectrum of a CD2C12 solution of Ru(OEP)(dms)2(approximately 5 mM) to which an excess of a mixture containing 3:1dms/dmso (neat) has been added. Under these conditions, the majorRu(OEP) species in solution is Ru(OEP)(dms)(dmso). ^ 51Figure 2.9. 1 11-nmr spectrum of an acidic CD 2C12 solution of Ru(OEP)(dms) 2 35 hafter exposure to 1 atm of 0 2 at room temperature (cf. figure 2.7); S =-solvent. ^  54Figure 2.10. 111-nmr spectrum of Ru(OEP)(dms)2 13F4; 20.0° C in CD 2C12 ; S ---solvent. ^  56Figure 2.11. Crystal structure of Ru(OEP)(decMS) 2 +BF4; selected bond lengthsand angles are given in table 2.3. ^  59Figure 2.12. 'H-nmr spectrum of (a) a mixture (approximately 1:1) ofRu(OEP)(dms)2 +BF4 and Me4N +Ru(OEP)(PhC00)2 about 1 h aftermixing; (b) pure Me4lsr-Ru(OEP)(PhC00)2. Both spectra in CD 2C12 at20.0° C, and systems sealed under vacuum; S --2 solvent. ^ 64Figure 2.13. Cyclic voltammogram of a solution (CH2C12/n-Bu4N +BF4) initiallycontaining 0.78 mM Ru(OEP)(decMS) 2 , 71 mM decMS, and 25 mMdecMSO. ^  69Figure 2.14. 'H-nmr spectrum of a C 6D6 solution, initially containing 8.2 mMRu(OEP)(dms)2 and 8.2 mM PhCOOH, which was exposed to 1 atm of 0 2for about 36 h at room temperature; S 7--.- solvent, g s-- grease, ? .. .-unidentifed signals    72Figure 2.15. 1 H-nmr spectrum of a C6D6 solution, initially containing 2.3 mMRu(OEP)(Et2S)2 and 3.3 mM PhCOOH, which was exposed to 1 atm of 0 2for about 12 h at 35° C; S 7.-- solvent, g --- grease, ? as unidentifiedsignals. ^  75xiiiFigure 2.16. 1H-nmr spectrum of a C 6D6 solution, initially a suspension ofRe(OEP)(dms)2 +BF4 and Me4N + Ru III(0EP)(PhC00) 2 (approximately4x106 mol of each), which was allowed to stand overnight under vacuum;S =.---- solvent, ? Fa- unidentified signals. ^  78Figure 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 thelight source. Key components: (A) Thermostatted and insulated oil bath;(B) Reaction vessel; (C) Oil manometer; (D) Mercury burette andreservoir; (E) Projection lamp; (F) Aluminum foil; (G) Compressed airmanifold; (H) Screen. (1)-(12): Various taps and valves; see text forexplanations^  89Figure 3.2. Dependence of Et2SO production rate on reaction vessel illumination.[Ru(OEP)(Et2S)2] = 0.34 mM; [PhCOOH] = 5.3 mM; [Et 2S] = 0.74 M;the reaction was carried out in benzene solution at 35° C, in a flaskexposed to the air. Reaction progress was followed by gaschromatography. ^  94Figure 3.3. (a) Uv/visible spectra of Ru(OEP)(Et2S)2 , and of the yellow and bluefilters used to test which wavelengths are necessary for Et 2S oxidation toproceed. (b) Effects of the cutoff filters on the rate of Et2SO production, asmeasured by 02-absorption at 35° C; in each case, a benzene solutioninitially containing 0.84 mM Ru(OEP)(Et 2S)2 , 24 mM PhCOOH, and 0.74M Et2S was exposed to 0.81 atm of 02 (corrected for benzene vapourpressure). ^  95Figure 3.4. Scheme showing the types of electronic transitions which can occur ind6 six-coordinate ruthenium porphyrins (adapted from reference 8). ^ 97Figure 3.5. Two possible mechanisms for the photochemical stage of the 0 2-oxidation of Et2S catalyzed by Ru(OEP)(Et 2S)2 : a) porphyrin 7-7r*transition, followed by transfer of the excited electron to 02 ; b) directmetal-to-porphyrin charge-transfer, followed by transfer of the excitedelectron to 02^  98xivFigure 3.6. Relationship between the light energy absorbed by Ru(OEP)(Et 2S)2 at525 nm, and the relative free energy changes associated with varioustransformations; see text for details. ^  102Figure 3.7. Gas chromatographic trace of a benzene solution initially containing0.42 mM Ru(OEP)(Et2S)2 , 6.5 mM benzoic acid, and 0.74 M Et 2S,exposed to 0.81 atm of 0 2 (corrected for benzene vapour pressure) at 35°C for 2.5 h. 4.89 min: Et2S2 ; 6.05 min: Et2SO; 7.11 min: Et2SO2 ; 7.90min: n-undecane; 9.30 min: benzoic acid. The signal at 13.16 min is thatof an unidentified product; the rest of the unidentified signals are present atthe start of the reaction. ^  104Figure 3.8. Scheme proposed for the 02-oxidation of Et2S to Et2SO, catalyzed byRu(OEP)(Et2S)2 and PhCOOH (dotted pathways imply that these processescan be neglected under catalytic conditions).   106Figure 3.9. A typical plot showing the accumulation of Et2S0 with time,determined by monitoring the 02-uptake (see section 3.5 for full details).For this experiment at 35° C, the initial concentrations of the reagents are:[Ru(OEP)(Et2S)2] = 0.202 mM; [PhCOOH] = 24.4 mM; [Et2S] = 0.742M; p02 = 0.813 atm (corrected for benzene vapour pressure). ^ 108Figure 3.10. Relationship between the light energy absorbed byRu(OEP)(Et2S)(Et250) at 525 nm, and the free energy changes associatedwith various transformations. AG° for the oxidation at the metal ofRu ll(OEP)(Et2S)(Et250) was estimated from the CV data for the analogousRu(OEP)(decMS)(decMS0) system (see section 2.5 and figure 2.13); forthe one-electron ring oxidation, AG° is assumed to be the same as in theRu(OEP)(Et2S)2 system (see figure 3.6). ^  110Figure 3.11 Uvivis spectra of a benzene solution initially containing 0.202 mMRu(OEP)(Et2S)2 , 0.742 M Et2S, and no benzoic acid, at various times afterexposure to a light source, and 0.813 atm of 0 2 (corrected for benzenevapour pressure). The same results were obtained ^  111Figure 3.12. Scheme showing the proposed mechanisms for the sequentialX Vsubstitution of two Et2SO ligands by Et2S in Ru(OEP)(Et2SO)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)    114Figure 3.13. Uv/vis spectral changes observed as: (a) a benzene solution initiallycontaining 3.4x106 M Ru(OEP)(Et2SO)2 and 0.19 M free Et2SO is titratedwith neat Et2S; (b) a benzene solution initially containing 1.7x105 MRu(OEP)(Et2S)2 and 0.74 M free Et2S is titrated with neat Et 2SO. T = 35°C for both experiments. ^  115Figure 3.14. A typical, fitted stopped-flow trace of the change in absorbance over100 ms, at X = 400.5 nm, when Et2S is substituted for Et2SO inRu(OEP)(Et2SO)2 . [Et2S] = 9.27+0.09 mM; [Et 2SO] = 1.18+0.03 mM;[Ru]c, = (3.44+0.07)x106 M. The first four points likely are in the deadtime of the instrument, and are neglected in the fit. ^  122Figure 3.15. Portions of the plots of [Et2S]/3 1 vs [Et2S] for data collected at X =400.5 nm over 100-ms time-frames. a) [Et2SO] = 1.18±0.03 mM; b)[Et2SO] = 17.7±0.2 mM. In each case [Ru] o = (3.44±0.07)x10-6 M. Theresidual plots show the full range of data collected; the main plots showonly the region in which $ increases (Q is the goodness of fit given theobtained x2 value). ^  123Figure 3.16. Portions of the plots of [Et2S]/vol vs. [Et2S] for data collected at X =400.5 nm over 100-ms time-frames. a) [Et 2SO] = 1.18+0.03 mM; b)[Et2SO] = 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 plotsshow only the region in which vol increases. ^  124Figure 3.17. A typical, fitted stopped-flow trace of the change in absorbance over100 s, at X = 402.8 nm, when Et 2S is substituted for Et2SO inRu(OEP)(Et2S)(Et2S0).[Et2S] = 18.6+0.2 mM; [Et2SO] = 1.18±0.03 mM; [Ru]o = (3.44+0.07)x10-6 M. 127Figure 3.18. Portions of the plots of: a) [Et 2S] 2/132 vs [Et2S], and b) [Et2S]2ivo2 vs[Et2S], 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-scalepoint at [Et2S] = 0.232+0.002 M for each plot; all of the data aretabulated in appendix 2. ^  128Figure 3.19. Variation of the parameters 0 1 and 7 1 from experiment toexperiment, when all reagent concentrations are held constant. The errorbars represent the uncertainties estimated from fitting the raw stopped-flowdata^  131Figure 3.20. Weakening of 7r-bonds trans to a sulfoxide; 0 - bonds trans to thesulfoxide will also be weakened, since the sulfoxide can transfer more °-electron density to the Ru d z2 orbital than a comparable ligand incapable of7r-bonding (see text)^  137Figure 3.21. Visible spectra of pure Ru(OEP)(Et 2S)2 (3), a solution containingmostly Ru(OEP)(Et2S)(Et§0) (2, see text), and pure Ru(OEP)(Et 2SO)2 (1and 1'). The dashed lines indicate the region of all three spectra overwhich the integrated extinction coefficients were calculated (see text fordetails)^  144Figure 3.22. A plot of [Et2SO] vs. time, fitted using the least squares proceduredescribed in the text. For this experiment, the initial concentrations of thereagents are: [Ru(OEP)(Et2S)2] = 0.202 mM; [PhCOOH] = 2.31 mM;[Et2S] = 0.742 M; p02 = 0.813 atm (corrected for benzene vapourpressure). ^  147Figure 3.23. Plots of kobs vs.: (a) [Ru] o , with [PhCOOH] and [02] held constant at24.4 and 7.63 mM, respectively; (b) [PhCOOH], with [Ru] o and [02] heldconstant 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 errorbar magnitude in each case is given by a. ^  149Figure 3.24. Plots of kobs vs.: (a) [Ru] o , with [PhCOOH] and [02] held constant at24.4 and 7.63 mM, respectively; (b) [PhCOOH], with [Ru] o and [02] heldconstant at 0.202 and 7.63 mM, respectively. The error bar magnitude ineach case is given by .   151xviiFigure 3.25. Plots of the goodness of fit parameter (Q) vs.: (a) [Ru] o; (b)[PhCOOH]; (c) [02] for the fitting procedures illustrated in figures 3.23and 3.24, and assuming that 0 = 0.85 (see text for details). ^ 155Figure 3.26. Plots of the goodness of fit parameter (Q) vs.: (a) [Ru] o; (b)[PhCOOH]; (c) [02] for the fitting procedures illustrated in figures 3.21and 3.22, and assuming that 0 = 0.6 (see text for details). ^ 160Figure 3.27. A plot of [Et2SO] vs. time, fitted using: (a) the least squaresprocedure described in the text; (b) the function [Et2SO] = 2k3 [Ru]ot. Forthis experiment, the initial concentrations of the reagents are:[Ru(OEP)(Et2S)2] = 0.0253 mM; [PhCOOH] = 24.4 mM; [02] = 7.63mM; [Et2S] = 0.742 M. ^  164Figure 4.1. Mechanism proposed for the sequential substitution of two Et 2SOligands by Et2S, assuming that in solution the bis(sulfoxide) species existsas a mixture of the S- and 0-bound linkage isomers. ^ 174Figure 4.2. Mechanism proposed for the 0 2-oxidation of Et2S to Et2SO, catalyzedby Ru(OEP)(Et2S)2 and PhCOOH (dotted pathways imply that theseprocesses can be neglected, or do not occur, under catalytic conditions; seethe assumptions on pp. 140-141). ^  190Figure 4.3. Alternative mechanism for the photochemical stage of the 0 2-oxidationof Et2S catalyzed by Ru(OEP)(Et2S)2; see text for details. ^ 206xviiiLIST OF ABBREVIATIONS AND SYMBOLSWhere possible, all abbreviations used are those recommended in: "Handbook forAuthors". Amer. Chem. Soc. Publications, Washington, D. C., 1978; pp. 29-47. Thefollowing is a list of specialized abbreviations and symbols used in this thesis.Symbol or Abbreviation^ Meaning^AZBN^ azoisobutyronitrileCp cyclopentadienyl anionCT^ charge transferCV cyclic voltammetryd^ doubletdecMS n-decylmethylsulfidedecMSO^ n-decylmethylsulfoxideDMA N,N'-dimethylacetamidedms^ dimethylsulfidedmso dimethylsulfoxidem^ multipletNHE normal hydrogen electrodeOCP^meso-tetra(2,6-dichlorophenyl)porphyrinato dianionOEP 2,3,7,8,12,13,17,18-octaethylporphyrinato dianionPorp^ any general porphyrinato dianionxixppm^ parts per millionpy pyridineq^ quartetqn quintets^ singletSCE saturated calomel electrodesx^ sextett tripletTMP^ meso-tetramesitylporphyrinato dianionTPP meso-tetraphenylporphyrinato dianionXXACKNOWLEDGEMENTSI wish to thank all of those who helped me, directly or indirectly, to complete thiswork. First, I wish to express my deepest gratitude to Professor B. R. James, for hisexpert guidance and support during the course of my studies; it has been a pleasure towork for him. I also owe special thanks to my wife Muriel, not only for her unfailingmoral support, but also for doing the illustrating for the thesis. My thanks to colleaguesin both the B. R. James and D. Dolphin research groups, for their friendship and helpfuldiscussions; many an idea crystallized while sharing theories over coffee! In the samevein I wish to thank my good friends K. Barnard and S. Habib, for enduring innumerablequestions about numerical analysis, and coming up with helpful answers. I am alsograteful 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 bythe nmr, Elemental Analysis, Electronic, Glassblowing and Mechanical shop personnelare deeply appreciated. Finally, I would like to thank my family, especially my parentsand my brother, for their unfailing love and support.1CHAPTER 1INTRODUCTION1.1 General IntroductionThe 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 definean equatorial plane, and the porphyrin dianion, formed by removing the two internalprotons, is a planar tetradentate chelating agent capable of forming coordinationcompounds with all the transition and lanthanide metals, as well as many of the maingroup metals and semimetals, and a number of actinides.'Iron porphyrins are ubiquitous in natural protein and enzyme systems, and havebeen identified as vital components in the active sites of such diverse molecules ashemoglobin which is an oxygen transport protein, the cytochromes which perform anassortment of oxidation-reduction tasks, and oxygenases which catalyze selectiveoxidations using 0 2 . 2 Because of their importance in natural systems, iron porphyrinshave 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 industrialoxidation processes.'As mentioned, porphyrin systems containing almost every metal in the periodictable have now been synthesized and characterized.' In large part the interest inmetalloporphyrins other than Fe(Porp) has also been fuelled by a desire to better^Ri^R2OEP C7HSTPP^H^C6H5TMP^H^2, 4, 6-Me3C6H2OCP^H^2, 6-C1,,C6H3Figure 1.1. Structure of the porphyrin ring skeleton3understand the natural porphyrin systems;' much can be learned about one element bycomparing and contrasting its behaviour with that of other elements. Because rutheniumis immediately below iron in the periodic table, the possibility of comparing andcontrasting ruthenium porphyrins with iron porphyrins is especially intriguing, and since1969 various ruthenium porphyrins have been synthesized and characterized."Despite the fact that it has been over twenty years since the first rutheniumporphyrin complex was prepared, it still appears too early to assess the full impact of theruthenium porphyrin studies on the understanding of the naturally occurring ironporphyrin systems; what can be said for sure is that the study of ruthenium porphyrinshas 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 rutheniumporphyrins and, in this respect, the dimeric complexes such as [Ru(OEP)] 26 and[Ru(OEP)BF4]27 (OEP^dianion of octaethylporphyrin), and the four-coordinateRu(TMP) 8 (TMP^dianion of tetramesitylporphyrin) deserve special mention (seefigure 1.1 for porphyrin systems). These complexes are coordinatively unsaturated, andexhibit many remarkable physical and chemical properties." The lack of axial ligandsalso makes these complexes excellent starting materials for the preparation of otherRu(Porp) complexes (Porp = dianion of a porphyrin in general); indeed, using thedimeric and four-coordinate complexes as starting materials, a wide variety of Ru ° , Ru",Rum , RuN and Ruvi materials has now been synthesized."Investigations into the reactivity of various ruthenium porphyrins have also yieldedinteresting catalytic properties in reactions as diverse as the decarbonylation ofaldehydes,' and the 02-oxidation of various organic compounds, including olefins to4epoxides." One problem with some of the catalysis studies carried out to date is thatoften 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-oxidationof phosphines (see below).' However, the advances in synthetic methods of recentyears, and the isolation and concomitant characterization of higher-valent Ru(Porp)complexes (notably of Ru g , Ru l`' and Ruv1 species)9 now makes it possible to identifyintermediates in complex reaction pathways, which in turn means that detailedmechanistic studies are now feasible. This thesis describes just such a study, on theautoxidation of thioethers to sulfoxides catalyzed by Ru(OEP)(RR'S) 2 complexes (R andR' 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 showedthat Ru(OEP)(PPh 3)2 catalyzes the autoxidation of free PPh3 to OPPh3 (see section l.2). 12As the subject of a detailed study, the selective oxidation of sulfides to sulfoxides wasmore attractive than the oxidation of PPh 3 to OPPh3 , because of the potential commercialvalue of the former process; 13 ' 14 this consideration played a part in the initial decisionof which system to investigate further. As will be seen in the following two sections ofthis chapter, many advances have been made in the field of catalytic 0 2-oxidation ofthioethers 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 inmore detail in chapter 5). Nevertheless, this thesis project has revealed some interestingproperties of ruthenium porphyrins, some of which may have bearing on the results of5earlier investigations on catalyzed 0 2-oxidation of PPh 3 12 , and the catalyzeddecarbonylation of aldehydes,' for which mechanistic details were lacking.1.2 Reactivity of Ruthenium Porphyrins with DioxygenEarly studies on the reactivity of Ru(Porp) complexes with dioxygen focused onRu 11 ^and commented on the high stability of the Re species to oxidation by airwhen compared to the then known Fe ll analogues."'" The stability was rationalized interms of the larger ruthenium d-orbitals leading to greater ligand field stabilization by theporphyrin, as well as to more efficient metal-to-porphyrin ir-backbonding. 16,17 WhileRe(Porp) complexes are more thermodynamically stable to oxidation than Fe ll(Porp)complexes, those prepared in the early studies were exceptionally stable, and many air-sensitive Ru(Porp) complexes have been prepared since that time, 18 " 9 including speciesthat bind 02 reversibly.' The first Re(Porp) complexes isolated contained CO as anaxial ligand, and it was proposed that efficient 7-backbonding from the ruthenium d-orbitals 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 COligand). 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(Rum + e ---' Re) reduction potentials as much as 0.6 V lower than those of theRu(Porp)CO complexes, they also appeared to be rather stable to air-oxidation. 17Proceeding from the hypothesis that 02-oxidation required initial coordination of 0 2 to themetal center, the apparent stability of the Ru(Porp)L2 complexes was attributed to the fact6that all of these compounds were substitutionally relatively inert; Ru(TPP)py 2 (TPP -rmdianion of tetraphenylporphyrin, see figure 1.1), for instance, took a week under 1 atmCO at room temperature to give the thermodynamically favoured (carbonyl)pyridineproduct. ° In recent years many Ru(Porp) complexes have been prepared with labile axialligands such as MeCN, THF, N2 and Ph2S 8 ' 19 '2° and a series of monomeric and dimericcomplexes exemplified by Ru(TMP) g , [Ru(OEP)1 2 and [Ru(TPP)]2, 6 which contain noextraneous axial ligands have been isolated; all such complexes are invariably extremelyair- sensitive.If a Ru 11(Porp)L2 complex is substitutionally inert, one could still envision an"outer sphere" electron transfer from Ru n to 02 . In fact, such a mechanism has beeninvoked in several instances; for example, in the 02-oxidation of PPh3 to OPPh 3 catalyzedby Ru(OEP)(PPh3)2, mentioned at the end of the last section, the initial step in the cyclewas proposed to be"Ru11(OEP)(PPh 3)2 + 02 c'-'- Ru 111(OEP)(PPh3)2 + + °2^ 1.1However, this reaction is highly unfavourable thermodynamically,' and a proton sourceis required to promote the subsequent reactions:02 - ± H + R-'' H02^1.22H02 -, H202 + 02^ 1.37The disproportionation reaction 1.3 is irreversible, Z2 and it was hypothesized that thisstep makes possible the otherwise unfavourable outer sphere oxidation of Ru(OEP)(PPh 3)2complexes by 02 . The following steps were proposed to account for the phosphineoxidation, and to regenerate the Run species and complete the catalytic cycle: 12H202 + PPh3 Ar-". OPPh3 + H2O^ 1.42Re(OEP)(PPh3)2 ÷ + H2O + PPh3  2Ru 11(OEP)(PPh3)2 + 2H+ + OPPh3 1.5Equations 1.1-1.5 constitute a net catalytic pathway by which two moles of PPh 3 areoxidized by one mole of 0 2 :2PPh3 + 02  2OPPh 3^1.6Outer sphere electron transfer is a major topic of this thesis, and it will be seen inchapter 3 that, for some systems at least, the presence of a proton source is notthermodynamically sufficient to permit a process such as equation 1.1 to occur; thereaction also requires a light source to provide the necessary energy. The study referredto above mentions difficulty in obtaining reproducible kinetic data, and it is possible thatthis difficulty arose from an unrecognized light dependence.In the absence of an oxygen atom acceptor such as PPh 3 , 02-oxidation ofRu(OEP)L2 and Ru(TPP)L2 complexes (where L =--- a neutral ligand such as THF) often8leads, in the presence of an anion source X- , ultimately to the formation of thethermodynamically stable [Ruw(Porp)M 20. 9ca" For example, if the complexRu(OEP)(Ph2S)2 is exposed to air, it is rapidly oxidized to [Ru(OEP)OH] 20, and the freedthioether 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 extensivelysince that time. 9c ,23,24 The A-oxo dimers appear to be quite resistant to reduction, and sotheir formation is a problem if one wants to establish a system for catalytic O 2-oxidationusing Ru(Porp) complexes. Of note, although resistant to reduction, there is evidence thatkt-oxo dimers can be slowly demetallated in benzene solution, according to the followingreaction: 12[Ru(OEP)(OH)] 20 + H2O --> 2RuO2 + 2H2(OEP)^ 1.7If the ortho (and para) protons on the phenyls of TPP are replaced by methylgroups, 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 thanTPP systems) and a TMP system. The phenyl rings of TMP are perpendicular to theporphyrin plane, and space filling molecular models show that the o-methyls crowd the9(a)(b)Figure 1.2. Sample structures of Ru(OEP)L2 and Ru(TMP)L2 complexes.a) Ru(OEP)(Ph 2S)2 (taken from reference 19); b) Ru(TMP)(THF)(N2) (taken fromreference 8b).10axial 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 alabile axial ligand such as MeCN or THF, has been shown to be the trans-dioxo speciesRuv1(TMP)(0) 2 . 8,9b,ii Unlike the A-oxo dimers, which do not act as 0-atom donors,Ruv1(TMP)(0)2 reacts readily with oxygen atom acceptors such as olefins" and organicsulfides,''' to give the corresponding epoxides and sulfoxides. This type of reaction (0-atom transfer from metal-oxo species generated via 02) has generated considerableinterest in recent years, and several studies have been published on the subject ;4,96,11,25,26two examples will be considered in detail.In their 1985 paper, Groves and Quinn reported that Ru(TMP)(0)2 will catalyzethe 02-oxidation of various alkenes to their corresponding epoxides, with two moles ofepoxide being produced for every mole of 0 2 consumed." The trans-dioxo species wasalso found to oxidize alkenes stoichiometrically in the absence of 0 2 , if pyridine wasadded to the reaction mixture. Thus the products of the stoichiometric oxidation ofnorbornene were about 1.6 equivalents of norbornene oxide and Ru 11(TMP)py2 ." Themechanism proposed for the catalytic oxidation is shown in figure 1.3. The trans-Ruvldioxo species transfers an 0-atom to an alkene, leaving an epoxide and0=RuNTMP); this species disproportionates to Ru v1(TMP)(0)2 and Ru(TMP), which isimmediately oxidized back to 0=Ru"(TMP) by 02 . The intermediacy of the0=RuNTMP) species has since been verified by independent spectroscopic studies, ashas its sensitivity to disproportionation.' Structures of trans-Ru(OCP)(02)28 andRu(OCP(C0)(Styrene Oxide) 29 have been reported also, where OCP21/2 0VIM11Figure 1.3. Proposed catalytic cycle for the epoxidation of olefins catalyzed byRu(TMP)(0) 2 (taken from reference 11).12("octachioroporphyrin") is the dianion of meso-tetra(2,6-dichlorophenyl)porphyrin (seebelow).Studies carried out in our laboratories have focused in detail on the reactions ofRu(TMP)(0) 2 with phenol and with dialkylsulfides,"'''' the latter reactions are directlyrelated to the subject of this thesis, and will be discussed in some detail. Uv/vis and 'H-nmr experiments showed that if excess of a dialkylsulfide such as Et 2S was added to abenzene solution of Ru(TMP)(0) 2 under argon (or dioxygen), Ru"(TMP)(QSR2)2 ,Ru1(TMP)(QSR2)(0SR2), and Ru"(TMP)(0SR2)2 were produced consecutively (0 and Ssignify oxygen- and sulfur-bound sulfoxides, respectively). The mechanism (supported bykinetic data) proposed for these transformations was:Ru(TMP)(0) 2 + SR2^[O=Ru(TMP)QSR2] 1.8[0 =Ru(TMP)QSR2] + SR2^Ru(TMP)(QSR2)2 1.9Ru(TMP)(QSR2)2 - Ru(TMP)(OSR2)(OSR2) 1.10Ru(TMP)(OSR2)(OSR2)^Ru(TMP)(0SR2)2 1.11The O=Ru(TMP)QSR2 intermediate was not observed experimentally, and kinetic dataimplied that reaction 1.9 was much faster than 1.8. Interestingly, this situation is differentfrom 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 it13appears that the substrate being oxidized plays an important role in determining thepreferred oxidation state of the detected ruthenium species. The data imply thatRuvi(TMP)(0)2 is more effective than Ru w(TMP)0 for olefin epoxidation, whileRuw(TMP)(0)(OSR2) is more effective than Re l(TMP)(0) 2 for 0-atom transfer tothioethers. Both reactions 1.8 and 1.9 are much faster than the subsequent axial ligandisomerization reactions 1.10 and 1.11; once formed, Ru(TMP)(0SR 2)2 is substitutionallyinert under the ambient reaction conditions. " ' 9h ' 25The Ru(TMP)/02 system will catalytically oxidize dialkylsulfides selectively to thecorresponding sulfoxides; however, the catalysis stops after about 8 turnovers at ambientconditions. 9b '" ' 25 The catalysis was considered to occur via the loss of the 0-bondedsulfoxides from Ru(TMP)COSR 2)2 to regenerate under 02 the trans-dioxo species, whileformation of the substitutionally inert Ru(TMP)(0SR 2)2 inhibited the catalytic cycle. Athigher temperatures (e.g. 65° C), up to 15 turnovers were recorded; however, underthese conditions rapid catalyst degradation occurred.More efficient catalytic oxidation of dialkylsulfides was obtained by using trans-Ru(OCP)(0) 2 as a catalyst instead of the TMP system. 9" The axial sites of Ru(OCP) aresterically hindered as in Ru(TMP), so that again tc-oxo dimer formation is prevented. Inaddition, the electron-withdrawing chloro groups on the phenyls make the porphyrin moreresistant to self-oxidation, a well established phenomenon.' The greater robustness ofRu(OCP)(0) 2 , compared to the TMP system, allowed its use at temperatures as high as100° C, and, under these conditions, more than 30 equivalents of dialkylsulfide could beoxidized to sulfoxide, with no observable decomposition of the catalyst. 9"h Of note, inaddition to making the catalyst more resistant to self-oxidation, the Cl substituents also14make 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 increasedreaction rates even at room temperatures, and second, Ru(OCP)(0SR 2)2 is stabilizedrelative to the S-bound isomers."'" Previous reports in the 1970s (on non-porphyrinsystems) have suggested that S-bonded dimethylsulfoxide (dmso) complexes of rutheniumare favoured in cases where the metal center is electron-rich (in which case Ru- ,S 7r-backbonding can reduce the electron density on the metal), whereas 0-bonding isfavoured when the metal center is more electron-deficient: 3°51 however, more recentfindings on both dmso and tetramethylenesulfoxide derivatives of Ru ll suggest that stericfactors dominate the choice of oxygen- versus sulfur-bonding.'1.3 Reactivity of Dialkylsulfides with DioxygenUnder 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 asazoisobutyronitrile (AZBN), autoxidation of the dialkylsulfides proceeds via hydrogenatom abstraction; the observed product distribution has been rationalized by the followingmechanistic scheme: 33Stage 1R'CH2SR" + R . --> R'(CH•)SR"^(Chain Initiation)^ 1.12R'(CH .)SR" + 02 --> R'CH(02•)SR"^ 1.1315R'CH(02)SR" + R'CH2SR" --> R'CH(02H)SR" + R'(CH .)SR" 1.14Stage 2R'CH(02H)SR" + R'CH2SR" --. R'CH(OH)SR" + R'CH2(SO)R" 1.15Stage 3R'CH(OH)SR" -> R'CHO + R"SH 1.16R`CH(OH)SR" + R"SH --> H 2O + Complex sulfides 1.17As 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 otherresearchers in the field, has been to try to find catalysts which result in the selective(preferably exclusive) production of dialkylsulfoxides, 13 or sometimes dialkylsulfones. 13bIn 1985 Riley and Correa reported that, in polar solvents, and under conditions ofhigh temperature (>100° C) and 02 pressure (- 40 atm), dialkylsulfides were slowly butselectively oxidized to the corresponding sulfoxides.' The mechanism suggested for thisreaction was"16R2S + 02 --). R2S + . + 02-^1.18R2S+ . + 02 --a, R2S +00 .^1.19R2S + 00 . + 02 . --* R2S + 00- + 02^ 1.20R2S + 00- + R2S -" 2R2S 0^ 1.21Two later papers 15 '36 reported that cerium(IV) ammonium nitrate is a very efficientcatalyst for the process just described; it was proposed that cerium(IV), being a betteroxidant than 02 , was now responsible for the initial one-electron oxidation of the R2S(reaction 1.18). 15 .3' ThusR2S + CeN --* R2S+ . + Cem^1.22The thioether radical cation could then undergo reaction 1.19, after which the Ce w wouldbe regenerated according to the processR2S÷00 . + Cern -- R2S +00- + CeN^1.23Finally, two sulfoxides would be regenerated according to equation 1.21. This system isreportedly very efficient; thus, for example, in a 9:1 CH 3CN/H20 solution, containingabout 0.017 M ceric ammonium nitrate and 1.0 M tetrahydrothiophene under 125 psi 0 217pressure, 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 laboratoryand discussed in section 1.2, 9l),' ,25 appear to be the only ones, apart from a system to bedescribed in this thesis, in which the selective catalytic 0 2-oxidation of dialkylsulfides tothe corresponding sulfoxides is accomplished with potentially useful turnovers. Othersystems for the metal-complex catalyzed 02-oxidation of thioethers to sulfoxides havebeen described,' but in every case a stoichiometric reagent other than 02 was alsorequired. Two such systems are given as examples.In 1984 Riley and Shumate reported that cis-RuC1 2(dmso)4 and trans-RuBr2(dms0)4catalyzed selective oxidation of various dialkylsulfides to their corresponding sulfoxides,under 100 psi of 02 at 100° C. 37 This reaction proceeded only in alcoholic solvents.From kinetic studies and product analysis, the following mechanistic scheme wasproposed:"Run" + 2H+ + 02 -, "Ruw" + H202 1.24R2S + H202 -* R2SO + H2O 1.25"Re" + Me2CHOH --> "Re" + Me2C=O +2H+ 1.26The 1984 article gave no conclusions as to the nature of the actual catalytic species, butlater studies provided evidence which suggested that the trans,trans,trans-RuX2(SR2)2(dmso)2 species are the starting catalysts.' No further details were given on18the possible nature of the Ru iv intermediate. The original paper cited the lack of freeradical products of alcohol oxidation, and separate studies with various discrete Ru mspecies 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 involvedthe 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 thesulfide.' The following mechanism was proposed for the sulfide oxidation:Rhmdmso + DMA^RIPDMA + dmso 1.27RhmDMA + H2 "'" [RAIDMA] + 2H+ 1.28[Rh iDMAJ + 02 -, Rhm(022)(DMA) 1.29Rhm(022-)(DMA) + H2 '- [Rh'DMAJ + H202 1.30H202 + Ph2S --> H2O + Ph2SO 1.31Steps 1.27 and 1.28 generate the 0 2-sensitive catalyst; the catalysis operates via steps1.29-1.31. Attempts at carrying out these reactions in other solvents, such as 1,2-dichloroethane, were not successful. Interestingly, more basic dialkylsulfides were not19oxidized by the RhC13(dmso) 3 system. This suggested that, in this case, coordination bysulfides inactivated a potentially catalytic system. 391.4 Outline of this ThesisEarlier work from these laboratories had noted briefly that Ru(OEP)(decMS) 2(decMS = decylmethylsulfide) could catalyze the air-oxidation of free decMS inbenzene; 19 '43 this catalysis was very slow, but could be accelerated if the solutions weremade acidic. The product distributions observed for the catalytic reaction variedunpredictably, and decMSO was not generally the only product; however, in the absenceof excess thioether, exposure of Ru(OEP)(decMS) 2 to air resulted in its slow but cleanstoichiometric oxidation to Ru(OEP)(decMS)(decMSO). Furthermore, addition of anexcess of decMS to the Ru(OEP)(decMS)(decMSO) solution regenerated the startingRu(OEP)(decMS) 2 complex, thus constituting one turn of a catalytic cycle.'The first part of the investigation described in this thesis focussed on elucidatingthe mechanism of the stoichiometric 02-oxidation of Ru(OEP)(decMS) 2 and otherRu(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 theselective 02-oxidation of free thioethers to the corresponding sulfoxides. The conditionsunder which such catalysis can take place, along with a detailed kinetic analysis of thecatalytic system, are all included in chapter 3. The derivations of rate laws, used in thekinetic analysis described in chapter 3, are given in chapter 4.20NOTES AND REFERENCESFOR CHAPTER 11. 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 byTransition 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 chemistryinclude: 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 BritishColumbia, 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, 5790.2112. 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 ofOrganotransition 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 HomogeneousCatalysis, Amsterdam, August, 1992.29. Groves, J. T.; Han, Y; Engen, D. V. J. Chem. Soc., Chem. Commun. 1990, 436.2230. 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, andreferences therein.43. James, B. R.; Pacheco, A.; Rettig, S. J.; Thorburn, I. S.; Ball, R. G.; Ibers, J. A. J.Mol. Catal. 1987, 41, 147.23CHAPTER 2REACTION OF Ru(OEP)(RR'S)2 COMPLEXES WITH DIOXYGENIN ACIDIC MEDIA2.1 IntroductionPrevious studies carried out in our laboratories showed that if a benzene solutionof Ru(OEP)(decMS)2 (decMS -= n-decylmethylsulfide) was exposed to air for anextended period of time (from a week to a few months), the complex underwent ligandoxidation to give Ru(OEP)(decMS)(decMSO) and Ru(OEP)(decMSO) 2 (decMSO ---n-decylmethylsulfoxide) as the major products, along with other minor products." Laterstudies have shown that Ru(OEP)(dms) 2 (dms :---: dimethylsulfide) and Ru(OEP)(Et2S)2have similar reactivity, both in benzene and other solvent systems.' The degree ofreactivity of the complex, as well as the exact product distribution observed, depend notonly on the dialkylsulfide and solvent used, but also on the dryness of the solvent andother variables which are difficult to quantify. Because of this it is difficult to getreproducible results when studying such systems. On the other hand, if an acidic solutionof Ru(OEP)(RR'S) 2 (where R E-- methyl, ethyl or decyl and R' ----: methyl or ethyl) isexposed to air, the axial ligands are oxidized to the corresponding sulfoxides in a highlyreproducible manner, both in benzene (or toluene) and in methylene chloride.Furthermore, several intermediates are observable over the course of the oxidationprocess. In this chapter these intermediates are identified and characterized, and amechanism for the oxidation of the Ru(OEP)(RR'S) 2 complexes is proposed based on thepresence of the intermediates and other observations.242.2 Experimental2.2.1 General Reagents, Gases and SolventsAll non-deuterated solvents were obtained from BDH. Hydrocarbon solvents werereagent grade, and were stored in-vacuo over sodium benzophenone ketyl; all othersolvents were glass-distilled spectroscopic grade, and were stored in-vacuo over 3 Amolecular 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 glove-box was prepurified grade, all others were USP grade. Unless otherwise specified, allgases were used without further purification. A gas could be dried by passing it through adrying tower containing 3 A molecular sieves; for especially air-sensitive solutions, argonwas passed down a Ridox deoxygenation column prior to use.Air- or moisture-sensitive solids were stored in a glove-box, the N2 atmosphere ofwhich was continuously recirculated through a Dri-Train HE-439 purification towerpacked with 2.4 kg of 3 A molecular sieves, 1.5 kg of 7 A molecular sieves, and 2 kg ofRidox deoxygenation catalyst. This treatment kept the concentration of 0 2 and H2O below1 ppm, as evidenced by the long lifetime of an exposed 25-W light bulb filament withinthe box. 2The thioethers dms and Et 2S were obtained from Aldrich, while decMS wasobtained from Fairfield chemicals; all three were distilled prior to use,and their puritychecked by gas chromatography and 'H-nmr spectroscopy. Dimethylsulfoxide (dmso) wasspectrograde from BDH, while dmso-d6 was from MSD isotopes. Diethylsulfoxide anddecMSO were synthesized according to standard procedures."' 3 Both dmso and Et2SO25were stored under argon over 3 A molecular sieves; decMSO is a solid and notparticularly hygroscopic, so no special storage precautions were employed.Benzoic acid (PhCOOH) was of uncertain origin, but its purity was verified by1H-nmr spectroscopy, melting point comparison with literature values, and titration withNaOH. Tetrafluoroboric acid (HBF4) was obtained as a 48% aqueous solution fromMCB, and used without further purification.Tetramethylammonium hydroxide (Me4N+OH-) was obtained from Anachemiachemicals as a nominally 25% aqueous solution; tetra-n-butylammonium hydroxide wasnominally a 40% aqueous solution from BDH. Both were used without furtherpurification.Silver tetrafluoroborate (AgBF4) was obtained from Aldrich chemicals, and wasopened and stored in the glove-box.2.2.2 Tetramethylammonium Benzoate (Me 4N+PhC001A 0.9 M solution of PhCOOH in ethanol was added dropwise to about 4 g of 25%aqueous Me4N+OH- until the resultant mixture was slightly acidic to litmus(approximately 14 mL of acid solution were required). The water and ethanol wereremoved using a rotary evaporator, and the resultant solid was redissolved in ethanol (125mL); the mixture was refluxed for about 10-15 min, and then filtered to remove agreyish-white flaky precipitate. The volume of the filtered solution was reduced toapproximately 2 mL using a rotary evaporator, at which point 40 mL of diethyl etherwere added. The desired product was obtained as a white precipitate, which was filteredand dried overnight at 80° C. Me4N+PhC00- is extremely hygroscopic, and had to be26stored 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 IIH I7NO2 : C, 67.66;H, 8.78; N, 7.17. Found: C, 67.76; H, 8.60; N, 6.99. NMR (S; CD3CN or CD 2C12 , 20°C): 7.29 m (11„,, p), 7.96 m (Ho), 3.48 s (NCH 3).2.2.3 Tetra-n-butylammonium Tetrafluoroborate (n -Bu4N+13F41To about 95 g (0.146 mol) of n-Bu 4N+OH - solution was added enough HBF4solution to produce a pH-neutral mixture (checked by litmus test). The resulting whiteprecipitate was filtered off, washed with three 50-mL aliquots of ice-cold water, and thendried in-vacuo for 24 h. The dry powder was dissolved in 45 mL of ethyl acetate, passedthrough a filter paper to remove cloudiness, and then recrystallized by addingapproximately 0.6 equivalents of n-pentane, and cooling at -5° C for lh. After a secondrecrystallization procedure, the product was dried in-vacuo at room temperature for 48 h.Prepared in this way, n-Bu4N+13F4 showed no electrochemical activity in cyclicvoltammetric scans from -1.6 to +1.6 V.2.2.4 Ruthenium Porphyrin ComplexesRuthenium was obtained on loan from Johnson, Matthey Ltd, in the form ofRuC13 .3H20 (approximately 40% by weight). H 2OEP was kindly provided by Dr. D.Dolphin of this department.Ru3C0 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; for27all these compounds the spectroscopic data (nmr, uv/vis, ir) were in excellent agreementwith 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 andphotolysis equipment used in our laboratories for the syntheses of Ru 3CO 12 andRu(OEP)py2 can be found in reference la.The dimer [Ru(OEP)] 2 was prepared by high-vacuum pyrolysis of Ru(OEP)py2 , 6while the oxidized dimer [Ru(OEP))2(BF4)2 was prepared by adding 2 equivalents ofAgBF4 to a benzene solution of [Ru(OEP)]2 . 7 Removal of metallic silver from theoxidized dimer required that a CH 2C12 solution of the complex be filtered through a Celitepad; the fine frits available in our laboratories were not fine enough to prevent thepassage of finely divided metallic silver. Both dimers are extremely air-sensitive, both insolution and in the solid state. The solids were stored in the glove-box. In solution thedimers were handled using vacuum-transfer techniques where possible; when this wasimpractical, manipulations were carried out as fast as possible under dry, deoxygenatedargon, using a combination of Schlenk and syringe techniques.'The synthesis and characterization of Ru(OEP)(decMS) 2 has been previouslydescribed.' Ru(OEP)(chns)2Approximately 25 AL (0.34 mmol) of dms and 5 mL of methylene chloride werevacuum-transferred onto 0.1083 g (0.085 mmol) of [Ru(OEP)] 2 , which immediately gavea red solution. The volume was increased to about 15 mL with n-hexane, and then slowlyreduced until traces of precipitate appeared. The solution was filtered, and the volume28further decreased until considerable precipitation occurred. This concentrate was nowheated to redissolve the complex, and then allowed to cool slowly, first to roomtemperature and then to 0° C. The dark purple crystalline Ru(OEP)(dms) 2 was filtered offand dried in vacuo at 70° C overnight. Yield: 0.104 g (0.137 mmol, 81%). Anal. calcd.for C40H56N4S2Ru: C, 63.37; H, 7.45; N, 7.39. Found: C, 63.47; H, 7.48; N, 7.20.NMR (5; CD2C12 , 20.0° C): OEP, 1.81 t (CH 3), 3.85 q (CH2), 9.32 s (Hineso); dms, -2.66s. Uv/vis (0.0445 mM soln. in C 6H6 containing 68 mM dms) Xmax (log E): 407.5(5.34)(Soret), 498 (4.17), 525 (4.42) nm. Ru(OEP)(Et2S) 2The procedure for the synthesis of Ru(OEP)(Et 2S)2 was analogous to that ofRu(OEP)(dms) 2 . Yield: 0.257 g (0.315 mmol, 85%). Anal. calcd. for C 44H64N4S2Ru: C,64.91; H, 7.92, N, 6.88. Found: C,64.73; H,7.87; N,6.68. NMR (6; CD2C12 , 20.0° C):OEP, 1.78 t (CH3), 3.96 q (CH2), 9.25 s (Knew); Et2S, - 1 .32 t (CH3), -2.47 q (CH2).Uv/vis (0.0340 mM soln. in C6H6 containing 74 mM Et2S) Xma. (log E): 409 (5.23)(Soret), 499 (4.13), 525 (4.39) nm. Ru(OEP)(dmso)2 and the dmso-d6 AnalogueRu(OEP)(dmso) 2 (where s implies s-bonded) was prepared by adding 16 AL (0.23mmol) 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, andthen the solvents were slowly removed until solid just appeared. The solution wasfiltered, and the volume further reduced until considerable precipitation occurred. The29microcrystalline product was filtered, and then dried in-vacuo overnight at 70° C. Thedmso-perdeuterated analogue was prepared in an identical manner, using dmso-d 6 as thesulfoxide source. Yields: approximately 80% in each case.' Anal. Calcd. forC40H56N402S2Ru: C, 60.81; H, 7.14; N, 7.09. Found: C, 60.39; H, 7.40; N, 6.78. NMR(5; CD2C12 , 20.0° C): OEP, 1.87 t (CH3), 3.98 q (CH2), 9.78 s (Hmem,. ,); dmso, -2.18 s.IR (cm- ', in Nujol): vso , 1105. Uv/vis (0.0169 mM soln. in C 6H6 containing 22.6 mMdmso) X.. (log E): 397.5 (5.44) (Soret), 533 (4.04) nm. Ru(OEP)(Et 2S0)2Ru(OEP)(Et250)2 was prepared in a manner analogous to that forRu(OEP)(dmso)2 . Yield: approximately 80%. 10 Anal. calcd. for C44H64N402S2Ru: C,62.45; H, 7.62; N, 6.62. Found: C, 62.32; H, 7.58; N, 6.68. NMR (45; CD 2C12 , 20.0°C): OEP, 1.84 t (CH3), 3.96 q (CH2), 9.70 s (Hmeso); Et2SO, -1.55 br (CH3), -2.12 br(CH2)444 -2.74 br (CH 2)b . Uv/vis (0.0390 mM soln. in C6H6 containing 4.7 mM Et2SO)X ^(log 6): 399.5 (5.49) (Soret), 527 (4.10) nm. Ru(OEP)(decMS0) 2To 0.0692 g (0.0545 mmol) of [Ru(OEP)] 2 were added 0.0501 g (0.245 mmol) ofdecMSO, and about 5 mL of benzene. The solution immediately became a bright, rubyred. After about 10 minutes the solvent was removed, the solid redissolved in about 6 mLof n-pentane, and the resulting solution filtered to remove small amounts of a brownsolid. The filtrate was then cooled to -100° C for 15 min to effect precipitation of thedesired product. Ru(OEP)(decMS0)2 was filtered off at - 100° C as a scarlet powder, and30dried in-vacuo overnight. Note- the complex is extremely lipophilic, and great care had tobe taken to avoid contamination with stopcock grease. Yield: approximately 80%. 10 Anal.Calcd. for C581-192N402S 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; C7D8 20.0° C): OEP, 1.86 t (CH 3), 3.96 q (CH2), 9.72s (imeso) ; decMSO, -2.34 s (SCH3), -2.78 m ( 1 CH2), -1.11 m (2CH2), -0.02 m (3CH2),0.37 qn (4CH2), 0.73 qn (5CH2), 0.95 qn ( 6CH2), 1.0-1.25 m ( -9CH2), 0.839 t (1°CH3).Uv/vis (0.0101 mM soln. in C 6D6 containing 0.20 mM decMSO) X...„ (log c): 399 (5.59)(Soret), 530 (4.15) nm. Ru(OEP)(dms) 2+BF4To 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-hexanewere added, and the total volume reduced until precipitation just occurred. The solutionwas filtered, and the volume further reduced until most of the desired complex hadprecipitated, and the supernatant was a very pale orange. The brownish-purple needleswere filtered off, washed with n-pentane, and then dried in vacuo at 70° C overnight.Yield: approximately 80%. 10 Anal. calcd. for C40H56N4S2RuBF4 : C, 56.86; H, 6.68; N,6.63. Found: C, 56.67; H, 6.70; N, 6.44. NMR (6; CD 2C12 , 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. inCH2C 12) X., (log c): 394 (5.05) (Soret), 505 (4.05), 533 (4.03) nm.312.2.4.7 Ru(OEP)(Et2S)2 +BF4The preparation of this complex was analogous to that described forRu(OEP)(dms)2 +13F4. Yield: approximately 80%. 10 Anal. calcd. for C 44H64N4S 2RuBF4 : C,58.66; H, 7.16; N, 6.22. Found: C, 58.39; H, 7.17; N, 6.15. NMR (6; CD2C12 , 20.0°C): OEP, 1.31 br (CH3), 23.09 br (CH2), 1.61 br (; Et2S, 3.57 br (CH2), 7.82 br(CH3). Uv/vis (0.0838 mM soln. in CH 2C12) Xi. (log e): 394 (4.98) (Soret), 505 (4.01),533 (3.98) nm. Ru(OEP)(decMS) 2+BFiTo 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 tothe orange soluble Ru(OEP)(decMS) 2 +13F4. This product was recrystallized frombenzene/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 thevolume of a benzene/heptane solution until precipitation just occurred, heating toredissolve the precipitate, then allowing the solution to cool slowly. Approximate yield:80%. 10 Anal. calcd. for C 68H92N4S 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 2C12 , 20.0° C): OEP, 1.44 br (CH3),23.13 br (CH 2), 1.83 br (H.eso) :1 decMS, 0.50 br (SCH3), 0.92 t ( 1°CH3); {Tentative: 9.06,br ( 1 CH2), 4.39 br (2CH2), 2.22 br (3CH2), 1.96 br (4CH2), 1.60 br (5CH2); signals areprogressively sharper, with the last two beginning to show fine structure; 1.44 br(6-9CH2)}. Uv/vis (0.0921 mM soln. in CH2 C12) X.., (log c): 394 (5.10) (Soret), 505(4.11), 533 (4.09) nm. Molar conductivity (1 mM soln. in CH 2C12) A = 52 fricm2mol-1.322.2.4.9 Me4N+Ru(OEP)(PhC00)2To 0.104 g (0.0725 mmol) of [Ru(OEP)]2+(BF4)2 were added 0.0629 g (0.322mmol) of Me4N -ThC00- , and about 10 mL of methylene chloride. The colour changedimmediately 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 Me4N +13F4, then further cooledto -100° C to precipitate the desired, crimson product. This was filtered off, washed withn-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 inthe 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 2C12 , 20° C): OEP, -0.72 br (CH3), 8.08 br (CH2), 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):2.2.5 InstrumentationWhere 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 lawas used. Ultraviolet/Visible Absorption SpectroscopyUv/vis spectra were recorded at 20.0° C on a Perkin-Elmer 552A spectro-photometer with the slit width adjusted to allow 2 nm resolution. To obtain extinctioncoefficients, the absorbance maximum was scanned manually to avoid errors due to401 (5.0) (Soret), 520 (3.9) nm.33delays 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. Infrared SpectroscopyThe ir spectra of Ru(OEP)(dms) 2 , Ru(OEP)(dmso)2 and its dmso-perdeuteratedanalogue were obtained on a Nicolet 5DX single beam ir spectrometer, operating inFourier transform mode. Samples were mulled in Nujol, and sandwiched between KBrplates. Proton Nuclear Magnetic Resonance Spectroscopy'H nmr spectra were collected at 20.0° C, using a Varian XL-300 FT instrument. ConductivityThe conductivity measurement was performed using a model RCM 15B1conductivity bridge from the Arthur H. Thomas company; the conductivity cell was of acommercial design (Yellow Springs instrument company), with a cell constant of 1.00-Icm . Cyclic VoltammetryCyclic voltammetric measurements were carried out using an EG and G PARModel 175 Universal programmer to control the potential sweep; this unit was linked to aModel 173 PAR potentiostat equipped with a model 176 current-to-voltage converter anda model 178 electrometer probe. Voltammetric traces were recorded on a Hewlett-34Packard Model 7005B X-Y recorder. Scan speed was 100 mV/s unless otherwiseindicated.All electrochemical experiments were carried out in methylene chloride solution,with approximately 0.12 M n-Bu4N+BF4 acting as the supporting electrolyte.The electrochemical cell, based on a design described by Van Duyne andReilley," was made by S. Rak of this department, and was devised for use withminimal volumes of solution (cyclic voltammograms could be obtained with as little as 2mL), and to allow manipulation of highly air-sensitive samples where necessary. Figure2.1 illustrates the cell. The Ag/AgCI reference electrode was a commercial design byMetrohm, and was filled with aqueous saturated KC1. Under the experimental conditionsemployed throughout this work, the Cp2Fe/Cp2Fe+ and Ru(OEP)py 2 +/Ru(OEP)PY212couples occurred at E°' = 0.58 ± 0.02 and 0.10 ± 0.02 V, respectively, relative to thereference. In a typical experiment involving air-sensitive compounds, a solutioncontaining the material to be analyzed and the supporting electrolyte was first prepared inflask (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 wasstoppered, the cell was connected to a vacuum pump at joint 3, and evacuated. At thispoint tap 7 was opened to introduce the electroactive solution into the cell, and thenargon was introduced via (3). Finally, under an argon purge, the salt bridge/referenceelectrode combination and the working/auxiliary electrode housing were installed at joints4 and 5 as shown in the illustration. Tap 1 was closed, the assembled cell was connectedto 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 solvent35Figure 2.1. Cyclic voltammetry cell: (A) platinum bead working electrode; (B) platinumwire spiral auxilliary electrode; (C) non-aqueous salt bridge; (D) aqueous Ag/AgC1reference electrode; (E) KC1 reservoir; (F) sample preparation flask.36with more viscosity than methylene chloride were used, it might not flow easily throughthe Luggin capillary. In that case, closing tap 2 and pressurizing the reference electrodecompartment might succeed in driving the solution through. Elemental AnalysisElemental analyses were carried out by P. Borda of this department.2.3 Characterization of Ru(OEP)(RR'S0) 2 ComplexesA sulfoxide ligand can conceivably bind to a metal center via either its sulfur oroxygen atom; experimentally, both types of complex have been observed, and theorieshave been proposed to explain the bonding in each case." The bonding between sulfurand oxygen in a free sulfoxide is represented by the following canonical structures:RR'S=O <^ -> RR'S+-0-I IIIn 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 stabilizecanonical structure II, and thus decrease the S-0 bond order relative to that of the freesulfoxide. On the other hand, coordination via sulfur would tend to intensify the positivecharge on the sulfur atom, thus destabilizing canonical structure II, and consequentlyincreasing the S-0 bond order relative to that of the free sulfoxide. As might be expected37then, S-bound and 0-bound metal sulfoxide complexes can be readily distinguished by irspectroscopy: 14 in the S-bound case the S-0 stretching frequency is higher than in thefree sulfoxide, whereas in the 0-bound case it is lower.The ir spectrum of Ru(OEP)(dmso) 2 shows a strong band, assigned to vso , at1105 cm -1 , as compared with 1055 cm -1 in free dmso; hence it is characterized as an S-bound complex, at least in the solid state. The ir spectra of the other twoRu(OEP)(RR'S0)2 complexes were not obtained; however, all three complexes hadsimilar nmr and uv/vis spectra, as well as electrochemical properties (see the nextsection), which suggests that they share the same bonding patterns. In solution, there isevidence that some isomerization may be taking place. Kinetic studies of substitution ofthe bis(sulfoxide) systems by dialkylsulfides show that one of the sulfoxides is stronglybound, 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 moreimmediate interest is possible evidence that an S-bound sulfoxide can revert to, or bereplaced by, an 0-bound sulfoxide in solution. The uv/vis spectra of each of the threebis(sulfoxide) complexes prepared vary somewhat with temperature, even in the presenceof a large excess of free sulfoxide ligand; to give an example, figure 2.2 shows thetemperature dependence of the Ru(OEP)(Et§0) 2 uv/vis spectrum. These variations arereversible, and are not due simply to ligand dissociation, although evidence for the latterprocess is also observed for dilute solutions containing no added free ligand (see section3.4). The best explanation for the temperature dependence of the uv/vis spectra is that insolution one of the sulfoxides can be either S-bound or 0-bound, and that the ratio ofisomeric forms depends on the temperature. Despite these observations, it will be shown527Increasing Temperature420^500^A,(nm)^60038Figure 2.2. Changes in the visible spectrum of a CH 2C12 solution containing 0.039 mMRu(OEP)(Et2SO)2 , and 4.72 mM free Et2SO, as the temperature is increased in 10°intervals, from 20-50° C.39in section 3.4 that, for the purposes of the present study, Ru(OEP)(RR'SO) 2 complexes insolution can be thought of as containing only S-bound sulfoxides without changing anyconclusions.It should be added that the 1H-nmr spectra of Ru(OEP)(Et2SO)2 andRu(OEP)(decMSO) 2 (see sections and are also somewhat temperaturedependent, and also solvent dependent. As an example of solvent dependence, at roomtemperature in CD 2C12 , the sulfoxide methyl and methylene 'H-nmr signals ofRu(OEP)(Et2SO) 2 are broad and lacking in fine structure; on the other hand, at the sametemperature but in C6D6 , the same signals are resolved multiplets. This topic will not bediscussed further, as no systematic studies were done; however, it is an interestingsubject which deserves more study in the future.The assignment of the pso ir band requires some comment. Previous studies havementioned the potential difficulty in distinguishing p so from the pcH, signals of thesulfoxide, and reported that this difficulty could be overcome by comparing data for thedmso complex with those for its dmso-perdeuterated analogue. 13 '" The poi, modes areisotopically shifted when the perdeuterated analogue is used, whereas the Pso signalsremain unchanged. In the case of Ru(OEP)(dmso)2 and Ru(OEP)(dmso-d 6)2 , the spectraobtained are essentially identical in the region from 500-1500 cm -1 . Presumably the C-Hand C-D rocking modes in these complexes are buried under signals attributable toRu(OEP). When the ir spectra of Ru(OEP)(dmso) 2 and the perdeuterated analogue arecompared with that of Ru(OEP)(dms) 2 , the only difference in the region mentioned is thatthe spectrum of Ru(OEP)(dms) 2 lacks the strong 1105 cm -1 band; the rest of the spectrumis virtually identical for Ru(OEP)(dms) 2 , Ru(OEP)(dmso)2 , and Ru(OEP)(dmso-d6)2 . This40confirms the assignment of this band as PSO•The peak positions of all the Ru(OEP)(RR'SO) 2 'H-nmr signals are typical ofthose observed for other related Ru n(OEP) species; in fact, the most complex spectrumcollected, that of Ru(OEP)(decMS0)2 , was assigned by direct analogy with the previouslyreported spectrum of Ru(OEP)(decMS) 2 . 9 The predominant factor which determines thepeak positions of any diamagnetic porphyrin species is the ring current generated by theporphyrin 7 electrons, 15°' 6 and the ring current effect as it relates specifically toRu(OEP)(decMS) 2 is discussed in detail in reference 9. This effect will not be discussedfurther at this time, but it has been extensively investigated, and several semi-quantitativemodels have been published."'"2.4 Characterization of Ru m(OEP) ComplexesOxidation of metalloporphyrins can occur either at the metal center or at theporphyrin ring, and again there is precedent for both possibilities.' Fuhrhop et al. firstobserved in 1973 that a uv/vis spectrum consisting of 2-3 broad bands covering thevisible 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, whichlooked very much like those of an unoxidized precursor, indicated that oxidation hadoccurred at the metal." This qualitative test for oxidation site location is now widelyrecognized as one of the primary methods of distinguishing the two possibilities.' Figure2.3a shows that the uv/vis spectra of Ru(OEP)(dms)2 and Ru(OEP)(dms)213F4 are quitesimilar, suggesting that oxidation in synthesis of the latter has occurred at the metal. Thespectra of the other Ru(OEP)(RR'S) 2 13F4 - complexes were essentially identical to that of52541^Run (OEP)(dms),Rum (0E13)(clins); BF, -4981505‘.5330.0X(nm) 6 100X10407.5I1.0-394/11I(a)320 400 500 70000320^400500X(nm) 600Figure 2.3. Uv/vis spectra in CH 2Cl2 of (a) Ru(OEP)(dms)2 and Ru(OEP)(dms)2 +BF4,and (b) Me4N+Ru(OEP)(PhC00)242the dms one; the spectrum of Me4/4+12.u(OEP)(PhC00)2 (figure 2.3b) could not becompared to that of the reduced analogue, but also exhibits a fairly localized absorptionmaximum at 520 nm, and no significant absorption above 600 nm. Again this issuggestive of oxidation at the metal.To the author's knowledge, all Ru"(Porp) 7-cation radical complexes observed todate contain CO as a 7-accepting axial ligand. It is believed that metal to carbonyl back-bonding in these complexes stabilizes the metal d orbitals of 7 symmetry to the pointwhere they are at lower energy than the highest occupied 7 orbital of the porphyrin ring,and that this is why the ring is preferentially oxidized. 19,20 Previous studies in ourlaboratories and elsewhere have shown that dialkylsulfide ligands do not partake insignificant metal to ligand 7-7* back-bonding,' and the cyclic voltammetric (CV) studiesshow (figure 2.4a) that the standard reduction potentials of all threeRu(OEP)(RR'S) 2 13F4 complexes prepared occur at around 0.22 ± 0.02 V relative toAg/AgC1; 21 such values are comparable to those obtained for systems such asRu(OEP)py2 +/Ru(OEP)py2 , which are known to undergo oxidation at the Metal, 19 ' 22 butare 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 around0.65-0.70V. 19 '23aA further interesting question arises from the above discussion. Althoughdialkylsulfides do not partake in significant metal-ligand 7-7* backbonding, there is quitea body of evidence that sulfoxides do.' Would this cause sulfoxide complexes toundergo ring oxidation? An in situ redox titration of Ru(OEP)(Et0) 2 with AgBF4 , gavea uv/vis spectrum (figure 2.5a) very similar to those of the Ru(OEP)(RIVS)2+13F40.74 0.201.0 -1.01.28(a)(b)1.31E vs. Ag/AgC1(C)430.25ClaFigure 2.4. Cyclic voltammograms in CH 2C12/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 theother dialkylsulfide and sulfoxide complexes are virtually indistinguishable from those ofthe dms and dmso complexes illustrated. Also, a CV identical to (a) was obtained forRu(OEP)(dms)2+BF4.czt0cA7006000 -450 Ä,(nm)(a)^0.5= Ru(OEP)(Et,SO),= Ru(OEP)(Et,S0), + AgBF4 (1 equivalent)....... ■roo ra■■■••■ss.4452526^240II/ CHsS/. CH3■•• Cl.H„„„,^/HaOH3CB F4-— OS CH3CH3)OEPr 8 I I T:el, ' 14FreeSulfoxideHmesoTIT /ft0 PPM^—2(b)2Figure 2.5. (a) Visible spectrum of a 1:1 mixture of Ru(OEP)(Et2SO)2 and AgBF4 inCH2C12 ; (b) 'H-nmr spectrum of a CD 2C12 solution initially containing [Ru(OEP)]2(BF4)2and free dmso in approximately 1:8 ratio; S^solvent, T = 20° C.45complexes (see figure 2.3a), suggesting that oxidation of the sulfoxide complexes alsoresults in Rum derivatives. Figure 2.5b shows the 111-nmr spectrum of an in situ mixtureof [Ru(OEP)] 2(BF4)2 and dmso, in CD2C12 at 20° C; this spectrum has several featuresquite similar to those seen in the corresponding Ru(OEP)(dms) 2 +13F4 spectrum (see figure2.10, and the discussion later in this section). However, the presence of two signals forthe OEP methylenes indicates that the two faces of the porphyrin are inequivalent (ie: theporphyrin plane is not a plane of symmetry in this complex). There are also several smallsignals, some of which can probably be assigned to another minor Ru(OEP) paramagneticproduct. The presence of these extra signals complicates the assignment of any signalsdue to coordinated dmso; however, the signals at 0.02 and 10.20 ppm each have thecorrect integration for one sulfoxide. Furthermore, if the whole experiment is repeatedusing dmso-d6 , both these signals are absent from the resulting spectrum. Based on thisuv/vis and 1H-nmr evidence, the major product of Ru(OEP)(RR'S0) 2 oxidation istentatively assigned as Ru m(OEP)(RR'S0)(RR'S0) +BF4; the nmr signal at 0.02 ppm isassigned 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 0-bound sulfoxide. The cyclic voltammograms for the Ru(OEP)(RR'S0) 2 complexes (figure2.4b) also show evidence of a change in coordination on changing the oxidation state; theoxidation wave has a maximum current at 0.74 V vs. Ag/AgC1, while the reductionmaximum occurs at 0.53 V vs. Ag/AgCl. The large peak to peak separation indicates thatthe complex being reduced is not the same one that was oxidized, but the shape of theCV does not change regardless of how many times the scan is repeated, which suggeststhat upon reduction the original complex is recovered intact. This is consistent with the46postulated mechanism:'Ru1(OEP)(RR'S0) 2^Ru ili(OEP)(RR'S0)2 4- + e^E°' .-- 0.74 V 2.1Rum(OEP)(RR'50) 2 + ‘='-' Rum(OEP)(RR'S0)(RR'S0) + 2.2Rum(OEP)(RR'S0)(RR'S0) + + e rr—'Run(OEP)(RR'S0)(RR'SO)^E°' --,, 0.53 V 2.3Ru ll(OEP)(RR'S0)(RR'SO)-=*.' Ru(OEP)(RR'S0)2 2.4Note that 0.74 V is actually higher than the E°' values reported for Ru(OEP)(C0), 19,23aand so if both sulfoxides were to remain S-bound, ring oxidation might be predicted. It ispossible that ring oxidation does occur initially, and that internal electron transfer takesplace after one of the sulfoxides rearranges to yield the 0-bound isomer. Internal electrontransfer upon modification of the coordination sphere has been previously documented forruthenium porphyrins.''''Both the Ru(OEP)(RR'S) 2 and Ru(OEP)(RR'S0) 2 complexes exhibit a secondredox couple at around 1.3 V (figures 2.4a,b). No further investigation of this couple wascarried out in this work, but previous studies in our laboratories have yielded evidencethat the second oxidation of similar complexes containing two neutral axial ligands47occurred at the ring at around 1.3 V, to yield the Ru m 7-cation radical. 23a Figure 2.3cshows the corresponding redox couple (0.23 V) for Me 4N+Ru(OEP)(PhC00)2. Noticethat the coordination of two anionic ligands on the metal center renders the complexmuch more easily oxidizable; in fact, oxidation of the bis(benzoate) ruthenium(III) speciesis as easy as the one-electron oxidation of the Ru 11(OEP)(RR'S) 2 complexes. This pointwill be very important in the following section. Presumably, given the ease of oxidation,electron abstraction from Me4N+Ru(OEP)(PhC00)2 takes place at the metal to generateRu(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 toRu(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)(Et2S)2 +BF4, Ru(OEP)(decMS)2 +BF4 and Me4N+Ru(OEP)(PhC00)2 are shiftedconsiderably from their characteristic diamagnetic positions, which is typical forparamagnetic complexes. 258 The magnitudes and directions of the observed paramagneticshifts (from 0-20 ppm, with the methylene proton signals shifting downfield, and themeso proton signals shifting upfield) are fairly representative of those seen for Rum(OEP)low spin complexes (no Rum(Porp) high spin complexes have ever been observed); 26Ru 1"(OEP) complexes generally (but not always) show much greater shifts (as high as 100ppm). 27 The spectra of Ru(OEP)(dms) 2 13F4, Ru(OEP)(Et2S)2 +BF4 andMe4N +Ru(OEP)(PhC00) 2 - are assigned primarily based on the relative intensities of allthe signals. The spectrum for Ru(OEP)(decMS) 2+13F4 (figure 2.6) was more difficult tointerpret. The porphyrin signals and the SCH 3 signals are assigned by analogy to the10(CH, )SCH 39^7^5^3^1/N./N.,..N.,N7NS''''I ,CH 3limeso—MM Ru Elm-- CH,/ sNrN/NVNVN./10^8^6^4 (CH 3)6EP.,,BF;^6 9 (CH 2( CH, )0a„1111,111111124^22'( CH, )1111111-11111111-1r111 1 111111-111 1 11111-1111 1 1111 1 1117 1 111 11 1111 1 1111 11111- 11/1111111111111111111111111111111111111110^9^8^7^6^5^4^3^^– 1^0^-1`PPMFigure 2.6. 'H-nmr spectrum of Ru(OEP)(decMS) 2 +13F4- in CD2C12 , taken at 20.0° C; S E solvent.49simpler systems, while the signal due to the thioether 1°CH3 is unshifted relative to eitherthat of the free ligand or the Ru"-coordinated analogue.' A peak at 9.06 ppm istentatively assigned to ( 1 CH2), based on its integration and the fact that it is the broadestof the unassigned signals. A series of progressively sharper signals at 4.39, 2.22, 1.96,and 1.60 ppm are assigned to (2CH2)-(5CH2); the last two actually show some finestructure. Finally, the signals for (6-9CH2) 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 MethyleneChlorideFigure 2.7 shows the 'H-nmr spectral changes over time as a solution containingabout 20 mM Ru(OEP)(dms)2 and 12 mM benzoic acid in CD 2C12 is exposed to 1 atm of02 at room temperature. For simplicity only part of the spectrum is shown, butcomparable 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, spectralchanges analogous to those illustrated in figure 2.5 are observed, at least in the 5-25 ppmregion; below this, the spectra of the reaction mixtures are too complicated to interpretreadily.The two sharp singlets seen between 9.5 and 10 ppm are assigned to the OEPmeso 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 withdmso, or of Ru(OEP)(dmso) 2 with dms, the mixed species could be unequivocallyidentified by uv/vis or 'H-nmr data (see for example figure 2.8). In fact, for themss / s ■I ,^I11.■ Ru-■ — Rulill■ + e -I 135 h360 min312 min234 min97 min28 min /Tr I 1.111^II(1/1111111^r^I^Trill-ill-III im16^ th 14^A' I^r^tirtyririvrtrit^ Ia PPMFigure 2.7. 11-1-nmr spectral changes over time after an acidic CD 2C12 solution of Ru(OEP)(dms) 2 is exposed to 1 atm of 02 atroom temperature (approximately 20° C). The peak assignments for each species are summarized in table 2.2.O 0Ru—■00PhCO— Rum■ The two small signals at around11.8 and 16 ppm are due touncharacterized impuritiespresent before reaction began. ofAII[ri—41^I^I^I—2 PPMHmeso0 0NRumII N0dmsFreedFreeI^I^1^I0Figure 2.8. 1H-nmr spectrum of a CD2C12 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)Ru(OEP)(dms)(dmso).[10 Frill'2I^Fto which an excess of a mixturespecies in solution isI^- I^I^I^T^1^I^I6 40H3 C II CH 3RuHmeso^IH3C .• CH3CH3-CH,Table 2.1Summary of the 'H-nmr Peak Positions in CD 2C12 forthe Ru(OEP) Complexes Discussed in Section 2.5OEP Signals (ppm)CH3^CH2 HinesoAxial Ligand Signals (ppm)dms^dmso^PhCOOH.^H. HpRu(OEP)(dms) 2 1.81,t 3.85,q 9.32,s -2.66,sRu(OEP)(dms)(dmso) 1.83,t 3.92,m 9.60,s -2.87,s -2.07,sRu(OEP)(dnig) 2 1.87,t 3.98,q 9.78,s -2.18,sRu(OEP)(dms)2 4- BF4- a 1.52b 23.85 1.73 -0.17 - _ _Ru(OEP)(dms)(PhCOO) 0.46 16.75,12.87 4.07 -0.49 - 15.34 9.84 8.75Me4N + Ru(OEP)(PhC00)2c -0.72 8.08 2.72 - - 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 4N + counterion is seen at 5.64 ppm.53analogous system involving Et 2S and Et2SO, the equilibrium constants as well as the rateconstants for the substitution processes were determined by stopped-flowspectrophotometry; this will be fully discussed in section 3.4.Initially, very little of the bis sulfoxide complex is seen. In fact, in all of thespectra 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-sulfoxideis the major Ru(OEP) product. Another important point seen in figure 2.9 is that after 35h 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 COOHproton, clearly identifiable at 11.4 ppm before the reaction was initiated, is no longervisible. A broad, underlying hump is visible around 5 ppm in figure 2.9 (most clearlyseen in the integral scan), which suggests that water is now present, and the COOHproton is rapidly exchanging with it. In the spectra collected from 28 to 360 min, thebenzoate phenyl proton signals are shifted significantly from their positions in benzoicacid; this is likely due to interaction of PhC00 - anions with paramagnetic Rum(OEP)(and possibly RUN) species (see below). Presumably PhC00 - counter-ions wouldexchange rapidly with PhCOOH, and only time-averaged 1H-nmr phenyl signals would beobserved. 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 theregion 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 +1311C00 -and Ru(OEP)(dms) 2 (all of the peak positions, for all of the spectra collected, are listed inIIIIIIIIFIT1ri UI j I I I I^I 1 I (TT1littlurt -trr-ttItiri Fl E Tr l^II II I IA 1 I] I 11 I I -1 -1 4 1 ^FIT-1-141-T1-11-11-1/1111111111111A^16^14 tk^10^ 4^ - PR4^-4Figure 2.9. 'H-nmr spectrum of an acidic CD 2C12 solution of Ru(OEP)(dms)2 35 h after exposure to 1 atm of 02 at room^temperature (cf. figure 2.7); S ^solvent.55table 2.2). Figure 2.10 shows the spectrum of pure Ru(OEP)(dms) 2 +13F4. When thiscomplex 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 theconcentration ratio of Rum/Run. This shows that electron transfer between Ru(OEP)(dms) 2and Ru(OEP)(dms) 2 +X- (X^PhCOO, BF4) at 20° C is very rapid. The followinganalysis provides an idea of just how fast the electron transfer is. For the case in which aproton can be at one of two sites (in this case either in a Rum environment or a Ru llenvironment), the necessary condition for detecting separate resonances for the proton ineach environment is given by r' > 2"/(27,6a,), where T 1 is the lifetime of the proton ateach site, and Ai) is the separation of the peaks (in Hz) when no exchange is takingplace.' For the OEP methylene protons, the peak separation between the Ru ll and theRum 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) 2and Ru(OEP)(dms) 2 +13F4 in a mixture of the two species, r ' cannot be larger than3.8)(10' s at 20° C.In figure 2.7, the OEP methylene signal shifts over time towards the Ru mposition, at the same time decreasing in overall intensity. This shows that the overallconcentration of the two species is decreasing, while the ratio of Ru m/Rull is increasingwith 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 spectrumcollected. Based on the oxidation mechanism proposed later in this section, wehypothesize that the concentration of Ru(OEP)(dms)2 ÷PhC00 - is in a steady state formost of the reaction, while that of Ru(OEP)(dms) 2 decreases steadily.CH3...... ,.... CH3SI..,,,,■RuHmeso00.0 S "S,,,...,H3C^CH3BF4/CH3CH2(CH3)oEP.---------(CH2)0EPLagliga".86"a"...""w risA•^inummoninLajimesoFigure 2.10. 'H-nmr spectrum of Ru(OEP)(dms) 2 13F4; 20.0° C in CD 2C12 ; S ---  solvent.Table 2.2Positions of the 1H-mnr Signals (bobs), Assigned toRu1(OEP)(dms) 2 + Ru111(OEP)(dms) 2+ PhC00-in the Experiment Illustrated in Figure 2.7, and the CalculatedRemaining Mole Fraction of Ru(OEP)(dms) 2 (NurTime(min) CH3 CH2Sa,„ (NH)Hmeso SCH328 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: Nn = (sobs - (5m)/(Sin - (in), where bn and Om are the values of 6 (in ppm)for Ru"(OEP)(dms) 2 and Rum(OEP)(dins)2 +BE4, respectively (6 for Ru(OEP)(dms)2 + is assumed to be the same whether thecounter-ion is PhC00 - or BEI--58The rapid electron transfer giving rise to the observed time-averaged nmrspectrum almost certainly occurs via an outer-sphere process. Such processes have beenextensively documented in porphyrin systems, and the porphyrin ring is thought tomediate facile electron transfer from a donor to the metal center or vice-versa.' Wehave obtained the crystal structure of Ru(OEP)(decMS)2 +13F4 (figure 2.11), which isexpected to be closely analogous to that of Ru(OEP)(dms)213F4. 29 Table 2.3 comparesselected 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 bondlength between the two species are within about 0.020 A, while the corresponding bondangles 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, aswell as other complexes containing Ru-S bonds.' The geometrical differences betweenRu(OEP)(decMS) 2 and Ru(OEP)(decMS)2 +13F4 are not significant when compared to thevariations found in this survey. It is clear that the change in oxidation state does notsignificantly affect the geometry of the complex. Thus electron transfer between the twoRu species requires minimal bond reorganization, and this leads to fast and efficientelectron exchange." Note that in a 1971 article,' Stynes and Ibers point out that achange in spin state upon oxidation or reduction will reduce the electron exchange rate toa much greater extent than even a relatively large change in bond lengths. As mentionedpreviously, no Ru m(OEP) high spin complex has ever been detected, and all of theavailable spectroscopic data for Ru(OEP)(dms) 2+13F4 are similar to those of previouslyreported Rum(OEP) low spin d5 complexes; the fast electron exchange between Ru ll andRum 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 2.3.60Table 2.3Selected Bond Distances (A) and Bond Angles (deg)for Ru(OEP)(decMS) 2 and Ru(OEP)(decMS) 2+BF4 aDistancesRu(OEP)(decMS) 2 Ru(OEP)(decMS)2+BF4Ru-S(1) 2.376 (1) 2.383 (6)Ru-S(2) 2.361 (1) (b)Ru-N(1) 2.044 (3) 2.029 (6)Ru-N(2) 2.044 (3) 2.045 (5)Ru-N(3) 2.056 (3) (b)Ru-N(4) 2.041 (3) (b)AnglesN(1)-Ru-S(1) 90.2 (1) 85.6 (2)N(2)-Ru-S(1) 86.9 (1) 90.1 (2)N(3)-Ru-S(1) 90.9 (1) (b)N(4)-Ru-S(1) 94.0 (1) (b)N(1)-Ru-S(2) 90.7 (1) 94.4 (2)N(2)-Ru-S(2) 94.7 (1) 89.9 (2)N(3)-Ru-S(2) 88.3 (1) (b)N(4)-Ru-S(2) 84.5 (1) (b)S(1)-Ru-S(2) 178.27 (3) 180.00(a) Standard deviations in parentheses. (b) Ru(OEP)(decMS) 2 +13F4 has a crystallographicinversion center.61The two major signals in figure 2.7 which are shaded grey are attributable to theOEP methylene protons of a paramagnetic complex of formulationRu(OEP)(dms)(PhCOO) (see below); two signals are observed since in this case the twoaxial ligands are different, which makes the methylene protons magnetically inequivalent.The other signals which are shaded grey are also attributed to the same complex; thecomplete assignment is listed in table 2.1, and is discussed below. The signals due toRu(OEP)(dms)(PhCOO) maintain approximately the same intensity (e.g. relative to theimpurity at 16 ppm) until the last (35 h) spectrum, in which their intensity is greatlydiminished (figure 2.9). At this point the signals are also slightly but significantly shiftedrelative to their position in earlier spectra. No immediate explanation is available for thisobservation; all of the signals initially assigned to the Ru(OEP)(dms)(PhCOO) complexare still present in the final spectrum, but shifted to varying degrees. It is possible that inthe first five spectra the signals are actually time-averages due to exchange betweenRu(OEP)(dms)(PhCOO) and some other complex, and that by the time of the finalcollected spectrum the concentration of this exchanging complex is negligible.The presence of Ru(OEP)(dms)(PhCOO) and Ru(OEP)(dms) 2+PhC00- is bestexplained by the following reaction sequence:2Ru ll(OEP)(dms) 2 + 02 + 2PhCOOH -3 2Ru m(0EP)(dms) 2 +PhC00- + H202 2.5Rum(OEP)(dms) 2 +PhC00 - T'—' Rum(OEP)(dms)(PhCOO) + dms^2.662Step one would involve initial electron transfer from Re to 0 2 to form Rum and thesuperoxide anion, followed by superoxide protonation and subsequent disproportionationto give hydrogen peroxide and dioxygen. The latter process is known to be very fast, andirreversible,' 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 andassociated anion. This is convenient for book-keeping purposes, but it is also meant tosuggest a physical picture: given the low dielectric constant of the CH 2C12 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 initialcoordination of 02 to the metal center (inner-sphere), or by direct outer-sphere electrontransfer; there is precedence for both mechanisms.' For the stoichiometric processbeing discussed here, the inner sphere mechanism is almost certainly the only significantpathway, as evidenced by the fact that the reaction can be stopped completely if an excessof 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 axialbinding site. Thermodynamically, the direct formation of superoxide via an outer-sphereelectron transfer is extremely unfavourable; the (02 + e^02) standard reductionpotential 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 Vreported in section 2.4, gives a cell potential of about -1 V. This translates to anequilibrium constant value of about 10' 7 (for Re + 02 -"-=' Rum + 02 -). Theoretically,even a highly unfavourable equilibrium can be overcome if the product removal in a63subsequent step (e.g. in this case, by protonation of superoxide) is faster than the reversereaction; however, product removal cannot overcome the effect of an initial, slowforward reaction. In this case it appears that outer sphere electron transfer from Ru ll to02 is not only thermodynamically unfavourable, but also kinetically slow, at least undernormal laboratory conditions. In chapter 3 it will be seen that Ru(OEP)(RR'S) 2 complexescan react with 02 and PhCOOH in the presence of excess dialkylsulfide, if the solution isirradiated with a reasonably intense source of visible light; in this case, the reaction ishypothesized to take place via an outer sphere process, but light is required to supply theextra energy.Hydrogen peroxide is known to react rapidly with dialkylsulfides, especially innon-hydroxylic solvents.' Thus the H202 produced in reaction 2.5 is expected to reactrapidly with free dms (produced in reaction 2.6) to give water and dmso:H202 + dms --> H2O + dmso^ 2.7Hydrogen peroxide could also react with coordinated dms, but free dms is a strongernucleophile.Numerous unsuccessful attempts were made to prepare Ru(OEP)(dms)(PhCOO)pure; figure 2.12a, which shows the 11-1-nmr spectrum obtained for an approximately 1:1mixture of Ru(OEP)(dms) 2 +13F4 and Me4N+Ru(OEP)(PhC00) 2 - , illustrates the basicproblem (figure 2.12b shows the spectrum of pure Me 4N+Ru(OEP)(PhC00)2 forcomparison). The major signals in the spectrum are attributable to the desired complexRu(OEP)(dms)(PhCOO). Signals due to residual Me4N+Ru(OEP)(PhC00)2 are also(a)A64OPhC70Rum0,C.Ph0Me4N+( CH; )0EP,13^'^'^'^16^'i'd'1 1 1",1 1 - PPM(b)( CH2 )oEPNNCH, HPUL•%—..)HoFigure 2.12. 'H-nmr spectrum of (a) a mixture (approximately 1:1) ofRu(OEP)(dms) 2 +BF4 and Me41•1 +12u(OEP)(PhC00)2 - about 1 h after mixing; (b) pureMe4N+Ru(OEP)(PhC00)2. Both spectra in CD 2C12 at 20.0° C, and systems sealed undervacuum; S =-= solvent.65present because the original mixture was not exactly 1:1, but this is not a factor when thereaction 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 andRu(OEP)(dms)(dmso) to be present as well, in essentially a 1:1 proportion. Attempts tocrystallize out the desired product using hydrocarbon solvents resulted in a dramaticincrease in the concentrations of Re species, this time with a predominance ofRu(OEP)(dms)2 . In every attempt to prepare Ru(OEP)(dms)(PhCOO), Ru(OEP)(dms)2and Ru(OEP)(dms)(dmso) were obtained as co-products; in CH2C12 the species were intrace amounts and 1:1 proportion, but as soon as hydrocarbons were added, largeamounts 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 itsexistence, 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 adisproportionation such as the following can take place:Rum(OEP)(dms) 2 +PhC00- + Rum(OEP)(dms)(PhCOO) ‘=-''Ru ll(OEP)(dms) 2 + Ru iv(OEP)(dms)(PhC00) +PhC00-^2.8In this scenario, coordination of the benzoate to the Ru m metal center brings theRum/Ruw redox couple into the range of the Ru(OEP)(dms)2 +/Ru(OEP)(dms)2 couple; theCV studies discussed in section 2.4 already show how coordination of two benzoates to66Rum can decrease its oxidation potential from about 1.3 to 0.22 V, making it almost aseasy to oxidize to RIP as it is to oxidize Run(OEP)(Et2S)2 to the corresponding Rumspecies. The presence of Ru N could well explain the slight shifts observed in theRu(OEP)(dms)(PhCOO) 'H-nmr signals while the stoichiometric oxidation reaction isunder 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 ofRu(OEP)(dms)(dmso) by the following sequence of reactions:Ruiv(OEP)(dms)(PhC00) +PhC00 - + H2O cz--'0=RuN(OEP)(dms) + 2PhCOOH 2.90=RuNOEP)(dms) + dms --> Ru ll(OEP)(dms)(dmso) 2.10Run(OEP)(dms)(dmso)^Run(OEP)(dms) + dmso 2.11Ruil(OEP)(dms) + dmso^Ru il(OEP)(dms)(dmso) 2.12The conversion of coordinated dmso to dmso could alternatively involve anintramolecular process and a 7-bonded S =0 moiety in the transition state,' althoughsome kinetic findings imply otherwise; this will be discussed in section Finally,as free dmso accumulates, the bis sulfoxide complex would be formed via67Ru(OEP)(dms)(dmso) + dmso --='' Ru(OEP)(dmso) 2 + dms^2.13Equation 2.8 can be thought of as an acid-base reaction leaving a hydroxide as counter-ion to the RuN cationic species, followed by nucleophilic addition of the hydroxide to thecoordinated benzoate, and subsequent displacement of the Ru"-oxo. Alternatively, theacid-base reaction could be followed by a simple displacement of the coordinatedbenzoate by the hydroxide, followed by deprotonation of the coordinated ligand. Water inthe 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 isRun(OEP)(dm s)2 + 02 Ru ll(OEP)(dm50)2^ 2.14As previously mentioned, the benzoic acid is not consumed in the reaction, and actsmerely as a catalyst.It should be emphasized that although equations 2.8 and 2.9 fit well into thescheme for the observed reactivity of Ru(OEP)(dms)2 , they are meant to suggest a general"Ruw =0" mechanism whereby the reaction takes place, and not necessarily the exactmechanism. There are a considerable number of variations which could be proposed forequations 2.8 and 2.9; a particularly plausible example might be:Rum(OEP)(dms)(PhC00) + H 2O --"- Rum(OEP)(dms)(OH) + PhCOOH^2.8'68Rum(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 aspart of the reaction pathway.Further equilibria might arise as free dmso accumulates from reaction 2.7. Someof the sulfoxide might tend to coordinate to Re:Rum(OEP)(dms) 2 +PhC00- + dmso Rum(OEP)(dms)(dmso) +PhC00 - + dms 2.15The cyclic voltammetry experiments show (figure 2.4b) that coordination of a sulfoxideto Run' makes the metal much more reducible than its dialkylsulfide counterpart; thus if aspecies such as Ru(OEP)(dms)(dmso) +PhC00- is formed during the Ru(OEP)(dms)2oxidation sequence, it will be rapidly and preferentially reduced to the Ru" form, eitherin 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 primarilyRu(OEP)(decMS)(decMS0) prepared by mixing 0.78 mM Ru(OEP)(decMS) 2 , 71 mMdecMS, and 25 mM decMSO (all three Ru(OEP)(RR'S)(RR'SO) complexes have adistinctive band at 404 nm in their uv/vis spectra, and this can be used to investigate thecomposition of the above mixture). Initially, as the potential is scanned in the positivedirection, the major signal, attributed to the oxidation of Ru(OEP)(decMS)(DecMS0), isfound at 0.59 V; the signal at 0.28, attributed to Ru(OEP)(decMS) 2 oxidation, is minor0.210.59Figure 2.13. Cyclic voltammogram of a solution (CH 2C12/n-Bu4N+BF4) initiallycontaining 0.78 mM Ru(OEP)(decMS) 2 , 71 mM decMS, and 25 mM decMSO.6970by comparison. As the potential is scanned back in the negative direction, the peak due toRum(OEP)(decMS) 2 + reduction (at 0.21 V) is now the major one, while that due toRum(OEP)(decMS)(decMS0) + reduction (at 0.50 V) is comparatively minor. Theobservation is explained by the following reaction sequence:Ru ll(OEP)(decMS)(decMS0) Rum(OEP)(decMS)(decMS0) -1- + e^2.16Rum(OEP)(decMS)(decMSO) + decMS Rum(OEP)(decMS)2 + + decMSO 2.17Rum(OEP)(decMS)2 + + e- Ru ll(OEP)(decMS)2^2.18This experiment shows that sulfide coordination to Rum is preferred over sulfoxidecoordination; thus equation 2.15 should not play an important role in the stoichiometricoxidation, except possibly at the point when most of the sulfide has been converted tosulfoxide.All of the alternate reaction pathways proposed, though different in detail toequations 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 Rum species which has had its oxidationpotential lowered upon replacement of one coordinated thioether by an anionic ligand,and the resulting Ru Iv species is converted to O=Ru"(OEP)(dms).712.6 Reaction of Ru(OEP)(RR'S) 2 Complexes with Dioxygen and Benzoic Acid inHydrocarbon SolventsIn benzene or toluene containing benzoic acid, exposure of Ru(OEP)(dms) 2 ,Ru(OEP)(Et2S)2 or Ru(OEP)(decMS) 2 to 02 , under conditions analogous to thosedescribed for the reactions in methylene chloride, also ultimately results in the productionof the Ru(OEP) mono- and bis- sulfoxide complexes. In a general sense, the mechanismsuggested in equations 2.5-2.13 is consistent with the reactivity observed in benzene ortoluene; however, the lower polarity of these solvents (dielectric constant ,- r- 2) doesresult in some minor, but interesting, differences between what is observed in methylenechloride, and what is observed in, say, benzene.Figure 2.14 shows the 'H-nmr spectrum of a C 6D6 solution containing 8.2 mMRu(OEP)(dms) 2 and 8.2 mM PhCOOH, which was exposed to 1 atm of 02 for about 36 hat room temperature (table 2.4 summarizes the peak assignments). Several points arenoteworthy about this reaction. First, it is much slower than the analogous reaction inmethylene chloride; figure 2.9 shows that, after 35 h, a substantial proportion of theRu(OEP) has been converted to Ru(OEP)(dmso)2 , and no Ru(OEP)(dms) 2 can bedetected. In the reaction illustrated in figure 2.14, only about 66% of the originalcomplex has reacted to give Ru(OEP)(dms)(dmso), and the bis(sulfoxide) is present intrace amounts. A second point is that no significant amounts of Ru m complexes arevisible in the reaction mixture (actually, trace amounts of Ru(OEP)(dms)(PhCOO) aredetectable, 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 ofRum(OEP)(dms)(PhC00) (table 2.4) could be detected in significant quantities, but evenAIun.A0PhCOOHrA-NA0PhCOOHr•■■-••■ Tr-r-r"T"1-r-r-rT2Pk11111- T^ 1'^r rrirl r I r 111 -1--11 -11111i1 -11I- 1- 1- 11 - 11.1D^ 6Figure 2.14. 'H-nmr spectrum of a C 6D6 solution, initially containing 8.2 mM Ru(OEP)(dms) 2 and 8.2 mM PhCOOH, whichwas exposed to 1 atm of 0 2 for about 36 h at room temperature; S^solvent, g^grease, ?^unidentifed signals.Table 2.4Summary of the 'H-nmr Peak Positions in C 6D6 forthe dms- and dmso-Containing Ru(OEP) Complexes Discussed in Section 2.6OEP Signals (ppm)^Axial Ligand Signals (ppm)CH3^CH2^Hmeso^dms^dmso^PhCOOHo^H.^HpRu(OEP)(dms)2Ru(OEP)(dms)(dmso)Ru(OEP)(dm50)2 aRu(OEP)(dms)(PhCOO) b1.90,t1.88,t1.93,t0.303.90,q3.93,m3.99,q15.73, 12.339.62,s9.85,s9.94,s4.12-2.68,s-2.94,s0.20-2.08,s-2.32,s- 16.88 9.77 —8.45'(a) This spectrum was obtained in C7D 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 establishthe exact peak position.74under 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-polarbenzene solvent, and also equation 2.6, in which Ru(OEP)(dms) 2 +1311C00- is consideredto dissociate dms and form Ru(OEP)(dms)(PhCOO) must lie far to the right. Both ofthese factors would contribute to making the overall reaction slower in hydrocarbonsolvents (cf. equation 2.8). A third feature of figure 2.14 worth pointing out is thepresence of the trace signals at 4.3 and 10.1 ppm. The presence of both these signals wasnoted in our earlier studies on the oxidation of Ru(OEP)(decMS) 2 ," although the signalswere much more prominent la There is no immediately apparent assignment for the signalat 4.3 ppm, but that at 10.1 ppm is almost certainly attributable to the meso proton of aRu ll(OEP) complex.' It is impossible to be sure which complex is giving rise to thissignal, but it may be a Ru(OEP)(CO)L species (L --. a neutral ligand, possibly dms ordmso), as such species exhibit an Hines, signal at around 10.1 ppm in benzene.' It is wellknown 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 noobvious source of CO has been documented, although often without explanation (but seebelow). 1a,22,38,39The presence of end-products other than the sulfoxide complexes (which aredesired within the catalytic 02-oxidation of thioethers to sulfoxide; see chapter 3) seemsto be characteristic of the reactions carried out in hydrocarbon solvents. Figure 2.15shows the result of exposing a solution containing 2.3 mM Ru(OEP)(Et 2S)2 and 3.3 mM13 s1RuPhCFree Et2Sand Et2S0g-4AsFigure 2.15. 'H-nmr spectrum of a C 6D6 solution, initially containing 2.3 mM Ru(OEP)(Et 2S)2 and 3.3 mM PhCOOH, whichwas exposed to 1 atm of 0 2 for about 12 h at 35° C; S^solvent, g^grease, ?^unidentified signals.Table 2.5Summary of the 'H-nmr Peak Positions in C6D6 forthe Et2S- and Et2SO-Containing Ru(OEP) Complexes Discussed in Section 2.6OEP Signals (ppm)^ Axial Ligand Signals (ppm)Ru(OEP)(Et2S)2Ru(OEP)(Et2S)(Et25.0)Ru(OEP)(Et2_SO)2 bRu(OEP)(Et2S)(PhC00)CH31.91,t1.91,t1.90,t0.24CH23.91,q3.96,m3.94,q15.40, 12.36HMESO9.65,s9.85,s9.90,s— 4.1 6Et2S^Et2 S 0CH2^CH3^CH2^CH3-2.34,q^-1.49,t-1.4 to -2.7'^-1.4 to -2.7'-(2.11,2.68)c -1.65,t8.22^— 4.1 dHo17.00PhCOOHm-9.80Hp8.556(a) These signals have not yet been unequivocably assigned.(b) This spectrum was obtained in C71:0 8 .(c) For Ru(OEP)(Et250)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,77PhCOOH, to 1 atm of 02 for 12 h at 35° C (these are the conditions under which theexperiments described in the next chapter were run, except that in the latter an excess ofthioether was added). The peak assignments for figure 2.15 are given in table 2.5. Forthe Et2S system, Ru ffi(OEP)(Et2S)(PhC00) does accumulate significantly (in fact thesignals attributable to this complex were present within 20 min of starting the reaction). Itappears that Rum(OEP)(Et2S)(PhC00) is significantly more "stable" than its dmscounterpart under the reaction conditions. Still, there is no evidence in figure 2.15 for thepresence of Ru m(OEP)(Et2S)2 +PhC00 -; thus even for the Et2S complex, the ionic speciesis not stable in the less polar solvent, so that the Et 2S equivalent of equation 2.6 lies farto the right. What little Ru(OEP)(Et 2S)2 +1311C00- is produced perhaps rapidly undergoesthe disproportionation reaction 2.8 and subsequent reactions, to give neutral species suchas 0=Ru(OEP)(Et2S), and eventually Ru(OEP)(Et2S)(Et2S0). Figure 2.15 also shows thesignals at about 4.3 and 10.1 ppm (note that here the 4.3 signal is quite intense), and alsotwo other signals of about equal intensity near 9.5 ppm. Again, one can only speculate asto the identity of the complexes which give rise to these signals, but previous studies haveshown that the meso protons of complexes having the form [Ru N(OEP)L] 20 (L ananionic ligand) have signals around 9.5 ppm in benzene solution.' These so-called A-oxo dimers are well known thermodynamic sinks in ruthenium porphyrin chemistry when02 and H2O are present, and so it is likely that the two signals at around 9.5 ppm infigure 2.15 are due to two complexes of this type (perhaps with L^PhCOO and/orOH)."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 aAsow RIu13 sRums0PhCsRu/ 1 10A_P-OSPhCOOH PhCOOHIlifir I rIr IfT FT114T-111]^IV.^Tlbrg^r-ri 11111i^ r^I 1- r- r-Figure 2.16. 'H-nmr spectrum of a C 6D6 solution, initially a suspension of Ru m(OEP)(dms)2 +13F4- andsolvent, ?^unidentified signals.Me4N+Rum(OEP)(PhC00)2(approximately 4x10 6 mol of each), which was allowed to stand overnight under vacuum; Sr tlitTliFfilPPM^-479solution obtained by allowing a suspension of Ru(OEP)(dms) 2 + 13F4 andMe4N+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 6D6 . At the time the spectrum wastaken, all of the solid had dissolved, and the resulting solution was dark red-orange. Thespectrum shows that Ru(OEP)(dms)2 and Ru(OEP)(dms)(dmso) are formed in anapproximately 3:1 ratio, along with comparatively small amounts ofRu(OEP)(dms)(PhCOO), and other unidentified Re products. This is a very differentproduct distribution from that obtained when Ru(OEP)(dms) 2 +13F4 andMe4N+Ru(OEP)(PhC00)2 are mixed under vacuum in CD 2C12 (see figure 2.12a in theprevious section); in this solvent, the major product is Ru(OEP)(dms)(PhCOO), and thesmall quantities of Ru(OEP)(dms) 2 and Ru(OEP)(dms)(dmso) observed can be attributedto the presence of a trace amount of water, which presumably allows reactions 2.8-2.13to take place to a limited extent. It appears that in benzene, the Ru m species aresufficiently unstable in solution that, even in the absence of H2O, an alternative reductionpathway is being used to generate substantial amounts of Ru(II). One plausible route isvia a process formally described by:Rum(OEP)(dms) 2 +BF4" + Me4N+Ru(OEP)(PhC00)2 -'Ru"(OEP)(dms) 2 + "(PhCOO)2 " + Me4N +BF4 + Unidentified Ru n Products 2.19In practice, benzoyl peroxide is not observed; however, this could be because the benzoylradicals react further with other compounds in solution, which would explain the presenceof the other unidentified products, and also of coordinated dmso. In hydrocarbon solvent,80such free-radical processes might take place to a limited extent under even under 0 2atmospheres, when H 2O is available (from the reaction of dms with H 202 , equation 2.7),which could also help explain the formation of unidentified Ru(OEP) products obtained inthe aerobic oxidations of Ru(OEP)(dms)2 and Ru(OEP)(Et2S)2 in hydrocarbon solutions.For example, the presence of the PhCOO radical in aerobic conditions could initiate auto-oxidation of the thioethers. This is known to produce, among other products, aldehydes, 35and it has been shown that Ru(OEP) complexes can catalyze the decarbonylation ofaldehydes.'" 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 subsequentdecarbonylation of the primary auto-oxidation products.Despite the minor side products which are observed when Ru(OEP)(RR'S) 2complexes react with 0 2 and PhCOOH, it does appear that the major oxidation pathwaycan be described by equations 2.5-2.13, whether the oxidation is carried out in methylenechloride or benzene. This conclusion becomes a key assumption in the experimentsdescribed in the following chapter.81REFERENCES AND NOTESFOR CHAPTER 21. 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 supernatantsafter recrystallization showed only negligible color, which suggests that any losses in yieldwere due primarily to incomplete transfer of the precipitate from the filter to the weighingvial. For approximately 100 mg quantities of a precipitate, 80-90% transfer was commonlyobtained.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 20below), which is the same within experimental error; the SCE is 0.04V higher than that ofAg/AgC1 (relative to NHE) in aqueous solution (Brady, J. E.; Humiston, G. E. GeneralChemistry, 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.8214. 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., ElsevierScientific, 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, andthe experimental uncertainty in the obtained E°' values is estimated at +0.02 V. Thereforethe 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 the0-bound isomer in Ru(dmso) complexes after metal-centered oxidation was previouslyobserved for Run(NH3)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 isomerizationprocess.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. 1986,787.8328. 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, JohnWiley 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 foundin: 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 ischaracteristic 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 inthe 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, 939.84CHAPTER 3A MECHANISTIC STUDY OF THE02-OXIDATION OF DIETHYLSULFIDECATALYZED BY Ru(OEP)(Et2S)23.1 IntroductionIn the previous chapter a mechanism was proposed for the stoichiometric oxidationof Ru(OEP)(RR'S)2 complexes to Ru(OEP)(RR'S)(RR'50) and Ru(OEP)(Et 250)2 bydioxygen in acidic organic media. It is clear that, in the presence of a large excess ofdialkylsulfide, the starting bis(thioether) complex could be regenerated fromRu(OEP)(RR'S)(RIV50), thus making the process catalytic. This assumption wasconfirmed experimentally, and in the process new insights were obtained. In particular, acompletely new and interesting feature of the catalytic reaction became apparent, namelyits rate dependence on visible light. This chapter begins by summarizing qualitativefeatures peculiar to the catalytic process. Based on these, and on the conclusions drawn inchapter 2 about the stoichiometric oxidations, a mechanism for the catalytic oxidation ofdialkylsulfides is proposed. The second part of the chapter deals with the kinetic analysisof quantitative stopped-flow and oxygen-uptake experiments, which were used to monitorthe catalytic process. The data are fitted to a rate law derived from the proposedmechanism; the actual derivation of the rate law is deferred to chapter 4.All of the studies discussed in this chapter refer specifically to Et2S oxidationcatalyzed by Ru(OEP)(Et 2S)2 , in benzene. Qualitatively, excess dms in the presence ofRu(OEP)(dms) 2 and decMS in the presence of Ru(OEP)(decMS) 2 were found be oxidizedin the same way as Et2S in the presence of Ru(OEP)(Et2S)2 , and the systems exhibited85qualitative dependences on the same variables. Furthermore, all the reactions proceededin either methylene chloride or toluene; in fact, it was already shown in chapter 2 that thestoichiometric reaction proceeds more cleanly in methylene chloride than in benzene, andthis is probably true of the catalytic system as well; unfortunately the high vapourpressure of methylene chloride was a problem when quantitative studies were attempted.Dimethylsulfide also had the problem of high vapour pressure.3.2 Experimental3.2.1 Materialsn-Undecane, used as an internal standard for the GC measurements, was fromAldrich. The origins or methods of preparation of all other materials used in theexperiments described in this chapter were previously described in chapter Stopped-Flow Experiments3.2.2.1 Sample HandlingAll experiments were carried out under aerobic conditions; no special precautionswere taken to exclude air or water. It is assumed that side-reactions with these potentialreagents are slow enough to be ignored under the conditions of high sulfide and sulfoxideconcentrations used, and indeed the excellent reproducibility of the results verifies thisassumption (see section 3.4). For any given experiment, one of the drive syringes wasfilled with a benzene solution of Et 2S, and the other with a benzene solution ofRu(OEP)(Et2SO)2 and Et2SO. One experiment was taken to be the average of fivestopped-flow runs done at constant concentration of all reagents. In any given series of86experiments, the concentration of Et 2S was varied, while the concentrations of thereagents in the other syringe were held constant. A blank run in which the Et 2S syringecontained only benzene was carried out for each series. The free ligand concentrations(Et2S and Et2SO) were always held high enough so that they would remain effectivelyconstant for the duration of an experiment. InstrumentationAll stopped-flow experiments were carried out on an Applied Photophysics modelSF.17MV stopped-flow spectrophotometer, equipped with 2.5 mL drive syringes. Apressure of 650 kPa was used to drive the syringes.' A constant temperature of35.0+0.1° C was achieved using a Grant LTD 6 constant-temperature bath connected tothe stopped-flow sample handling unit via Tygon tubing.Changes in the reaction mixture were monitored by following the absorbancechange at one of two wavelengths: 400.5, or 402.8 nm (see section 3.4.1). Theabsorbance change with time was monitored across a 1.00 cm path-length cell. Themonochromator entrance and exit slits were both set at 0.2 mm. A high brightness 150-WXenon arc lamp was used as the light source.3.2.3 Gas Chromatography3.2.3.1 Sample HandlingSample preparation and handling for gas chromatographic experiments wasessentially identical to that described below for the gas uptake experiments. The onlysignificant difference was that samples to be analyzed by gas chromatography had 23.787mM n-undecane added to them as an internal standard. InstrumentationGas chromatography was carried out on a Hewlett-Packard HP 5890A gaschromatograph, equipped with a 15 m x 0.20 mm HP-1 capillary column (0.33 Am filmthickness), a split capillary inlet (insert packed with 3% OV-1 on 100/120 chromosorbW-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 minto 170° C, and held for 15 min.3.2.4 Oxygen Uptake Experiments3.2.4.1 Sample HandlingUnless otherwise stated, all the gas uptake experiments were carried out in 10.0mL aliquots of a benzene solution, containing an initial Et 2S concentration of 0.742 M.For experiments in which Ru(OEP)(Et2S)2 concentrations of less than 0.5 mM wererequired, a stock solution containing about 5 mM Ru(OEP)(Et 2S)2 and 0.742 M Et2S wasfirst made up. The appropriate amount of this solution was then added to the reactionvessel using a Unimetrics microliter syringe, and the total volume made up to 10.0 mlwith a 0.742 M solution of Et 2S in benzene. Between experiments, the stockRu(OEP)(Et2S)2 solutions were kept in the dark, and all stock was used up in a maximumof three days. For experiments requiring Ru(OEP)(Et2S)2 concentrations greater than 0.588mM, the appropriate amount of crystalline complex was weighed out and added directlyto the reaction vessel.Crystalline benzoic acid was weighed out into a small glass bucket, which wassuspended 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 wassubjected to two freeze/pump/thaw degassing cycles in order to remove dissolvednitrogen. Apparatus SetupThe gas uptake apparatus used for this series of experiments was simply amodified version of a design which has seen extensive use in our laboratories,' so that afull 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 apparatuswas used to warrant some discussion.The complete apparatus is illustrated in figure 3.1. The principal design differencebetween this apparatus and its predecessors is in the use of high-vacuum Teflon valves atpositions 3 and 4, in place of standard greased stopcocks (figure 3.1a). When Teflonvalve 3 is closed to seal off the small volume of gas in the right arm of the oilmanometer, a significant pressure is exerted, causing a very noticeable change in the oillevels. Thus the oil manometer must be re-levelled before proceeding (see below). Inaddition, when valve 4 is closed, a much smaller but still measurable pressure changetakes place. This too must be compensated for (see below).Additional modifications to the apparatus were peculiar to this series ofto mercurymanometerto mercurymanometer(a),,Reaction flaskV assembly(b)89Figure 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. Keycomponents: (A) Thermostatted and insulated oil bath; (B) Reaction vessel; (C) Oilmanometer; (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 forexplanations.90experiments, and were required to keep the reaction solution intensely and constantlyilluminated. These modifications are illustrated in figure 3.1b. A GTE/Sylvania ENX 360Watt 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 bathhousing insulation, normally used to inspect visually the reaction mixture. A Powerstatvariable transformer was used to supply 30 V AC to the lamp. The insulation and theoutside walls of the oil bath housing had to be covered in foil (F) to protect them fromexcessive heating by the projection lamp. In addition, the lamp and exterior of the oilbath housing were constantly cooled by blowing compressed air over them via the funnelG, which was a common laboratory glass funnel. During operation, the operator wasprotected from the intense light by the screen (H), which was simply a sheet of cardboardcovered in aluminum foil. Normally a thermostatted heat source is required to keep theoil bath temperature constant. In this case a cooling source also had to be supplied tocounteract the uncontrolled heat provided by the projection lamp. The oil bath was cooledby water, supplied from a separate constant-temperature bath, and fed through a coppercoil immersed in the oil. With this setup, the temperature could be kept constant at34.85+0.15° C (but see sections and Finally, because the averagesurface 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 otherwisestated. The same flask and bucket were used in all of the experiments for the samereason.As benzene and Et2S both have a significant vapour pressure at the reactiontemperature, a measurable pressure change occurs as the temperature cycles between9134.70 and 35.00° C. This change is visible as an oscillatory motion of the levels in theoil 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 ifthese were taken at random times. To prevent this, all gas burette readings were takenwhen the temperature was at the minimum of 34.70° C.A typical experimental run proceeded as follows. The initial sample preparationwas 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 10minutes with the projection lamp off (30 minutes for gas pressures of 0.6 atm or less) ata 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 wasclosed. Oxygen was introduced through needle valve 10, until the oil manometer (C) wasnearly levelled (to within 3mm). The total pressure reading at the mercury manometerwas recorded; this reading was taken to be the total pressure under which the reactionwas carried out, and p0 2 was calculated by subtracting the benzene vapour pressure(147.66 mm Hg) 3a from this value (the solubility of 0 2 in benzene, at 35° C, is 9.279mM/ateb). Valves 4 and 6 were now closed, and from this point onward valve 6 wasused to introduce or remove oxygen from the part of the apparatus to its left, as requiredto keep the oil manometer level. The projection lamp was now turned on. This sometimesaltered the temperature cycle slightly, and so at the next temperature minimum the oilmanometer was checked and re-levelled if necessary. The initial reading was taken on themercury burette (D), the shaker stopped momentarily, and the reaction started bydropping the bucket containing the benzoic acid into the solution. After the shaker was92re-started, the experiment proceeded in the same way as it would with other versions ofthe gas uptake apparatus, with uptake readings taken each time a temperature minimumwas passed (approximately every 6-10 minutes). In experiments for which very littleuptake occurred over this time period, the oil level difference was first artificiallyenhanced by drawing a very slight vacuum via valve 6. Subsequent re-levelling was mucheasier than via a direct attempt to adjust for a very small level difference. This techniquecould also be used if too much 02 was introduced via valve 6, so that the level in theright hand side of the oil manometer was higher than that of the left.3.2.5 Data TreatmentRaw data from the stopped-flow experiments were analyzed on an Archimedesworkstation using a non-linear least squares fitting program, supplied with the stopped-flow instrumentation, which implements the Levenberg-Marquardt algorithm.''' Allother data analyses, including least-squares methods and numerical solution of differentialequations, were carried out on a PC using customized implementations of the programsfound in "Numerical Recipes, the Art of Scientific Computing (Quick Basic versions)". 6The complete customized programs are listed in appendix 1.3.3 Ru(OEP)(Et2S)2-Catalyzed 0 2-Oxidation of Et 2S in Benzene Solution - GeneralObservationsGas chromatographic studies show that in oxygenated solutions containingRu(OEP)(Et 2S)2 , benzoic acid, and an excess of free Et 2S at room temperature or at 35°C, the thioether is catalytically oxidized to Et 2SO. However, early attempts to study the93kinetics of this catalytic oxidation yielded erratic and generally irreproducible results.Eventually it was found that if the reaction mixture was irradiated by intense visible lightat all times, Et2SO was produced selectively and reproducibly. Figure 3.2 dramaticallyillustrates the effect light has on the reaction rate. For a benzene solution exposed to theair at 35° C, initially containing 0.34 mM Ru(OEP)(Et2S)2 , 5.3 mM PhCOOH, and 0.74M Et2S, sulfoxide production (followed by GC) stops completely whenever the irradiatinglamp is turned off, and starts again at the same rate whenever the lamp is turned onagain. This phenomenon is only observed in the case of catalytic oxidation, where a largeexcess of dialkylsulfide is present; the stoichiometric oxidation of Ru(OEP)(RR'S) 2complexes, described in detail in the previous chapter, proceeds equally readily in thepresence or absence of light.Assuming that the fate of the metalloporphyrin during the catalytic oxidation ofEt2S is similar to that observed in the absence of excess thioether (see sections 2.5 and2.6), a likely candidate for the light-dependent step is the initial one-electron transferfrom Ru(OEP)(Et2S)2 with 02 . In the presence of a large excess of sulfide, this stepprobably cannot proceed at any appreciable rate via the inner sphere mechanism proposedfor the stoichiometric oxidation, because of competition for the axial sites of the complexby the sulfide. On the other hand, light could provide the extra energy required toproceed via an outer-sphere process, previously shown to be highly unfavourable (seesection 2.5).To establish which of the Ru(Porp) bands are responsible for the observedphotochemistry, two gas uptake experiments were carried out using different cut-offfilters (figure 3.3a). Of interest, light above about 480 nm is found to be essential for/oon00.0180.015 -0.012 ---10 0.009-C/2C\1-4-JC40.006offoff o0-o on940.003 -0.0000.0 9.0Time (h)3.0^6.0 12.0^1 5 .0 18.0Figure 3.2. Dependence of Et 2SO production rate on reaction vessel illumination.[Ru(OEP)(Et2S)2] = 0.34 mM; [PhCOOH] = 5.3 mM; [Et 2S] = 0.74 M; the reactionwas carried out in benzene solution at 35° C, in a flask exposed to the air. Reactionprogress was followed by gas chromatography.–0.005 ^0 500^1000^1500^2000^2500^3000t(s)Figure 3.3. (a) Uv/visible spectra of Ru(OEP)(Et 2S)2 , and of the yellow and blue filtersused to test which wavelengths are necessary for Et 2S oxidation to proceed. (b) Effects ofthe cutoff filters on the rate of Et 2SO production, as measured by 0 2-absorption at 35° C;in each case, a benzene solution initially containing 0.84 mM Ru(OEP)(Et 2S)2 , 24 mMPhCOOH, and 0.74 M Et 2S was exposed to 0.81 atm of 0 2 (corrected for benzene vapourpressure).952.0 -------------(a)Ru(OEP)(Et2S)2 spectrum— — — Blue filterYellow filterX10320(b) 0.035 ^0.030 –0.025 –0.0200.015 –OciS 0.010–FL40.005 –401 0^500600(n m)• • No filter• —• Blue filter• —• Yellow filter700^8000.00096reaction; when the blue filter absorbing all light above about 480 nm is used, no catalysisat all takes place. Cutting off irradiation of the Soret band (the most intense and energeticin 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 isnot 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 lightintensity due to reflectance is expected.Figure 3.4 is a qualitative molecular orbital diagram showing the types oftransitions which give rise to the uv/vis spectrum of d6 six-coordinate rutheniumporphyrins.''' Both the Soret and the a bands are assigned to ir-ir* transitions in theporphyrin 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 thetransition which gives rise to the a band.' In addition to the 7r-7r" transitions, manymetalloporphyrin spectra,' including those of ruthenium porphyrins,' have low intensity"extra" bands; in the case of ruthenium porphyrins, these bands are attributed tometal(d)-to-porphyrin(a") charge transfer bands (see figure 3.4). 8 Theoretical studiessuggest that the dz2 and dx2,2 orbitals in Ru(Porp) complexes are too high in energy toplay any role in low energy light absorption.'Based on the available electronic transitions (figure 3.4), figure 3.5 illustrates twopossible 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 whenthe 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(d,d)II I^Iii^dxy (beg)dxz ,dyz (eg )•d72e (n*) dx2_y297S oret-band ••a2.(n)A(CFSE)Va lu(n)Porphyrin MetalFigure 3.4. Scheme showing the types of electronic transitions which can occur in d6 six-coordinate ruthenium porphyrins (adapted from reference 8).98Ru ff(0EP)(Et , S) 2(a)Run • ---•tuEr) * (Et ,S),6'[Ril i(OEP)+ (Et ,S) 2]02 -k7^k-7[Ru lii(OEP) Et , S)21+02PhCOOHk8^kHO0.5 02 0.5 H2O, 0.5 H 20f.1( (OEP)(Et 2 S)21 -ThC00 -0.5 Et,S 0.5 Et,S0(b)Ruttt(OEP) .(Et 2S), Ru ll(OEP)+tEt 2S),0, -III (0EP)(Et 2S)2l+02-k7PhCOOH^0.5 02kd'^---)o. HO0.5 H O  kox > 0.5 H2O0.5 Et,S 0.5 Et,S0[Ru in(OEP)(Et 2S)21+PhC00 -Figure 3.5. Two possible mechanisms for the photochemical stage of the 02-oxidation ofEt2S catalyzed by Ru(OEP)(Et 2S)2 : a) porphyrin 7-7* transition, followed by transfer ofthe excited electron to 0 2 ; b) direct metal-to-porphyrin charge-transfer, followed bytransfer of the excited electron to 02.99abstracted by 02 in the second step (k6), leaving a 7-cation radical. As mentioned insection 2.4, the metal d orbitals lie at higher energy than the porphyrin 7 orbitals undermost 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 thesuperoxide drive the reaction forward. The reaction k_ 6 , represents a pathway by whichRu(OEP)(Et2S)2 +02 can revert back to Ru(OEP)(Et 2S)2 ; the prime emphasizes the factthat this is not the reverse of k6 . Figure 3.5b illustrates an alternative mechanism, inwhich 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)(Et2S)2 +02 speciesdirectly (k6), which reacts with PhCOOH as before (k 7). Apart from the a,$ bands, theonly other band resolved in the visible spectrum of Ru(OEP)(Et2S)2 (figure 3.3a) is atapproximately 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 (figure3.3a). Nevertheless, there might be a charge-transfer band somewhere in the 480-540 nmregion, and this band might be hidden by the more intense ot,f3 bands. Metal(d)-to-porphyrin(7*) charge-transfer is symmetry forbidden, so the bands arising from thisprocess would be weak and easily masked.If a 7-7 * transition is giving rise to the photochemical effect, then on the basis offigure 3.4, it is difficult to rationalize why light absorption in the Soret region does notlead to reaction; nevertheless, this would not be the first instance in which the Soret andthe c«, f3 bands behave differently, even when the simple molecular orbital picture predictsthat they should behave in the same way. For example, it is well established that formany metalloporphyrins, 7 including Ru n porphyrins, 8 the 0/03 bands are hypsochromically100shifted (i.e. to shorter wavelength) relative to those of the free-base porphyrins. Based onthe simple molecular orbital rationale portrayed in figure 3.4, this phenomenon has beenattributed to back-donation of electron density from the metal e g d-orbitals to theporphyrin eg le-orbitals, which would raise the energy of the latter. This simple model isquite useful, and has been used to rationalize, for example, the fact that the a,f3 bandsshift 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 asthe axial ligand accepts more electron density from the metal, less density will betransferred to the porphyrin Ir a orbitals, and their energy will drop: 7 ' 8 Despite itsusefulness, the simple model has one serious flaw: a review of the electronic spectra ofseveral Run(OEP) complexes' shows that their Soret bands are not hypsochromicallyshifted from the free-base position, and there is no obvious correlation between Soretpeak position and the ir-acidity of the axial ligands. The simple model predicts that metal-to-porphyrin 7-7* backbonding should cause the Soret to shift hypsochromically by thesame amount (in energy units) as the cr,(3 bands. The fact that this is not the observedbehaviour suggests that there is some kind of interaction between the metal and theporphyrin, 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. Thequestion of which band is responsible for the observed photochemistry is discussed againin section, at which point kinetic evidence is presented which tends to rule out the7-7 * transition mediated mechanism shown in figure 3.5a.At this point it is worth looking at the predicted thermodynamics of some of thereactions shown in figures 3.5. Recall that in section 2.5 the cell potential for a one-101electron transfer from Ru(OEP)(Et2S)2 to 02 was estimated at about -1 V, whichtranslates to a free energy barrier of about 95 kJ/mol. Assuming for the moment thatRu(OEP)(Et2S)2 absorbs only at X = 525 nm, this will supply the porphyrin complex with228 kJ/mole. Combining these two relationships allows us to writeRun(OEP) *(Et2S)2 + 02 Rum(OEP)(Et2S) 2 +02 AG° = -133 kJ/mol^3.1Hence light of wavelength around 525 nm provides more than enough energy to allow theoverall process of interest to proceed. Moreover, the standard reduction potential for theprocess Ru ll(OEP)'(Et2S)2/Rull(OEP)(Et 2S)2 is expected to have a value around 0.64 V,which is the standard reduction potential for the Ru ll(OEP)+•(C0)/Run(OEP)(CO) system(recall section 2.4).' ° At the very most, the ring reduction potential might be as high asthat of the free base (0EPH 2 + 10EPH2), which was previously recorded as 0.83 V.' 0 Thelatter value (using a value of -0.8 V for the 02/02 - couple, see section 2.5) gives a cellpotential 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 enoughenergy to overcome even this high barrier:Rull(OEP)*(Et2S)2 + 02 Ru ll(OEP)•(Et2S)202 AG° = -74 kJ/mol^3.2Figure 3.6 summarizes the suggested free energy relationships, which relate directly tothe mechanism shown in figure 3.5a. The same general relationships will hold if theAG°= 95 kJ/mol[Rum(OEP)(Et2S )21 + 02-Ru ll (OEP)*(Et2S)202AG°= 154 kJ/mo[RuII(OEP)- (Et2S)21 02AG°= -74 kJ/molAG°=-133 kJ/molAG°=-59 kJ/molAEabs= 228 kJ/molRun (OEP)(Et2 S)202Figure 3.6. Relationship between the light energy absorbed by Ru(OEP)(Et2S)2 at 525 nm, and the relative free energychanges associated with various transformations; see text for details.103photochemical reaction is proceeding via an initial metal-to-ligand charge transfer (figure3.5b), 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 initiallycontaining 0.42 mM Ru(OEP)(Et2S)2 , 6.5 mM benzoic acid, and 0.74 M Et 2S, which wasexposed to 0.81 atm of oxygen (corrected for benzene vapour pressure) at 35° C for2.5 h under irradiation. The major oxidation product is Et 2SO, with minor amounts ofEt2SO2 , Et2S 2 , and one other unidentified side product. Initially, the way in which Et 2SOwas selectively produced came as a surprise. Earlier studies carried out in ourlaboratories, which looked at 02-oxidation of decMS catalyzed by Ru(OEP)(decMS) 2 ,revealed sulfur product distributions which were akin to those of dialkylsulfide free-radical autoxidation ll (for example, didecyldisulfide was a major product); sulfoxide wasnot obtained as a single product.' In the present case, an autoxidation type of reactionwould be expected to initially produce EtSH in concentrations comparable to those ofEt2SO; the thiol would then further react to produce Et 2S2 (see section 1.3). 11,12Therefore, the lack of a significant Et2S2 signal in figure 3.7 also suggests that thiol wasnever a major product of reaction. In a series of experiments in which total oxygenuptake for a reaction was compared to Et 2SO produced (as determined by gaschromatography) over 1.8-2.5 h periods, the stoichiometry of 2 moles of Et 2SO producedfor every mole of 02 consumed, which is implicitly suggested by the type of mechanismbeing proposed, was confirmed. As an example, when a solution containing 0.420 mMRu(OEP)(Et2S)2 , 9.86 mM PhCOOH, and 0.742 M Et 2S was irradiated under 0.812 atmof oxygen (corrected for benzene vapour pressure) at 34.85° C for 1.9 h,1 1 1 H Tit (min)104Figure 3.7. Gas chromatographic trace of a benzene solution initially containing 0.42 mMRu(OEP)(Et 2S)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 2S2 ; 6.05 min:Et2SO; 7.11 min: Et 2S02 ; 7.90 min: n-undecane; 9.30 min: benzoic acid. The signal at13.16 min is that of an unidentified product; the rest of the unidentified signals arepresent at the start of the reaction.10532.9 ± 0.4 mM Et2SO 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 theearly experiments was carefully re-examined by GC, and found to contain somedecanethiol and other impurities; this almost certainly explains the presence ofdidecyldisulfide as a reaction product in those experiments.Figure 3.8 provides a scheme for the overall catalytic cycle, which takes intoaccount the conclusions of chapter 2, and the observed light dependence when excesssulfide is present. The reaction path flows counterclockwise, starting at Ru(OEP)(Et 2S)2 ,which is just left of the top of the circle. The first four steps (k 5 to k8) correspond to thephotochemical mechanism portrayed in figure 3.5a, and result in the production of onemole of Et2SO, one of H 2O, and two moles of Ru(OEP)(Et 2S)2 +13hC00 - for every twomoles of Ru(OEP)(Et 2S)2 oxidized. At this stage, no evidence has been given to favoureither mechanism 3.5a or 3.5b; figure 3.8 incorporates mechanism 3.5a because, as willbe seen in sections 3.5 and 4.3.2, this mechanism can be tested directly.The next two steps in the catalytic cycle (k9 and k10) represent one of the possibledisproportionation processes suggested in the previous chapter (section 2.5). Whicheverprocess (or combination of processes) is actually going on, disproportionation will giverise to one mole of a R e species for every two moles of Ru(OEP)(Et2S)2 originallyoxidized (with regeneration of one mole of Ru(OEP)(Et 2S)2). Note that all of the stepsbeyond superoxide protonation are portrayed as irreversible; it is assumed that, in thepresence of high concentrations of Et 2S, all of the Ru ifi and Re species will beconsumed as rapidly as they are produced.k_6 ,^2Ru11(OEP)(El 2S)2by^k_s2Ru II(OEPAEt2S),2[Rul 1(OEP)t(Et ,S),]02 -k2[R ulli(OEP)(E t 2S)21+02 -PhCOOH •••XHO, < -[Ruiv(OEP)(Et 2 S )(PhC00)]+OffPhCOOHH,0[Ru lv(OEP)(Et 2S)(PhC00)113hC00106PhCOOHEt, SOI IRuH(OEP)(Et SO),^ii^Ru II(0EP)(Et,SOXEt2S 0)k-1^,""Ig 4,„.■Ruil(OEP)(Et ,S0)Et2 S - -^1114k, I-Ruil(OEP)(Et ,S)(Et,S0) -4re^InternalRearrangementEt2S k 3 IL. 3Et, SORull(OEP)(Et ,S )02 coordinationRu(OEP)(Et ,S)(02 )k1 4 r/RUII (OENEt-)S)(E00)1°1\(.13^ Et, S0=Ruiv(OEP)(Et ,S)PhCOOHk 1041/4 RuIII(0EP)(Et,S)(PhC00)2[Rum(OEP)(Et 2S)2 rPhC00 .2H0,Ica^ ky0,^ Et,SH, 0,1,-Ox r•-•--- Et ,S,S0H,0Figure 3.8. Scheme proposed for the 0 2-oxidation of Et2S to Et2SO, catalyzed byRu(OEP)(Et2S)2 and PhCOOH (dotted pathways imply that these processes can beneglected, or do not occur, under catalytic conditions).107Reaction of the Ru"' species with water and free Et2S producesRu(OEP)(Et2S)(Et2S0) (k 11 to 1( 13), which can either isomerize to giveRu(OEP)(Et2S)(a250), or react with Et 2S to regenerate Ru(OEP)(Et2S)2 . In the lattercase, another mole of free sulfoxide is liberated, to give a total of two moles of freeEt2SO produced for every turn of the catalytic cycle. In either case, the two moles ofPhCOOH used to "trap" the high valent Ru species are regenerated at the end of thecycle, and the net result of the process is to produce 2 moles of Et2SO for every mole of02 consumed. The production of two of the possible isomers of Ru(OEP)(Et2SO)2 (at thetop of the scheme), and direct 02 coordination to Ru" (vertical pathway), are bothportrayed using dashed arrows. This emphasizes that although both processes are knownto occur when the concentration of free Et2S is low, they are probably not importantunder catalytic conditions. The equilibria between Ru(OEP)(Et 2S) 2 , Ru(OEP)(Et2S)(Et250)and Ru(OEP)(Et2SO)2 , and the possibility of internal rearrangement ofRu(OEP)(Et2S)(Et2SQ) to the S-bound isomer, also portrayed with a dashed arrow in thefigure, will be further discussed in the next two sections.In the scheme portrayed in figure 3.8, any possible reaction ofRu(OEP)(Et2S)(Et250) (or indeed Ru(OEP)(Et 2SO)2) with dioxygen is neglected; thesecomplexes are outside of the catalytic cycle. This means that, according to the model, asEt2SO is produced, it should have an inhibitory effect on the reaction rate, depending onthe equilibria governing formation of the sulfoxide-containing complexes. Figure 3.9shows a plot of [Et2SO] vs. time, obtained from an oxygen uptake experiment, and thereaction rate is indeed found to decrease with time (this decrease is not accounted for bythe drop in [Et2S] with time, which is less than 5% over the whole measured interval).108t (s)Figure 3.9. A typical plot showing the accumulation of Et 2S0 with time, determined bymonitoring the 02-uptake (see section 3.5 for full details). For this experiment at 35° C,the initial concentrations of the reagents are: [Ru(OEP)(Et2S)2] = 0.202 mM; [PhC001-1]= 24.4 mM; [Et2S] = 0.742 M; p0 2 = 0.813 atm (corrected for benzene vapourpressure).109Section 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 beseen, the derived rate law fits the experimental data remarkably well; however, the samereasoning used earlier to show that electron transfer from Ru(OEP)(Et2S)2 to 02 isenergetically quite feasible in solutions irradiated by visible light, shows that the lessfavourable electron transfer from Ru(OEP)(Et 2S)(Et250) to 02 is also possible under theseconditions. Figure 3.10 summarizes the relevant energy relationships; a full discussion onthe possible role of electron transfer from Ru(OEP)(Et2S)(Et250) directly to oxygen isdeferred to section second omission in figure 3.8 is any mention of catalyst degradation (this is acommon weakness of nearly all postulated catalytic cycles). In chapter 2 it was pointedout that the stoichiometric reaction of 0 2 with Ru(OEP)(RR'S) 2 complexes in acidicbenzene solutions was not as clean as in methylene chloride, and that small amounts ofunidentified 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 someextent in the catalytic system and, indeed, monitoring the reaction mixtures for extendedperiods (20 h) by uv/vis, clearly showed that catalyst degradation occurred, but at a slowrate compared to the catalytic rate. Of interest, this catalyst degradation is not aciddependent, and proceeds at about the same rate with or without added acid, provided thatthe reaction solution is illuminated (see below). The uv/vis spectrum of a reactionmixture, initially containing 0.202 mM Ru(OEP)(Et 2S)2 and 0.742 M Et2S (but nobenzoic 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 corresponding0111•11•■[Rull(OEP)'(Et2S)(Et2S0)102[Ru11l(OEP)(Et2S)(Et2S0)]+02-^AG°=-2OkJ/molAG°_-74kJ/molAG°=-94kJ/mol AG°=154kJ/molAG°=134kJ/molRu(OEP)*(Et2S)(Et2S0)02AEab,228kJ/molRull(OEP)(Et2S)(Et2S0)0,Figure 3.10. Relationship between the light energy absorbed by Ru(OEP)(Et 2S)(Et250) at 525 nm, and the free energychanges associated with various transformations. AG° for the oxidation at the metal of RAOEP)(Et 2S)(Et250) was estimatedfrom the CV data for the analogous Ru(OEP)(decMS)(decMS0) system (see section 2.5 and figure 2.13); for the one-electronring 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, ^ 1420 500^k(nrr )^600^ 700Figure 3.11 Uv/vis spectra of a benzene solution initially containing 0.202 mM Ru(OEP)(Et 2S)2 , 0.742 M Et2S, and nobenzoic 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.112Ru(OEP)(decMS)2/decMS systems.' The spectrum shows broad bands extending to 700nm, and no major band at 525 nm, which suggests that very little or none ofRu(OEP)(Et2S)2 , Ru(OEP)(Et2S)(Et25.0) or Ru(OEP)(Et2SO)2 remain in solution (thevisible spectra of the three Ru ll species are illustrated later in figure 3.21, p.144). Therelatively sharp band at 549 nm is notable, since this is the position (551 ± 4 nm) atwhich all known Ru(OEP)(CO)L (L = a neutral ligand) have their a bands;' recall fromsection 2.6 that there is evidence of a Ru(OEP)(CO)L complex being a minor product inthe stoichiometric oxidation of Ru(OEP)(RR'S) 2 in benzene and toluene solutions. Sincenone of Ru(OEP)(Et2S)2 , Ru(OEP)(Et2S)(Et250) or Ru(OEP)(Et2SO)2 absorb significantlyabove 600 nm, the absorbance in this region by a reaction mixture at any given time canbe used as a crude estimate of catalyst degradation, with the absorbance after 24 hrepresenting maximum degradation. Such an analysis was carried out on the spectrum infigure 3.11, and on several catalytic reaction mixtures containing benzoic acid, andcatalyst degradation was estimated to be 7-12% over a 2.5 h period. Note that the errorincurred in neglecting catalyst degradation (i.e. ignoring the decrease in reaction thatcatalyst degradation will produce) will tend to compensate for any error incurred byassuming non-reactivity of Ru(OEP)(Et 2S)(Et250) toward 0 2; this will be discussedfurther in section mentioned, all of the assumptions inherent in figure 3.8 will be discussed againin section 3.5, after a rate law for the reaction has been derived. The next section dealswith a quantitative study of the equilibria between Ru(OEP)(Et2S)2 ,Ru(OEP)(Et2S)(Et250) and Ru(OEP)(Et2SO)2 , which were studied independently from therest of the catalytic cycle using stopped-flow experiments.1133.4 Stopped-flow Analysis of Et 2SO Substitution by Et2S in Ru(OEP)(Et2SO) 2 inBenzene Solution3.4.1 Data Treatment and ResultsThe equilibria between Ru(OEP)(Et 2S)2 , Ru(OEP)(Et2S)(Et250), andRu(OEP)(Et2SO)2 were studied in isolation from the rest of the cycle outlined in figure3.8, using stopped-flow techniques. The details of deriving the rate laws will be discussedfully in chapter 4,t but the likely probability that in solution Ru(OEP)(Et2SO)2 exists asan equilibrium mixture of Ru(OEP)(Et250)2 and Ru(OEP)(Et250)(Et2S0) (see section 2.3)is accounted for in the derivation. In practice, the system was studied by starting with asolution of Ru(OEP)(Et2SO)2 and excess Et 2SO, and adding an excess of Et2S to it, whichis the reverse of the processes which take place during catalysis; for clarity, figure 3.12shows the substitution steps in isolation. It turns out that substitution of the first sulfoxidein Ru(OEP)(Et2SO)2 takes place on the 100 ms timescale, which is about 1000 timesfaster than that of the second. Thus the first equilibrium between Ru(OEP)(Et2SO)2 andRu(OEP)(Et2S)(Et250) is established before the second reaction has begun, whichsimplifies the rate laws considerably, since the two steps can be studied independently.In addition to occurring on very different timescales, the two substitutionequilibria occur in sufficiently different Et 2S/Et2SO concentration regimes to allow someuseful observations to be made by time-independent uv/vis spectroscopy. Thus figure3.13a shows successive uv/vis spectra obtained for a solution, initially containing 3.4x10 -6M Ru(OEP)(Et2SO) 2 and 0.19 M Et 2SO, as it was titrated with neat Et 2S. The band whichIt is possible to understand sections 3.4 and 3.5 in a qualitative way without goingthrough the theory given in chapter 4; however, many readers will find it helpful to readchapter 4 concurrently with the next two sections of this chapter.First Substitution EquilibriumEN SORu (OEP)(Et 250)2^ ENS1^k- 2Et? SO^Ru (0EP)(Et , SO)^Ru (0EP)(Et /S)(Et,S0)k ,Ru (0EP)(Et , SOXEt2S0)1'Second Substitution Equilibrium^EN SO^ ENSRu(OEP)(Et2S)(Et20)^jk^Ru (0EP)(Et 2S) k^4Ru (OEP)(Et,S)2^k k-42^EN SO ENS114ENS 2kS()Figure 3.12. Scheme showing the proposed mechanisms for the sequential substitution oftwo Et2SO ligands by Et 2S in Ru(OEP)(Et2S0)2 . In solution, the bis-sulfoxide species isbelieved to exist as a mixture of the S- and 0-bound linkage isomers (see section 2.3).115[Et2S](M) A404 A400 . 50.0 0.490 1.2940.018 0.676 1.0940.037 0.781 0.9650.056 0.842 0.8710.096 0.917 0.7750.14 0.952 0.689A,(nm)(a) 1.5 000320 420[Et2S0](M)^A409 A404^0.0^0.335^0.2040.0095 0.305^0.2730.019^0.282^0.3230.028 0.265^0.3590.038^0.251^0.3880.047 0.240^0.4090.057^0.231^0.4250 404.0(b) 0.5350^ A,(nm)^420Figure 3.13. Uv/vis spectral changes observed as: (a) a benzene solution initiallycontaining 3.4x10 M Ru(OEP)(Et2SO)2 and 0.19 M free Et2SO is titrated with neat Et2S;(b) a benzene solution initially containing 1.7x10' M Ru(OEP)(Et 2S)2 and 0.74 M freeEt2S is titrated with neat Et2SO. T = 35° C for both experiments.116grows in at 404.0 nm is attributed to Ru(OEP)(Et2S)(Et250). Similarly, figure 3.13bshows successive uv/vis spectra obtained for a solution, initially containing 1.7x10 5 MRu(OEP)(Et 2S)2 and 0.74 M Et 2S, as it was titrated with neat Et2SO; again, the bandappearing at 404 nm is attributed to Ru(OEP)(Et2S)(Et2S0). The spectra in figures 3.13aand 3.13b both show at least three isosbestic points; isosbestics can result from a) asimple equilibrium between two absorbing species, or b) formation of a third absorbingspecies from a fixed ratio of two other species. The latter case applies to the firstequilibrium in figure 3.12, where Ru(OEP)(Et2S)(Et250) is formed from a fixed ratio ofRu(OEP)(Et 2S0)2 and Ru(OEP)(Et2S0)(Et2SD), during the titration with Et2S (in bothsubstitution equilibria, the 5-coordinate intermediates are assumed to be present innegligible amounts). The equilibrium between Ru(OEP)(Et 2S0)2 andRu(OEP)(Et250)(Et2S0) is independent of either Et 2SO or Et2S concentrations:K' = [1']/[1]^ 3.3where 1 =--. Ru(OEP)(Et2S0)2 ; 1' -=-- Ru(OEP)(Et250)(Et2S0); andK' --. Ic i lc_p/lcr lc_ i^3.4The equilibrium ratio of Ru(OEP)(Et250)2 to Ru(OEP)(Et250)(Et2S0) remains constantregardless of the free [Et2SO] (or [Et2S]) ligand concentrations, and thus the Beer-Lambert expression for a solution containing Ru(OEP)(Et 250)2 , Ru(OEP)(Et2a0)(Et2S0)and Ru(OEP)(Et2S)(Et25.0), can be written as117A = (e l + erIC)1[1] + €21[2]^ 3.5where2 =--- Ru(OEP)(Et2S)(EtzSO)and A is the experimentally observed absorbance, e l , el , and €2 are the extinctioncoefficients 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 atthe isosbestic wavelength X = 402.8 nm, no change is detected in the absorbance at anytime, showing that the equilibrium between Ru(OEP)(Et 250)2 andRu(OEP)(Et250)(Et2S0) is not even transiently disturbed. The importance of thisobservation will become apparent below, and in section 4.2.In the stopped-flow experiments discussed in the remainder of this section, the twosubstitution equilibria were monitored at different wavelengths. The first was followed atX = 400.5 nm, which is the absorption maximum for Ru(OEP)(Et 2SO)2 solutions at 35°C (see figure 3.13a). During the second substitution, the equilibrium between the mono-and bis-sulfoxide species must be considered and, as will be seen in section 4.2, it issimpler to follow the second substitution reaction at an isosbestic wavelength for amixture of Ru(OEP)(Et2SO)2 and Ru(OEP)(Et2S)(Et2S0) species. The isosbesticwavelength chosen was X = 402.8 nm (see figure 3.13a).118Now, with the assumption that the changes in free [Et 2S] and [Et2SO] arenegligible over the whole reaction, and given that the equilibrium ratio betweenRu(OEP)(Et250)2 and Ru(OEP)(Et250)(Et2S0) is not disturbed at any time, theabsorbance changes as a function of time for X = 400.5nm over the first 100 ms, and forX = 402.8nm over 100 s, will both be described by a simple exponential decay equation(see section 4.2):A = a + 1.3 e-61)^3.6whereA =-,--- The absorbance at time t^ 3.7a = A0 - (3^3.8(A0 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 ofthe concentrations of the various reagents in solution; of course, the form of thesefunctions is different for the first and second substitution reactions. Before discussing thefunctions, one other term should be defined, namely119v.^(dA/dt) 1 = 0 = -7/3^3.9where vo is the rate of change of the absorbance at the start of the reaction. For both thesubstitution steps, 13 and vo are the two most informative parameters. For the firstsubstitution reaction, /3 and vo are given by (see section 4.2)11 = -fRuL4cilEt2sl/(K, ApplEt2soi + [Et2S])^ 3.10vol = k1App[Ru] 4ciUt2SVOCI[Et2S 0] + [Et2S])^3.11where[Ru]. -= [1] + [1'] + [2]^ 3.12AE I ' --= (62 - (€1 + e 1 ,K')/(1 + K'))1 at X = 400.5 nm^3.13K IApp ==..- K I/(1 + K')^3.14Ic iApp .. k,/(1 + K') + k 1 ,/(1 + (IC) -)^3.15Kmi —= (k, + k_ v)/k2^3.16K 1 -= k 1k2/k_ 1 1(2^3.17120K' was previously defined (equation 3.4), as were the three extinction coefficients ci , Erand €2 , and the path length 1 of the absorbing species.Equations 3.10 and 3.11 (for variation of fl, and v 0, with [Et2S] at a fixed [Et2SO])are the typical rectangular hyperbolas with zero intercept so commonly seen in kineticanalyses," and can be rearranged into linear form:[Et2S]/f, = c 1 + c2 [Et2S]^ 3.18[Et2S]/voi = c3 + c4 [Et2S]^ 3.19whereCI =-. [Et2SO]c2/K,APP^ 3.20c2 =--  - 1/[RU]AE, '^ 3.21C3 -=' [Et2S0]C41(ml^ 3.22C4 --."^-C2/1C1App^ 3.23Two sets of experiments were carried out, one with [Et 2SO] = 1.18+0.03 mM,the other with [Et2SO] = 17.7±0.2 mM. In each case, [Et2S] was varied from 0.119 mMto 0.464 M over several runs, and a,„8 1 ,7 1 were evaluated using the Levenberg-121Marquardt algorithm."' 6 These values were then used to generate the variables [Et2S]/fl 1and [Et2S]/vol , which were plotted against [Et 2S]. Equations 3.18 and 3.19 could then befitted to these plots using linear regression, ultimately yielding the desired equilibriumand 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 tabulatedvalues of a 1 ,(3 1 ,7 1 . Figures 3.15 and 3.16 show the fitted plots of equations 3.18 and 3.19for the two sets of experiments. Finally, table 3.1 summarizes the obtained values of allthe relevant parameters; their significance is discussed in section 3.4.3.For the second substitution reaction, the concentration functions of the parametersare somewhat more complicated in that linear functions of [Et 2S] at constant [Et2SO] andTable 3.1Fundamental Parameters Derived fromEquations 3.18 and 3.19[Et2S0Jx103(M)AE4„,0.5ix10-5(M-tcm-')KIA,„, k,App (s') K. k, (s')1.18±0.03 -(1.92±0.04) 2.8±0.1 135±2 0.85±0.03 41±217.7+0.2 -(2.03±0.05) 2.58±0.06 131±3 0.74 ±0.02 37+2Averageparametervalues-(1.97±0.05) 2.7±0.1 133±2 0.79±0.06 39+2A = a l +^(710a l = —0.153)3 1 =0.633= 123.2 s 10.50 ^0.40 -0.30-0.20 -0.10 -0.00-—0.10 -,1\10, op%Dik'1.QP,6°°04,,Poi^ddo cb.7., 1,0,122—0.20 II^ ,0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10Time (s)Figure 3.14. A typical, fitted stopped-flow trace of the change in absorbance over 100ms, at X = 400.5 nm, when Et 2S is substituted for Et2S0 in Ru(OEP)(Et2S0)2 . [Et2S] =9.27±0.09 mM; [Et2S0] = 1.18+0.03 mM; [Ru] o = (3.44+0.07)x10' M. The firstfour points likely are in the dead time of the instrument, and are neglected in the fit.0.0030.000—0.0030.005 -0.002 0.004 0.006 0.008 0.010 0.0120.05 0.10 0.15 0.20 0.250.02^0.04^0.06^0.08 0.10^0.120.000 (N,^0-0.0040.00 0.10^[Et2s] (M)^0.20^0.300.020Q = 0.41(a)c 1 = (6.36 ± 0.16)x10-4 Mc2 = 1.516 ± 0.016X2 = 12.50.0000.0000.0100.000.00"zz 0.0040.000-0.0100.000.18(b)c l = (9.85 ± 0.15)x10 -3 Mc2 = 1.436 ± 0.018X2 = 14.4Q = 0.16123[Et2S]/19 1 = c i^c2 [Et2S]Figure 3.15. Portions of the plots of [Et 2S]/O I vs [Et2S] for data collected at X = 400.5nm over 100-ms time-frames. a) [Et2SO] = 1.18±0.03 mM; b) [Et2SO] = 17.7±0.2mM. In each case [Ru]. = (3.44+0.07)x10 M. The residual plots show the full range ofdata collected; the main plots show only the region in which 0, increases (Q is thegoodness of fit given the obtained x2 value").0.20-1.5E-5 -^0.250.008 0.0120.0041.60E 41.20E-4 -8.00E-5 -4.00E-5 -(a)c3 = (1.563 ± 0.032)x10 -5 M sc4 = (1.122 ± 0.015)x10 -2 sx2 = 1.98Q =^1.5E 5^^ai^0.0 ^0.05 3(b)1.20E-3:3ci)c.)M 6.00E-4 - X2 = 21.6c 3 = (2.632 ± 0.042)x10 -4 M sc4 = (1.096 ± 0.019)x10 -2 sQ = 0.0170.000.00^5.0E 5 ^^0.0 ^-5.0E 5 ^0.000.06 0.100.04 0.120.02 0.080.10 0.300.20124[Et2S]/°o 1 = c 3 + c4[Et2S][Et2S]Figure 3.16. Portions of the plots of [Et 2S]ivol vs [Et2S] for data collected at X = 400.5nm over 100-ms time-frames. a) [Et 2SO] = 1.18+0.03 mM; b) [Et 2SO] = 17.7+0.2mM. In each case, [Ru]. = (3.44±0.07)x10' M. The residual plots show the full rangeof data collected; the main plots show only the region in which v c,1 increases.125[Ru]o cannot be obtained. Nevertheless, analysis analogous to that which yieldedequations 3.18 and 3.19 (see section 4.2) gives the following quadratic functions:[Et2S] 2/(32 = d 1 [Et2S] 2 + d2 [Et2S] + d3^3.24[Et2S]/V02 = d4[Et2S] 2 + d5[Et2S] + d6^ 3.25whered 1 -... aRuLAE27 1^3.26d2 .-=.- [Et2SO]d 1 /K2^3.27d3 =-- = d2[Et2SO]/KIApp^ 3.28d4 E-- d i/k3^3.29d5 -=-- (Km2 + (KiApp)4 )[Et2SOld4^ 3.30d6 ---= 1C2[Et2SO] 2d4/Kmpp^ 3.31126AE2' ==- (E3 - E2) 1= (63 - (61 + e 1 -K')/(1 + K'))1at the isosbestic wavelength X = 402.8 nm 3.32[Ru]. [1] + [1'] + [2] + [3] 3.33K.2 k_3/k4 3.34K2 k3k4/1c--3k4 3.35Also, 3 represents Ru(OEP)(Et2S)2 , and E3 is its extinction coefficient. Functions 3.24 and3.25 are linear in their dependence on the parameters d 1 -d6 , and so it is still possible todo least-squares minimization without resorting to iterative methods. 5a'6 One set ofexperiments was carried out, with [Et2SO] = 1.18 + 0.03 mM, and a varying [Et 2S].Figure 3.17 shows a typical absorbance vs. time plot for X = 402.8 nm; again, theremaining plots are collected in appendix 2, along with the tabulated values of a2 ,[32 ,72 .Figure 3.18 shows the plots of equations 3.24 and 3.25, fitted to the data using thetechnique of singular value decomposition followed by back-substitution,* 5" to obtainthe least-squares fit parameters. Table 3.2 summarizes the values of the equilibriumconstant and the rate constants obtained from equations 3.24and 3.25; their significance is discussed in section—(72t)A z-  a2 + , 2 ea 2 = —0.127fl2 = 0.289.y2 = 0.0706 s -10.15 0 -U(Ts0 0.050 -(/)0.)725 —0.050 -c4—0.150^0 20^40^60^80Time (s)1000.003720.00004 —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 Et2SO in Ru(OEP)(Et 2S)(Et250).[Et2S] = 18.6+0.2 mM; [Et 2SO] = 1.18+0.03 mM; [Rid, = (3.44+0.07)x10' M.0.06 0.080.04 0.10 0.120.0300.025 -w^0' 020 -CCL.\ 0.015 -N41-" 0.010 -0.005 -128(a)^, 2 a^A^2 +^A^/t, 2 =^[1.11.201^11.2[J,1.21-1]^d3d = 1.662 ± 0.023d2 = (3.264 ± 0.086)x10 -2 Md3 = (1.81 ± 0.24)x10 -5 M2X2 = 4.07Q = 0.912.0E 40.0-2.0E 4 ^0.00 0.06 0.04 0.080.600.50 -N^0.40 -0 0.30 -(nN 0.20 -0.10 -(b)[Et2S] 2/v02 = d4 [Et2S]2 + d5 [Et2S] + d6d = 44 48 + 0 42 sd 5 = (6.64 ± 0 68)x10-2 M sd = (4.3 ± 1 4)x10-5 M2 sX2 = 14.8Q = 0.0970.000.00^0.02 0.04 0.06 0.08 0.10 0.121.7^3.0E 3U0-3.0E 3 ^0.001^1^10.02 0.04 0.06[Et2S10.08 0.10^0.12Figure 3.18. Portions of the plots of: a) [Et 2S] 2//32 vs [Et2S], and b) [Et2S] 2/v02 vs [Et2S],for data collected at X = 402.8 nm over 100-s time-frames. [Et2SO] = 1.18+0.03 mM;[Ru]. = (3.44+0.07)x10 M. There is one off-scale point at [Et 2S] = 0.232+0.002 Mfor each plot; all of the data are tabulated in appendix 2.129Table 3.2Fundamental Parameters Derived fromEquations 3.24 and 3.25[Et2SO]x103^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± Error Analysis3.4.2.1 Uncertainties in the Solution ConcentrationsSmall amounts of the pure reagents were used to make up the initial stocksolutions. Ru(OEP)(Et 2SO)2 was weighed out in approximately 5 mg quantities on ananalytical balance with a precision of a = 1.9x104 g (based on 38 weighings of the sameobject over a time period of 1.5 months). The liquid reagents were measured out usingUnimetrics microliter syringes with stated precisions of 1 %. Once the stock solutionswere made up, serial dilution using larger scale volumetric apparatus contributed little toincreasing the uncertainties in the solution concentrations. Instrumental UncertaintiesBlank runs carried out with each series of experiments, both on the 100 ms andthe 100 s timescales, showed that the baseline was not flat (see appendix 2). The raw datawere therefore corrected by subtracting the blank from each individual run. Noindependent estimate of the measurement error in the absorbance was available, so ameasure of the goodness of fit of the proposed exponential decay model to the data couldnot be obtained from the least squares analysis. 5a Instead, an estimate of the measurement130error was calculated from the least squares analysis assuming that the exponential decaymodel (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 offigures 3.14 and 3.17, that there is a good fit of the theoretical curves to the data, bothon the 100 ms and the 100 s timescales. A minor oscillatory deviation of theexperimentally observed data points from the theoretical values is consistently observed inall of the absorbance vs. time plots obtained on the 100 ms timescale (see figure 3.12 andappendix 2). This is probably an artifact, and is small enough to be ignored. Uncertainties on the Millisecond TimescaleInitially equations 3.18 and 3.19 were fitted to the data obtained by monitoring the100 ms timescale, using the standard errors in a l , 0 1 , and y i , calculated from fittingequation 3.6, as weighting factors. The goodness of fit values (Q) that resulted from thisprocedure were unacceptably low (less than 10 -5), which could not be accounted for byone or two outlier points." Thus, either the model being used was wrong, or there wereother sources of error beyond those already accounted for. sa Now if repeated stopped-flow experiments (5 run averages) were done without changing the concentration of anyof the reagents, the variation in the calculated parameters a l , [s,, y, from run to run wasfound to be much higher than the standard errors calculated for any given run (figure3.19). Moreover, in the case of parameter 0 1 , the variation was not entirely random, with0 1 appearing to decrease slightly with with increasing number of runs. Two series ofrepeated runs were carried out, one at each end of the Et 2S concentration range used. Inthe case of parameter 0,, the relative error is approximately the same (2.4%) at both1----.-I^1---,,f________----\\^I ^_TL-,__i-------i1^1^I^1^I^i^I^1^1^1(a)(c)11111111111 1 1^— (d )T^T0.095131 0.0900.085131[Et2S]/[Et2S0] = 0.10055.00yi 50.00 —(b)45.00 I^10^1^2^3^4^51^I^i^17^8^9^10^11Experiment number0.500le 0.4750.450[Et2S]/[Et2S0] = 7851^2^3^4 5^6^7^8^9 10 11 12 13 14Experiment numberFigure 3.19. Variation of the parameters 13 1 and -y 1 from experiment to experiment, whenall reagent concentrations are held constant. The error bars represent the uncertaintiesestimated from fitting the raw stopped-flow data.134.007 1 132.00130.000132extremes, and this is considered to remain constant for experiments done at intermediatevalues of [Et2S]. 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% tothe points corresponding to the lowest three Et2S concentrations, one of 0.87% to thethree highest concentration points, and the average value of 1.7% to the remainder. Thisprovides an educated guess as to the proper weighting. In figures 3.15 and 3.16, the errorbars represent the combination of the instrumental uncertainties as calculated by the aboveprocedures, and the uncertainty in the thioether concentration for the experimental pointin question. The goodness of fit values (reported in figures 3.15 and 3.16) are nowbetween 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 intable 3.1 shows them to agree within 10% or better. This suggests that the proposedmodel, together with the concomitant assumptions, adequately describe the system understudy, and the obtained values closely approximate the true equilibrium and rateconstants. In particular, within the context of this thesis, the key parameter is KiApp ,whose value affects the determination of all of the parameters in the second substitutionreaction, which is of fundamental importance in the catalytic oxidation cycle (see section3.5.1). Knowing K1APP to within 10% accuracy is certainly adequate for estimating itsrelatively minor effect on the second reaction. The difference between the equilibriumand rate constant values obtained in the two series of experiments is significantly greaterthan the uncertainties resulting from the least-squares fitting; however, since theinstrumental errors are not entirely random, one must be careful in assigning too much133quantitative meaning to the uncertainties derived from this procedure. In fact, the maindiscrepancy between the two sets of results could well be due to a difference in the datacollection method. For the experimental series which resulted in figures 3.15a and 3.16a,the data were collected sequentially starting at the lowest Et 2S concentration, and endingwith the highest. Probably as a result, the data points in these figures exhibit a slightunderlying curvature relative to the theoretical lines. On the other hand, the series whichresulted in figures 3.15b and 3.16b were collected in more random order, and the datapoints appear to be more randomly scattered about the theoretical line. As an indicationthat the uncertainties in the equilibrium and rate constant values are greater thansuggested from the least squares analysis, the uncertainties reported with the averageequilibrium and rate constants in table 3.1 are given as half the difference between thetwo sets of derived values.As to the most probable source of the abnormally high instrumental variation, itwas likely due to the Xenon arc lamp being quite old and deteriorating significantlyduring the time that the experiments were being carried out. This was evidenced by thefact that the photomultiplier gain had to be turned up quite frequently to obtain constantabsorbance readings. Normally this must be done over a period of months; during thecourse of the reported experiments, it was not unusual to have to adjust the gain twice inthe same day. As the gain is turned up, one expects the output signal to become lessstable.1343. Uncertainties in the One Hundred Second TimescaleThe error bars in figure 3.18 combine the uncertainty in the Et 2S concentrationand the instrumental uncertainties affecting the parameters CY2, 02, and 72 , as calculated inthe fitting of equation 3.6 to the data collected at X = 402.8 nm. The goodness of fitvalues (Q) derived from fitting data to equations 3.24 and 3.25 suggest reasonable fitsassuming these uncertainties, and the data points appear to be fairly randomly scatteredabove and below the theoretical curves in figure 3.18. Apparently, some of the sources oferror affecting the millisecond timescale were somehow compensated for over the longertime frame.Analysis of the intermediate results in the singular value decomposition solutionsof equations 3.24 and 3.25 showed the parameters d i -d6 to be determined uniquely. 5a'bThe experimental uncertainty calculated for parameter d 6 is high enough to make thevalue worthless for extracting rate constant data; nevertheless, both d 3 and d 6 aresignificantly different from zero, and the temptation to neglect them, which would allowequations 3.24 and 3.25 to be linearized, was resisted.For comparison with the values obtained over the 100 ms timescale, the value ofK iApp was independently determined to be 2.1 ± 0.3, by inserting the data collected inthe analysis of the second substitution reaction into the equation:K iApp = d2 [Et2S0]/d3^3.36Again, this value is significantly different statistically from the values calculated bystudying the first substitution reactions directly, but is close enough to suggest that any135uncertainties or mechanistic factors unaccounted for so far are relatively minor.Finally, and of importance, K2 was also determined independently from 'H-nmrexperiments. Thus the 'H-nmr spectra of three solutions, initially containing 1-2 mM[Ru(OEP)(Et2S)2], 0.45 M [Et2S], and 16, 40 and 79 mM [Et 2SO], respectively, werecollected using an aquisition time of 1.5 s, and a 7 s delay between pulses. K2 was thendetermined from the integral ratios of the meso signals (T, = 0.68 ±0.03 s) forRu(OEP)(Et2S)2 and Ru(OEP)(Et2S)(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 tothat obtained in the stopped-flow experiments.3.4.3 Discussion of the Parameter ValuesThe equilibrium constants obtained for the first (KiApp) and second (K2)substitution reactions (tables 3.1 and 3.2) show that, in a solution containing equalamounts of free Et2S and free Et2SO, Ru(OEP)(Et2S)(Et250) is the predominant species insolution; i.e. it is the thermodynamically most stable of the four complexes which canpossibly 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)(Et2S)) are similar forEt2S and Et2SO, as evidenced by Km values which are close to one. This means that thevalues of the equilibrium constants are essentially determined by the relative values of thedissociative rate constants for each reaction; i.e. Ic iApp/1(2 for the first substitution, andk3/k4 for the second.The observed values of K2, k3 and k4 can be rationalized in terms of the136sulfoxide's ability to act as a better 7-electron acceptor from the metal center, relative tothe 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-(Et2S) bond.Therefore it seems reasonable that Et 2SO should dissociate more slowly than Et2S (k3 <1(4), and hence that the Ru(OEP)(Et2S)(Et250) complex should be thermodynamicallymore stable than Ru(OEP)(Et2S)2 (K2 < 1).tThe large labilizing effect of a 7-accepting ligand on the ligand trans to it hasbeen well documented in Ru(Porp) systems, 16 ' 17 and has been shown to be especiallypronounced if the trans ligand is another 7-acceptor." This rationalizes why the Et2Sis more labile in Ru(OEP)(Et 2S)(Et250) than in Ru(OEP)(Et2S)2 (k2 > 1(4), and leads tothe prediction that Ru(OEP)(Et 2S)(Et250) is more stable than Ru(OEP)(Et 2S0)2 (K 1 >1).t Without knowing what fraction of Ru(OEP)(Et 2SO)2 is present asRu(OEP)(Et25.0)(Et2S0) in solution, the prediction cannot be verified directly; however,the solid-state it and electrochemical evidence from sections 2.3 and 2.4 suggest thatRu(OEP)(Et250)(Et2S0) is a relatively minor species in solution. Furthermore, recallfrom section 1.2 that the most stable isomer of Ru(TMP)(Et 2SO) 2 is known to be thebis(S-bound) one.' If the fraction of Ru(OEP)(Et 2S0)(Et2S0) is small (K' < < 1), thenK1^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 beenstudied extensively in square-planar Pt complexes, and a good qualitative theory has beenestablished.' In the present case, in which the ligand responsible for the transt This reflects the relative concentrations of the two metal complexes when equalconcentrations of free Et2S and Et2SO are present.1370I•„'"IFigure 3.20. Weakening of 7-bonds trans to a sulfoxide; a bonds trans to the sulfoxidewill also be weakened, since the sulfoxide can transfer more a-electron density to the Ruclz2 orbital than a comparable ligand incapable of 7-bonding (see text).138labilization is a 7-acceptor, the mechanism by which the phenomenon occurs can bevisualized according to figure 3.20. When the sulfoxide accepts electron density from theruthenium center via 7-7* back-bonding, there will be less electron density left on the 7r-bonding metal orbital for back-bonding to another 7-acceptor trans to the sulfoxide. Thusthe bond of a sulfoxide trans to the first sulfoxide will be especially weak. At the sametime, the back-bonding of the ruthenium to the sulfoxide has a synergistic effect on theRu-S a bond; as more electron density is put on the sulfoxide via the 7-bond, more ofthat density can be fed from the sulfur back to the ruthenium via the a bond. This willmean that the (1,2 orbital of the ruthenium will also be monopolized by the sulfoxide, andless available for bonding with a trans ligand L. Therefore even a a bond trans to thesulfoxide 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)(Et2S)2]3.5.1 Data Treatment and ResultsFor carrying out a quantitative kinetic analysis of the catalytic oxidation,monitoring the oxygen uptake proved to be more convenient than following Et 2SOproduction by gas chromatography. Although gc was useful in providing complementaryinformation, it did not yield quantitatively reliable results consistently under conditions ofhigher PhCOOH ([PhC001-1] > 5 mM) or Ru(OEP) ([Ru] o > 0.5 mM) concentration.The presence of PhCOOH tends to broaden the Et 2SO signals considerably when presentin high concentrations. The effect of high concentrations of Ru(OEP) is more subtle; theappearance of the chromatograms remains unchanged by repeated injections of reaction139mixtures initially containing higher concentrations of Ru(OEP)(Et 2S)2 , but standards runbefore and after monitoring the reactions show that the response factors for Et 2SO changeappreciably during the period of the monitoring process.Based on the mechanism proposed in figure 3.8, a system of five differentialequations can be derived (see section 4.3 for the derivations) to describe the rates ofappearance and disappearance of the major species in solution:d[2]/dt = klEt2S0][3]/[Et2S]0 - k3 [Et2S][2]/[Et2S]0+ kobs[Et2SO]PHEt2SL(Pl + 0[2]))^3.37-43 .1/dt = d[2]/dt^ 3.38d[Et2SO]/dt = kobs[3](2[Et2S]0 - [Et2SO])MEt2S] 0([3] + b[2]))+ k3 [Et2S][2]/[Et2S]0 - l 4[Et2S0][3]/[Et2S]0^3.39-d[Et2S]/dt = d[Et2SO]/dt^ 3.40-d[02]/dt = 0.5d[Et2S0]/dt^ 3.41whereIcobs =- vin(f[Ru]0)[02][PhCOOH]/((K.4 + [PhCOOH])(IC3 + [02]))^3.42140[Et2S].^[Et2S] + [Et 2S0]and also3.43Vin^0.5Ci k7/(k6, k7) 3.44EE 1(5/14.6 3.45Ka E.3 144(74((6' + k7)1(8) 3.46Again, 2^Ru(OEP)(Et2S)(Et250), and 3 im Ru(OEP)(Et2S)2 . The constants c 1 andand the function f[Ru],, are all part of an empirical expression, the significance of whichis discussed below.Note that at t = 0, [2] = 0, [3] = [Ru]o , [Et2SO] = 0, and [Et2S] = [Et2S]..Therefore:(d[2]/d0t = 0 = 0^ 3.47(d[Et2S0]/dt),= 0 = 21cobs^3.48i.e. the initial rate of [Et2S0] production is 21cobs . The forms of the initial rate equations3.47 and 3.48 have an important theoretical significance, which is discussed in section4. 3.37-3.41 were derived making all of the simplifying assumptionsdiscussed in section 3.3: a) all species other than Ru(OEP)(Et 2S)2 andRu(OEP)(Et2S)(Et2S0) are present in negligible, steady state concentrations; b) onlyRu(OEP)(Et2S)2 reacts with 02 ; 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)(Et2S)2 ; d)no catalyst degradation takes place during reaction; e) reaction of Ru(OEP)(Et2S)2 with 02via direct coordination of 0 2 to the metal center does not occur when excess thioether ispresent; f) rearrangement of Ru(OEP)(Et 2S)(Et2S0) to Ru(OEP)(Et2S)(Et2_80) occurs onlyvia the five-coordinate Ru(OEP)(Et 2S) intermediate (i.e. the reaction pathway in figure3.8 labelled "internal rearrangement" does not occur). In addition to these sixassumptions, based on the results of the stopped-flow studies described in the previoussection, two additional simplifying assumptions were made. First, the concentrations ofRu(OEP)(Et25.0)2 and Ru(OEP)(Et 2S0)(Et2SD) produced during the reaction wereneglected. For the fastest reactions studied, the ratio [Et 2SO]/[Et2S] at the end of thetypical time period monitored (1.7-2.5 h) was at most 0.1, which means that the[Ru(OEP)(Et2S0)2] would still be 30 times less than the [Ru(OEP)(Et2S)(Et250)], or 20times less than the [Ru(OEP)(Et2S)2] (using the values of K iApp and K2 listed in tables 3.1and 3.2). The second assumption was that K.2 is essentially equal to one, as determinedexperimentally (1.1+0.2, see section 3.4 and table 3.2).The expressionc i (f[Ru]o)[3]/([3] + tk[2])^ 3.49142is an empirical one meant to approximate Ia , the amount of light absorbed byRu(OEP)(Et2S)2 , for each turn of the catalytic cycle (I a^einsteins absorbed byRu(OEP)(Et2S)2 per liter per second). The true form of the function l a will becomplicated, and the theoretical problem of approximating it by a reasonably simplefunction is treated in detail in section 4.3.2; for the moment, only a summary isprovided. The approximate function consists of two distinguishable sub-functions, and theconstant c l . The first sub-function is fiRuL, which is intended to reflect what fraction ofthe total incident light will be absorbed by all the contents of the reaction flask for agiven [Rd,. As will be seen below, when the one-parameter functionf[Ru],, = 1 - exp(-10c2[Ru]o) + arctan(c2[Ru]o)^3.50is used (where c2 is the adjustable parameter), the resulting equation for k obs fits well allof 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 byf2^[M[3] + 0[2])^3.51Where€3dX/ f €2dX^ 3.52143Thus f2 represents what fraction of the total light absorbed by the solution is actuallyabsorbed by Ru(OEP)(Et2S)2 . Note that whereas c 1 and c2 are empirical parameters whosevalue depends on the geometry of the experimental apparatus, the value of 1k is dictatedby assumption (c) above; therefore b has chemical significance. Figure 3.21 illustratesthe region of the spectrum over which the integrals in equation 3.52 were evaluated. Theintegral values were obtained as follows. First, the spectra of separate 0.0340 mMsolutions of Ru(OEP)(Et2S)2 and Ru(OEP)(Et 2SO)2 , containing 74.2 mM Et2S and 2.22mM Et2SO, respectively, were collected. The desired region in each spectrum was thencut out and weighed; these weights represented, in effect, the integrated "absorbance" (inunits of g) of each species, over the region of interest. Thus an integrated "extinctioncoefficient" (in units of g n' cm - ') was calculated for each species. Next, the spectrumof a solution initially containing 0.0340 mM Ru(OEP)(Et 2S)2 , 74.2 mM Et2S and 44.9mM Et2SO was obtained, and the desired region cut out and weighed. The equilibriumconcentrations of Ru(OEP)(Et2S)2 , Ru(OEP)(Et2S)(EtA0) and Ru(OEP)(Et2SO)2 wereeasily obtained from the known values of the equilibrium constants K1APP and K2 (seesection 3.4, and tables 3.1 and 3.2); thus, the integrated extinction coefficient forRu(OEP)(Et2S)(Et250) (in units of g MAcm -1), being the only unknown value left, wasobtained directly from the Beer-Lambert law. The unusual units of the integratedextinction coefficients do not pose a problem, because they cancel out when the desiredratio 0 is calculated. The value of b calculated using the above procedurewas 0.86 ±^ X(nm)^ 700Figure 3.21. Visible spectra of pure Ru(OEP)(Et2S)2 ( 3), a solution containing mostlyRu(OEP)(Et2S)(Et250) (2, see text), and pure Ru(OEP)(Et2SO)2 (1 and 1'). The dashedlines indicate the region of all three spectra over which the integrated extinctioncoefficients were calculated (see text for details).145The constant c l is conceptually important in that it reflects the maximum attainablevalue of Ia . From equations 3.49 and 3.50, the maximum value of I a (when all of the lightincident on the solution is absorbed) is given by= 37rc 1/2^ 3.53Note that c 1 is itself a function of Io (the intensity of the incident light, commonly givenin einsteins dm -2 s'), the area of the cross-section of solution illuminated, and the solutionvolume (see section 4.3.2). Also, the area of the cross-section of solution illuminated is afunction of various geometrical parameters such as flask size, lamp orientation and flaskshaking speed. It was to keep c l constant over the whole series of experiments that allruns were carried out using the same solution volume, and great care was taken to keepevery part of the apparatus, including the flask, bucket, shaking speed and illuminationlamp orientation, the same from run to run. Some experiments were carried out in whicheither the volume or the shaking speed were deliberately varied; these will not bediscussed further here, except to say that changing the shaking speed did not have a greateffect on the observed results, but changing the volume did. The results of all theexperiments in which either solution volume or shaking speed were varied are listed inappendix 3 (section A3.3). For the experiments discussed in this thesis, only v., ratherthan co could be obtained (see equation 3.44); the relationship between c 1 and vm isfurther discussed at the end of section 1k calculated, and k3 , k4 known from the stopped-flow experiments, all of theunknown parameters in the differential equations 3.37-3.41 fall within the expression for146kobs . Within any one experiment, [PhCOOH], [02] and [Rd, were held constant, andtherefore kobs can be considered a pseudo rate constant, remaining unchanged for theduration of a single experiment. The initial conditions for the system of differentialequations 3.37-3.41 are known experimentally, and so only k obs is needed to solve thesystem numerically for a given run. To find the best value of kobs for a given run, aniterative algorithm, composed mainly of sub-programs from "Numerical Recipes", wasdevised. 5c,6 The complete program is listed in appendix 1, but essentially it works asfollows. The program is supplied with a copy of an experimentally derived [Et2SO] vs.time data set (where [Et2SO] = 2[02labsothed, the initial conditions for the data set, andtwo initial guesses as to the best value of k obs . The first part of the program, a standardnumerical integrator, uses these trial kobs values to generate two theoretical [Et2SO] vs.time data sets. These data sets are individually compared with the experimental results inleast-square fashion, and a x2 value is generated for each initially guessed kobs value. Thesecond part of the program then uses the first two (lcobs ,x2) pairs to generate new trialvalues of kobs according to a prescribed algorithm, and these are successively sent back tothe integrator until the lowest possible value of x2 is obtained. Figure 3.9, seen in section3.3, shows a typical [Et2SO] 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 therest of the corresponding plots are collected in appendix 3.The experiments performed are divided into three categories; for any givencategory, one of [Ru] o , [PhCOOH] or [02] was varied, while the other two were held0.0200.015 -0 0.010 -cnNw0.005 -0.0000 8000t (s)2000^4000 6000147Figure 3.22. A plot of [Et2SO] vs. time, fitted using the least squares procedure describedin the text. For this experiment, the initial concentrations of the reagents are:[Ru(OEP)(Et2S)2] = 0.202 mM; [PhCOOH] = 2.31 mM; [Et 2S] = 0.742 M; p02 =0.813 atm (corrected for benzene vapour pressure).148constant. Figure 3.23a shows a graph of kobs vs. [Ru]o for the data in which [Rd, wasvaried while keeping [0 2] and [PhCOOH] constant. Taking into account equations 3.42and 3.50, the data were fitted to the equationlcob. = P1( 1 - exp(-10c2[Ru]Q) + arctan(c2[RuD^ 3.54using the Leavenberg-Marquardt algorithm. 5" It follows directly from equations 3.42 and3.50 thatP1 =.-- v.[02][PhCOOH]/((Km4 + [PhCOOH])(K. + [02]))^3.55Figure 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 arectangular hyperbola with zero intercept, again using the Leavenberg-Marquardtalgorithm.Thuskb. = P2[PhCO0H]/(1C4 + [PhCOOH])^ 3.56whereP2 -''' Vm[02]( 1 - eXP(-10C2[RUL) + arctan(c2[Rulo)/( 1C3 + [0]2)^3.570.010^0.015[PhCOOH] (M)0.005 0.0200.00.000 0.025149I1.0E 5(a) kobs = P1(1 - exp(-10c2[Ru]o ) + arctan(c2[Ru] o ))8.0E-6 -Ipl = (4.3 ± 0.2) x 10 -6 M/sc2^(1.1 ± 0.2) x 103 M- 1a= 2.8 x 10 -7 M/s6.0E-6cno^•4 0E-6 -2.0E-6 -0.00 0^4.0E-4^8.0E-4[Ru] o (M)1.2E-3(b) kobs = p2[PhCOOH]/(Km4 + [Ph C 00H ])P2 =-- (7.5 ± 0.6) x 10 -6 M/sKm4 = (9 ± 2) x 10-3 Ma = 3.0 x 10 -7 M/sTT6.0E-6 -5.0E-6 -4.0E-6rn 3.0E-6 -02,0E-6 -1.0E-6 -p3 = (1.5 ± 0.2) x 10 -5 M/sKm3 = (1.4 ± 0 3) x 10 -2 Ma = 1.8 x 10 -7 M/s7.0E 66.0E-6 -5.0E-64.0E-6 -.2 3.0E-6 -02.0E-6 -1.0E-6 -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 24.4and 7.63 mM, respectively; (b) [PhCOOH], with [Ri]„ and [0 2] held constant at 0.408and 7.63 mM, respectively; (c) [02] with [M. and [PhCOOH] held constant at 0.408and 24.4 mM, respectively. The error bar magnitude in each case is given by150Finally, figure 3.23c illustrates the data obtained from experiments where [02] wasvaried, keeping [Rd :, and [PhCOOH] constant. These data were also fitted to arectangular hyperbola with zero intercept,L. = P3[02]/(Kn3 + [02])^ 3.58whereP3 -". Vm[PhCOOH](1 - eXP(-10C2[Ril]a) + arctan(c2[Ru]Y(Km4 + [PhCOOH]) 3.59In 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 thesame way). The results of these experiments are shown graphically in figure 3.24. Notethat, as expected, the parameters vm and c2 are different for these experiments, since theapparatus geometry was different (presumably it is the difference in the value of ci whichmakes the value of vm different). To avoid confusion, when referring to the second set ofexperiments, c 1 ,, c2 ,, pr , p2 , and v., are used instead of c l , c2 p i , p2 and vm . Thus, forexample, for the [Ru] o-dependence experiments, equations 3.54 and 3.55 become'cobs = P(1 - exp(- 10c2fRup + arc tan(c2TRul.)^3.608.0E-4[Ru] o (M)4.0E-4 1.2E-30 00.040.02^0.03[PhCOOli] (M)3.0E-6 -2.0E-6 -01.0E-6 -4.0E 6(b) kobs = p2 ,[PhC0 01-1 ]/(Km4 + [PhC001-1])p2 , = (3.6 ± 0.1) x 10-6 M/sKm4 = (5.4 ± 0.6) x 10 -3 Ma= 1.3 x 10 -7 M/s0. 00.01 0.050.00151(a) kobs p i ,(1 - exp(-10c2 ,[liu]0 ) + arctan(c2 ,[Ru] 0 )P1' = (2.3 ± 0.1) x 10 -6 M/s= (1.8 ± 0.3) x 103 M-1= 2.0 x 10 -7 M/s6.0E 6 -I5.0E-64.0E-6 -3.0E-6 -n02.0E-6 -Figure 3.24. Plots of kobs vs.: (a) [Ru]., with [PhCOOH] and [02] held constant at 24.4and 7.63 mM, respectively; (b) [PhC001-1], with [Ru] o and [02] held constant at 0.202and 7.63 mM, respectively. The error bar magnitude in each case is given by a.152wherePr -= ve [02][PhCOOH]/OK.4 + [PhCOOH])(IC3 + [02]))andv., =-- 0.5c 1 ,1c7/(k_6 , + 1(2)The values for K,3, K,4, vm and v., obtained in the two sets of experiments aretabulated in table 3.3.TABLE 3.3Fundamental Parameters Derived from the Plots of kobsvs. [Ru]0 , [PhCOOH] and [02]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 -6a) Only the result obtained from figure 3.22 is considered.b) The reported value is the average of the values obtained from a consideration ofPi, P2 and P3.c) The reported value is the average of the values obtained from a consideration of p l ,and p2 ,.3.613.621533.5.2 Error Analysis and Discussion3.5.2.1 Experimental UncertaintiesThe procedure used to weigh out reagents and prepare solutions was the same inthe oxygen-uptake experiments as in the stopped-flow experiments, and so theuncertainties in the reagent concentrations are expected to be similar in both cases.The major source of experimental uncertainty for the gas uptake experiments isundoubtedly associated with the gas uptake measurements themselves. It was estimatedthat 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 relationshipholds, regardless of the pressure at which the reaction was carried out. As mentioned insection, the vapour pressures of [Et 2S] and benzene caused a cyclic variation inthe oil manometer levels as the temperature cycled between 34.85 ± 0.15° C, which wascompensated for by always levelling the manometer at the temperature minimum. Now ifthe oil manometer were levelled either slightly before or after the minimum, thetemperature in the reaction flask would be higher than required, which would cause theuptake to be underestimated over that time period. Thus uncertainties due to non-levellingof the manometer exactly at the minimum should always lead to an underestimation of theuptake volume, provided that the temperature never dropped below the average minimum.Experimentally, the temperature fluctuation was found not to be perfectly predictable, andsometimes the minimum would drop below the average value (34.70° C) while themanometer was being levelled. This can be attributed to the complicated mixing processwhich 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 combined154uncertainty due to the difficulties in always levelling the oil manometer at the sametemperature. As an educated guess, the total uncertainty in the oxygen uptakemeasurement was estimated to be ±0.2 mM, twice the value suggested earlier for thelevelling of the manometer in the absence of the temperature-induced pressurefluctuations. The error bars in figures 3.9 and 3.22 show an uncertainty in [Et 2SO] of±0.4 mM, which is twice the postulated [02] uncertainty. Evaluation of the Kinetic ModelThe suitability of the proposed model can be evaluated at two distinct levels. Atthe first level, one wishes to asses how well the differential equations 3.37-3.41, aswritten, fit the raw data. At the second level, the question is how well does the proposedexpression 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 [02], obtained in the evaluation of K im for each uptake experiment. Forthe typical experiment performed, in which about 13-16 data points were collected, about95% 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 normallydistributed ^Most of the data points do indeed fall within this range, but there aresome notable exceptions.There are isolated data sets in figure 3.25 that have very low Q values (less than10'; see also appendix 3). When these data sets are examined (appendix 3), they arefound to have unusually high, but random scatter about the theoretical curve. Thus forthese data sets, the low Q values are almost certainly due to the fact that the measurement8.0E-3 1.0E-22.0E-3^1.20^1.00 -0.80 -0.60 -Q0.400.20 -0.00 -- 0.20 ^00 4.0E-3^6.0E-3[02] (M)1554.0E-4^1.20 ^1.00 -0.80 -0.60 -Q0.40 -0.20 -0.00 -- 0.20 ^001.20 ^1.00 -0.80 -0.60 -Q0.40 -0.20 -0.00 -- 0.20 ^00 2.0E-2^3.0E-2[PhCOOH] (M)8.0E-4[Ru]o (M)1.2E-34.0E-2^5.0E-2Figure 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).156errors 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 wasnot entirely predictable, and sometimes the temperature minimum either went below thatexpected, or didn't quite reach the minimum. Generally the deviations from the typicalcycle were not too bad, but occasionally the temperature minimum would be as much as0.1° C off the average, sometimes for a few points in a row. What makes thisphenomenon difficult to quantify is that the temperature cycle was clearly observed to bemore 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 astatistical point of view, the unpredicable temperature deviations represent a breakdownin the assumption that the measurement errors are normally distributed.Of greater concern than isolated "bad" data points, are identifiable regions inwhich several points in a row have low Q values. There are two such regions: the firstdata set in which [PhCOOH] was varied (figure 3.23b) shows many bad data points in arow, and all of the data collected at high [Ru]° (figures 3.23a and 3.24a) have low Qvalues.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 theseexperiments, 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 [02] and[Ru]° dependence experiments. A careful examination of the plots of [Et 2SO] vs. t for thefirst data set in which [PhCOOH] was varied (see appendix 3) shows no obvioussystematic deviations of the theoretical curves from the experimentally obtained data157points; however, the scatter of the data points is much greater in these plots than in otherdata sets. Moreover, the kob, vs. [PhC001.1] plots also show considerable scatter relativeto the other data sets. The high scatter is most likely attributable to the fact that this wasthe first set of data collected, and the technique required to obtain reproducible data hadnot yet been "perfected". The second set of kobs vs. [PhCOOH] data, collected severalmonths after the first, has generally higher Q values for the raw data, and much lessscatter in the replotted data.The cluster of low Q values observed at higher [Ru] o is of greater interest. In thiscase there is no obvious source of error which could account for the fact that in all of theexperiments in which [Ru], > 0.5 mM, the [Et 2SO] vs. t data (appendix 3) are poorlyfitted by the proposed rate law. It appears that in these cases the low Q values may beindicating 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 thatgenerally the theoretical curves arch over more than the experimental points. Forexperiments in which the total accumulation of Et 2SO is small, the scatter due toexperimental uncertainty tends to obscure this trend, but for experiments in which Et 2SOaccumulation 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 theexperimental points from the predicted curve is clearly visible. In the case of experimentscarried out at the highest [Ru] o , the arch in the theoretical curves is such that the curvesare outside the error bars of a significant number of the experimental points.A smaller than predicted curvature in the experimental [Et 2S] vs. t data means thatthe rate at which the reaction is slowing down with time is lower than predicted. Now158recall that accumulation of supposedly unreactive Ru(OEP)(Et 2S)(Et250) as the reactionprogresses is the only pathway included in the model by which Et2SO production canslow down. Therefore one possible explanation for the smaller than predicted curvature inthe experimental [Et2SO] vs. t data is that the mixed sulfide/sulfoxide complex perhapsreacts with 02 to some degree; as mentioned in section 3.3, the energy provided byyellow light is sufficient to allow this process to occur. If Ru ifi(OEP)(Et2S)(Et250) +02 - isindeed produced, then the rate law expressed in equations 3.37-3.41 could be modified toinclude the reaction of Ru(OEP)(Et 2S)(Et250) with 02 , 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:Rum(OEP)(Et2S)(Et250) +X - + Ru(OEP)(Et2S)2 -,Ru ll(OEP)(Et2S)(Et2.5.0) + Ru ffi(OEP)(Et2S)2 +X- AG° = -39 kJ/mol 3.63where X is either 02 or PhCOO. Therefore the one-electron transfer fromRu ll(OEP)(Et2S)2 to Rum(OEP)(Et2S)(Et250) +X- is thermodynamically favoured.Furthermore, the electron exchange is likely to be fast, as transfer from Ru(OEP)(Et2S)2to Ru(OEP)(Et2S)2 +X- is fast (see section 2.5). According to equation 3.63,Rull(OEP)(Et2S)(Et250) can be thought of as an "antenna", collecting the light energyrequired for electron transfer to occur, and eventually transferring it to Ru(OEP)(Et 2S)2 .Experimentally this energy transfer should have the effect of making lk lower thanexpected. Recall that is the ratio of the integral extinction coefficients ofRu(OEP)(Et2S)(Et250) and Ru(OEP)(Et2S)2 ; if some of the light energy absorbed by159Ru(OEP)(Et2S)(Et250) eventually leads to the production of Ru(OEP)(Et 2S)2 +X- , it willappear as if Ru(OEP)(Et 2S) 2 is absorbing more strongly, and Ru(OEP)(Et2S)(Et250) lessstrongly than expected, thus resulting in a lower 0 value.To test this hypothesis, all of the calculations were repeated, but this time 1// wasleft as an adjustable parameter, and a 2-dimensional X2 minimization routine was used tosimultaneously obtain the best values of 0 and Icon, (the program used for theminimization is reported in appendix 1). This procedure yielded an average 1,b value of0.6 ± 0.2. An important observation about the results of this analysis is that the variationin 0 was found to be independent of [Ru] 0 , [PhCOOH], or [02], while kobs increased withall three concentrations. According to the proposed model this is expected, since t,b is atrue constant, while kobs is only constant while [Ru] o , [PhCOOH] and [02] are heldconstant. Unfortunately, the rather large scatter seen for the values of both 0 and k thstends to obscure any trends which might be of interest. Therefore, instead of using thesedata 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 bsvalues will be artificially low; however, the important question is whether choosing a 0value 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 fitparameter 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], arenow quite good, and in fact the Q values overall are better and more randomly distributedthan those obtained for ik = 0.86. Exceptions are the data obtained in the initial aciddependence studies but, as mentioned before, these data were probably perturbed by^1.20 ^1.00 -0.80 -0.60 -Q0.40 -0.20 -0.00 -- 0.20 ^O 0^1.20 ^1.00 -0.80 -0.60 -Q0.40  -0.20 -0.00 -- 0.20O 01.20 ^1.00 -0.80 -0.60 -Q0.40 -0.20 -0.00 -- 0.20 ^O 0160o -o Data from figure 3.234.0E-4 8.0E-4[Ru] o (M)1.2E-32.0E-2^3.0E-2^4.0E-2^5.0E-2[PhCOOH] (M)2.0E-3 4.0E-3^6.0E-3[02] (M)8.0E-3 1.0E-2Figure 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).161uncharacteristically high experimental errors.There is, of course, another possible explanation for why equations 3.37-3.41 fitthe data better if 1G is set at 0.6 rather than 0.85, and that is that the photochemical effectcould 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 thissection could be wrong). If there is in fact a band hidden under the a,(3 envelopeoriginating from a metal-to porphyrin charge-transfer, it is impossible to directly evaluate0 for this band. Therefore, if this charge transfer is responsible for initiating thephotochemical reaction, lk would have to be treated as an adjustable parameter in akinetic analysis, as described in the previous paragraphs. Further evidence that a charge-transfer transition is indeed responsible for the observed photochemistry is presented laterin this section.Another simplification made in deriving the rate law was that no irreversibledecomposition of the Ru(OEP)(Et2S)2 catalyst occurred (assumption (d)). Any suchdegradation would cause the experimentally observed rate of Et 2SO production todecrease more rapidly than predicted. As mentioned above, the experimentally observedrate actually decreased less rapidly than predicted. This doesn't rule out catalystdegradation (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 isexperimentally 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 berelaxed. In so doing, the resultant modification in the rate law (i.e. empirically changing162the value of to fit the data) will automatically compensate for any effect which catalystdegradation might have upon the change in reaction rate with time. Note that the valuesof Kno , K„,4 and v., derived by plotting lcob. vs. [Ru] o , [PhCOOH] and [02] (figures 3.23and 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 issignificant, even if this could only be done by adjusting arbitrarily. One importantpoint is that even if equations 3.37-3.41 are considered to be completely empirical, theystill give values of the initial rates (i.e. 21c obs) which are much better than could beobtained from estimating tangent lines at the origin.Another point worth mentioning is that not all of the mechanisms which could bereasonably 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)(Et2S)(Et2SQ) isomerizes directly to Ru(OEP)(Et2S)(Et2S0), withoutthe sulfoxide dissociating into the bulk of the solution. A rate law was derived allowingfor internal sulfoxide rearrangement, and tested in the same way as the dissociative modeldescribed thus far (this represents a relaxation of assumption (f), listed at the begining ofthis section). The results of this analysis clearly show that the internal rearrangementcannot be an important pathway, assuming that the scheme proposed in figure 3.8 isotherwise a reasonable interpretation of the reaction mechanism. A detailed discussion ofthe analysis will not be included here (some theoretical elaboration is included in section4.3.3.1), but the results can be easily understood by looking at one of the experiments inwhich the alternate model fails most noticeably. Consider the case in which internal163rearrangement is assumed to be the only pathway by which Ru(OEP)(Et2S)(Et2S0) canrearrange to Ru(OEP)(Et2S)(Et250) (i.e. k14 = 0). If this were the situation, then themaximum rate for the oxidation reaction would be given by 2k 3[Ru]o . This rate would beattained for a rate determining loss of Et 2SO from the mixed thioether/sulfoxide species;i.e. kobs has to be sufficiently large, so that all of the Ru(OEP)(Et 2S)2 is rapidly convertedto Ru(OEP)(Et2S)(Et2.80). Figure 3.27 shows the results obtained for an experiment inwhich the reaction mixture initially contained0.0255 mM [Ru(OEP)(Et2S)2], 24.4 mM [PhCOOH], and 0.742 M [Et2S], under 0.813atm 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[Et2SO] = 2k3 [Ru]at^ 3.64This line falls somewhat below the experimental data, meaning that the rate at which[Et2SO] is produced exceeds that which is possible if k 3 is the rate limiting step. This initself is significant, but not conclusive evidence that the internal rearrangement modeldoes not work. After all, if the assumption that Ru(OEP)(Et 2S)(Et250) does not react with02 is relaxed, then the theoretical line could be made to go through the experimentalpoints. 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 steadystate in the first few seconds of reaction, after which the rate of Et2SO production shouldbe much closer to linear than is observed experimentally. Note that relaxing theassumption that Ru(OEP)(Et 2S)(Et25.0) does not react with 02 does not correct this0 0.01 -0.000^2000^4000^6000t (s)0.028000164Figure 3.27. A plot of [Et2SO] vs. time, fitted using: (a) the least squares proceduredescribed in the text; (b) the function [Et2SO] = 2k3 [Ru]ot. For this experiment, theinitial concentrations of all the reagents are: [Ru(OEP)(Et2S)2] = 0.0253 mM; [PhCOOH]= 24.4 mM; [02] = 7.63 mM; [Et2S] = 0.742 M.165problem; Ru(OEP)(Et2S)(Et25.0) will still accumulate to a maximum value within a fewseconds, after which the rate of Et2SO production will be essentially linear. If the internalrearrangement step is assumed to be significant, then it is necessary to invoke irreversiblecatalyst degradation (or some other, as yet unidentified mechanism) as a cause for theobserved decrease in [Et 2SO] production with time. Given that the rate law derivedwithout invoking internal rearrangement fits the collected data quite well, there seems noreason to consider these possibilities.The next point of discussion is an analysis of the parameters obtained from fittingthe plots of kobs vs. [Ri]° , [PhCOOH], and [02]. Table 3.3 lists these parameters. Noeffort was made to estimate the uncertainty in the kobs values directly from the raw data;the error bars in figures 3.23 and 3.24 were calculated during the least-squares fittingprocedures, assuming that the proposed models accurately described the data. This meansthat no independent statistical estimate of the goodness-of fit can be made for the replotanalyses. Note, however, that the scatter of the experimental points about the theoreticallines is fairly random, which tends to suggest that any deviations of the experimentalpoints from the theoretical curve are due to experimental errors, rather than to a failureof the model (the latter would generally lead to systematic over- or undershooting by thetheoretical curve of several experimental points in a row).As previously mentioned, the first k ob, vs. [PhCOOH] data set obtained were ofrather poor quality, and so only the parameters obtained from the analysis of the seconddata set are referred to in subsequent discussions. The calculated uncertainties in theparameters obtained from fitting the kb, vs. [02] plots are also quite large (14 % for p 3and 20 % for IC3). In this case the large uncertainties do not arise from unusually high166scatter of the data, but rather from the fact that the [0 2] concentration range studied wasfairly small; at the highest [02] 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 longextrapolation, and the degree of curvature in the plot (reflected by K,) is being estimatedfrom the curvature in a comparatively straight segment of the total curve.Despite the uncertainty in the calculated value of Km3 , this value provides someinteresting insights. Recall that Kno is the ratio k_5/k6 (equation 3.45), where 1(5 is thefirst order rate constant for the decay of the RAOEP)*(Et 2S)2 species back to the groundstate, and k6 is the second order rate constant governing the reaction of the excitedspecies with 02 (see figures 3.5a and 3.8). The value obtained for K. (0.014 + 0.003M) 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 101°^which is the upper limit imposedby the rate at which two species in solution diffuse towards each other. 13b This in turnmeans that k 5 cannot be greater than about 10 8 s'; however, as the following analysissuggests, the assumption made so far, that the a, f3 absorbance bands for the porphyrin7-7* transitions are responsible for the observed photochemistry, leads to the conclusionthat 1(5 should actually be > > 108 s-1 .The rate constant for the decay of a photoexcited state can be expressed as thesum of various more elementary rate constants; for k 5 one could writek_5^kf ^"other^ 3.65where kf is the rate constant for fluorescence emmission, and k the, is the rate constant for167deactivation via other processes, such as intersystem crossing/phosphorescence, andvarious radiationless processes.''''' There is a useful approximate relationship betweenthe magnitude of k f and that of the extinction coefficient at the absorbance peak: 22bkf ,--.-  (104e,nax) s -1^3.66For the a band at 525 nm, e n. is 2.5x104 1■4-1 cm-1 (see section, and so k f shouldbe about 2-3x10 8 s-1 . Experiments to investigate the optical emission properties of thesynthesized Ru(OEP) complexes were not done, but previous studies by other groupshave found that Ru(Porp) complexes in general show negligible fluorescence.' Thisimplies that the rate constant for the decay of the photoexcited state by processes otherthan fluorescence must be several orders of magnitude > k f, i.e. the excited state isquenched 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 T-r* 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 (assuggested in figure 3.5b, p. 98). A charge transfer transition such as the one pictured infigure 3.5b (k5 step) would be symmetry forbidden (see figure 3.4); 8 accordingly, Emax andtherefore k5 would be much smaller, and more reconcilable with the calculated K,,value. Furthermore, if a specific charge transfer band is responsible for the observedphotochemistry, this provides a more logical explanation as to why it is specifically lightabove 480 nm which is necessary, even though the Soret band at 407 nm is both more168energetic and more intense (see section 3.3).Modifying the overall mechanism proposed in figure 3.8 with the photochemistryof figure 3.5b does not affect the form of the rate equations; however, the parametersK.4 , vm (and v.,) have new meanings (cf. section 4.3.3):K.4 .=.- k_5 ,1(6 ,/(k7 (1c6, + k5 ,))^(cf. equation 3.46)^ 3.67v. --= 0.5c i^(cf. equation 3.44)^3.68v., ==--  0.5c l ,^(cf. equation 3.62)^3.69The fact that modifying the light dependence does not affect the form of thederived rate equations, given the data available, shows that it is unwise to attempt furtherinterpretation of the data, without first doing more detailed experiments focussed on thephotochemical phenomenon. However, it is worth considering one point, which could beof importance in designing future experiments.If the expressions obtained for v m and v.• in equations 3.68 and 3.69 arecompared 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 mand v., are simply equal to half of the geometrical parameters c i and c 1 ,, while in theoriginal mechanism these parameters were each multiplied by a factor of 1c 7/(k_6, +14Now, because the c l (or c 1 ) parameter is dependent only on the geometry of theapparatus and on the intensity of the light source, this parameter could be obtained169experimentally for a given apparatus setup by measuring the rate of a completely differentphotochemical reaction, for which the maximum rate was known to be dependent solelyon the geometry of the apparatus. Then, the calculated value of v m could be checked tosee if it was equal to 0.5c 1 , or whether it was significantly lower. In practice, thisexperiment 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 workwould be adequate.170NOTES AND REFERENCESFOR CHAPTER 31. This pressure was high enough to drive the syringes at the 35° C temperature reportedin this work; studies not reported here showed that for higher temperatures the drive syringesbecome 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 diethylsulfideon the total solvent vapour pressure was neglected in this series of experiments. b) 1UPACSolubility 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 discussessingular 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 backgroundfor the relevant programs. It is available in three different versions, with the routines inFortran, 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: NewYork, N. Y., 1991. The latter does not contain a detailed mathematical background of theprograms. 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, 5939.17111. 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, thefollowing summary may prove useful. Suppose we have a set of data points, each denotedby (yobs) 1 , and each with an associated measurement error a i . Now suppose that, accordingto a theoretical model, we calculate values (y ea, corresponding to each of the (v 1 Then,(yobs) 1 .•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 obtainingthis x2 value (or a higher one) if the model is assumed to be correct. Clearly, if Q is verylow, then the model could be wrong. In practice, reference 5a suggests that the odd Q valueas low as 10' may be tolerated if the distribution of the measurement errors is not perfectlynormal.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 11.22. TUITO, N. J. Modern Molecular Photochemistry, University Science Books, Mill Valley,CA., 1991; a) p. 176; b) p. 90.172CHAPTER 4RATE LAW DERIVATION FOR THE02-OXIDATION OF DIETHYLSULFIDECATALYZED BY Ru(OEP)(Et2S)24.1 IntroductionIn the last chapter a mechanism was suggested to account for the catalyticoxidation of Et2S to Et2SO by Ru(OEP)(Et 2S)2 , and a rate law based on this mechanismwas shown to accurately describe the quantitative production of Et2SO under a variety ofexperimental conditions, at least over a time period of 2h. In addition, the equilibriabetween Ru(OEP)(Et2S)2 , Ru(OEP)(Et2S)(Et250) and Ru(OEP)(Et2SO)2 were studiedindependently, and rate laws for the net substitution processes verified experimentally.This chapter gives the mathematical derivation of the rate laws for both the overallcatalytic cycle and the isolated equilibria. Most of the manipulations described are basedon well established kinetic data treatments (see for example, reference 13 in the previouschapter). An exception is in the empirical treatment of the Et2S oxidation rate dependenceon light, so this topic is given special attention.4.2 The Equilibria between Ru(OEP)(Et 2S)2 , Ru(OEP)(Et2S)(Et2SO) andRu(OEP)(Et2SO)24.2.1 Rate Law DerivationsIn the stopped-flow experiments described in the previous chapter, a solutioncontaining Ru(OEP)(Et 2SO)2 and Et2SO was mixed with another containing Et 2S. It wassuggested that the ensuing pair of substitution reactions proceeded according the scheme173outlined in figure 3.12, and shown again in figure 4.1. Experimentally, the firstsubstitution of a coordinated Et2SO by Et2S was found to progress much faster than thesecond, so the assumption is made that Ru(OEP)(Et 2SO)2 and Ru(OEP)(Et2S)(Et250) willachieve their equilibrium concentrations before the second substitution reaction hasproceeded to any appreciable extent. This allows the rate laws for the two substitutionprocesses to be derived independently, and the successful quantitative analysis of thekinetic data, described in section 3.4, substantiates this assumption.For the purpose of the derivations that follow, some shorthand notation will beused to make the equations less cumbersome. Thus:Ru(OEP)(Et250)2 = 1; Ru(OEP)(Et250)(Et2S0) = 1';Ru(OEP)(Et250) = 11 , first 5-coordinate intermediate;Ru(OEP)(Et 2S)(Et250) - 2;Ru(OEP)(Et2S) ----- 12 , second 5-coordinate intermediate;Ru(OEP)(Et2S)2---- 3.First Substitution Equilibrium174k1Ru (0EP)(Et SO)21^k-Et2S0kRu (0EP)(Et S0XEt 2S 0)1'Et 2 SOEt, S2Ru (0EP)(Et 2a0)^Ru (0EP)(Et 2S)(Et 25.0)k-,^2Et2S Et, SOSecond Substitution Equilibrium^Et, SO^ Et2 SkRu (0EP)(Et ,S)(Et,S0)^j4 ^Ru (0EP)(Et S)    Ru (0EP)(Et 2S)2k 3 k-k442^ a2)^Et 2 SO^ Et,sFigure 4.1. Mechanism proposed for the sequential substitution of two Et2SO ligands byEt2S, assuming that in solution the bis(sulfoxide) species exists as a mixture of the S- and0-bound linkage isomers.175For the first substitution process, the rate of appearance of 2 is described by thedifferential equationd[2]/dt = k2[I,J[Et2SJ - k2[2]^ 4.1Under conditions of high [Et 2SO] and [Et2S], I, is not expected to accumulate toany appreciable extent, so the following steady state approximation is made:d[I,]/dt = 0= k 1 [1] + 1(1411 + k-2[2] - [Ii]((k_i + k_1-)[Et2S0] + k2[Et2S]))^4.2Thus the concentration of I, will be given byII = (kiln + k i ln + k-2[2])/(((1 +k_1.)[Et2S0] +k2[Et2S])^4.3Usingk_ lApp ---E 1( 1 +1( 1 ,^ 4.4176and combining 4.3 and 4.4, and then substituting for I I in 4.1 yields, afterrearrangement,d[2]/dt = k2[Et2S](ki[1] + ki , [11)/(k_ iApp[Et2S0] + k 2 [Et2S])- k- 1 Appk-2 [Et2S 0] [2]/ OC_ 1 App[Et2S 0] + k2[Et2S])^ 4.5Now, because the equilibrium between 1 and 1' is independent of [Et 2S] and [Et2S0], andbecause the stopped-flow analysis of section 3.4 showed that the equilibrium is notdisturbed, even transiently, during the substitution process, the following relation holds atall times during the first substitution (and of course also the second) reaction:K' = [11/[1]^ 4.6whereK' ---.  ki k_v/lci lc_ I^4.7Equation 4.6 can be used to eliminate [1'] from 4.5. Straightforward algebra results inthe expressiond[2]/dt = kik2k_lApp[Et2S][ 1 ]4-1(kiApp[Et2S0] + k2 [Et2S]))- k_m ppk-2 [Et2S 0] [2] / (k_ 1 A pp [Et2S 0] + k2 [Et2S ] )^ 4.8177For any given experiment, the concentrations of [Et 2S] and [Et2SO] remainessentially unchanged throughought; we therefore define two pseudo rate constants,k if^kik2k_ lApp[Et2S]/(k_ 1 (k_mpp [Et2S0] + k2[Et2S]))^4.9k_iAppk_2[Et2SO]/(k_IAPp[Et2S0] + k2[Et2S])^4.10On defining [Ru]. as[Ru].^[1] + [1'] + [2] + [3]^ 4.11and 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')^ 4.12Now equations 4.8, 4.9, 4.10 and 4.12 can be combined to gived[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 todefine two more parameters; let1780 1^lcif[Ru] o/(1 + K')^ 4.1402 ---= k 1 /(1 + K') + kb.^ 4.15so thatd[2]/dt = 0 1 - 02 [2]^ 4.16This equation is integrated to give the desired expression for [2] as a function of time:[2] = (0 1/02)(1 - exp(-02t))^ 4.17Derivation of the rate law for the second substitution reaction begins by assumingthat 1,1' and 2 are in equilibrium, and that the concentration of 3 equals zero at the startof this reaction. The rate of appearance of 3 is then described by the differential equationd[3]/dt = 1(4[I2][Et2S] - k-4[3]^4.18A treatment analogous to that used for the first equilibrium allows us to rewrite equation4.18 in the formd[3]/dt = k2/2] - k2,[3]^ 4.19179wherek2f =a k3k4 [Et2S]/(k_3 [Et2S0] + k4[Et2S])^ 4.20k2, =--- k_3k.4[Et2SO]/OC-3[Et2S0] + k4[Et2S])^ 4.21K 1 is defined as the equilibrium constant between 1 and 2, and thereforeK 1 = [2][Et2S0]/[1][Et2S]^ 4.22Rearranging this expression and combining it with equations 4.6 and 4.11 gives[Ru]o = [2][Et2SO](1 + K')/K 1 [Et2S] + [2] + [3]^ 4.23And on definingKiAm r-=- K1/(1 + K')^ 4.24equation 4.23 becomes[Ru]. = [2]([Et2SO] + K lApprEt2SD/KIApp [Et2S] + [3]^ 4.25180which gives, after solving for [2],[2] = ([1( 1 ]0 - [3])K1App[Et2S]/([Et2S0] + KiApp[Et2S])^4.26LetA .-7-  K1App[Et2S]/aEt2S0] + KiApprEt2S1)^ 4.27Thus equation 4.19 can be rewritten asd[3]/dt = k2fA[Rul. - (k2fA + k20[3]^4.28This equation is identical in form to equation 4.13, and integrates to[3] = (03/04)( 1 - exp(-04t))^4.29where03 --= k2fA[Ru],,^ 4.3004 ...: k2fA + k21^ 4.311814.2.2 Correlation of Uv/Vis Absorbance Changes to the Derived Rate Laws4.2.2.1 First Substitution ReactionExperimentally, the reaction of Ru(OEP)(Et2SO)2 with Et2S was monitored byvisible absorption spectroscopy. The first substitution was followed at 400.5 nm, whichis the absorbance maximum for Ru(OEP)(Et 2SO)2 solutions at 35° C. From the Beer-Lambert law we can writeA = € 1 , 111 + f ill] + 62 '[2]= (e l ' + € 1 , 1C)[1] + f2 '[2]-= (El' + €1/KIRu])(1 + K') + [ 2](e2' - (e l ' + e 1 ,'K')/(1 + K'))^4.32The final form of equation 4.32 is obtained by substituting 4.6 for [1'], and then 4.12 for[1]. As defined, en ' --= €.1, where 1 is the path length of the solution whose absorbance isbeing measured.If A. is defined as the absorbance at t = 0, and nal. are the initialconcentrations of 1 and 1', thenA. = € 1 11] 0 + 6 1 ,1110^4.33[Ru]. = M. + [11.^ 4.34Since 1 and 1' are in equilibrium, equations 4.33,4.34 can be rewritten as182A0 = (e l ' + El/V)[IL[Ru]o = (1 + 1C)[1]0Solving equation 4.36 for [1] 0 and substituting into equation 4.33 yieldsA0 = (E l ' + fr'KIRul o/(1 + K')LetflAppf..- (el l + er 'K')/(1 + K')thenAo = e lApp f [RU]0The last two expressions can be used to simplify equation 4.32:A = A0 + (€2 1 - E lApp ')[2]^ 4.40If we defineAfi =- €2  - cup;^ 4.414.354.364.374.384.39183then equations 4.17, 4.40 and 4.41 can be combined to give the desired expression forthe change in absorbance as a function of time:A = 0 1 4E 1 V02 + Ao - 0 I 4E 1 'exp(-020/02^4.42This equation is equivalent to equation 3.6 (p. 118) if we definea 1  0 14002 + Ao^4.43Si 7--: Ao - a 14.444.45Equation 3.9 (p. 119), the expression for the initial rate of change of absorbance withtime, also follows directly from equation 4.42:Vol = -y1 R 1= 0 14 € 1 '^ 4.46Rearranging 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:184N1 = -OA f 1 102= -Ic If[Ru]0LIEMIc if + kal + K'))= -[Ru]0AE 1 '/(1 + (klr/klf)( 1 + K'))^4.47ki ral f = (k-1APP1C-2[Et2S O]/(k_mpp[Et2S 0] + k2rEt2S1))x(kik2k_iApp[Et2S]/(k-i(lc- 1app[Et2S0] + k2[Et2S])Y 1= k_ 1 k_2 [Et2S0]/k 1 lc2[Et2S]= [Et2SO]/K I [Et2S]^ 4.48Substituting 4.48 into 4.47, and rearranging, gives the final desired expression for 13:Si = -[Ru]AfilEt2SVOKIAppY l[Et2S0] + [Et2S])^(3.10) 4.49Similarly for v01 :voi = O i Ae l '= k1f[Ru],,A€ 1 1 /(1 + K')= (Ic ik2k_ ippp[Et2S]/ (k_i(k_iApp[Et2S 0] + k2[Et2S])))([Ru]0Ae1 '1(1 + K'))= (k_ 1App/(k_ 1 (1 + IC)))0c1[Et2S][Ru]aAEIRICI[Et2S0] + [Et2S])^4.50185k l k_mpp/k_ 1 (1 + K') = 101 + K') + k_pk i /(k_ i (1 + K'))= k,/(1 + K') + kv/(1 + (K') - ')kiApp^ 4.51Thereforev0, = klApp[Ru]4ellEt2Sli(Knil[Et2S0] + [Et 2S])^(3.11) 4.52The 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 ifRu(OEP)(Et2SO)2 were present as a single isomer; in this case, K lApp would be replacedsimply by K,. In the same way, the parameter Empp ' behaves like an extinction coefficientfor a single species, Ru(OEP)(Et 2SO)2 , provided that all the experiments are being carriedout at one temperature. Second Substitution ReactionThe second substitution reaction was followed at 402.8 nm, which is an isosbesticpoint for a mixture of Ru(OEP)(Et2SO)2 and Ru(OEP)(Et2S)(Et2SO) at a total fixedconcentration. The Beer-Lambert expression at any wavelength will beA = (e l ' +^+ E212] + c3 '[3]^ 4.53If equations 4.6 and 4.11 are used to eliminate [1] from equation 4.53, a little186rearranging simplifies the latter toA = A. - e1App'([2] + [3]) + €212] + €313]^ 4.54At the isosbestic point chosen, E2 ' - Empp f = 0, and thusA = Ao + [3](e3 ' - empp)^4.55Now if Ae2 ' is defined asAez ' =7- €3 ' ElApt:^ 4.56the desired expression for [3] as a function of absorbance is obtained:[3] = (A - Ao)/,A€2 '^4.57which, when combined with equation 4.29, gives the absorbance change as a function oftime:A = 03 ,6■62 '/84 + Ao - (03AE2 'exp(-040)/04^ 4.58187Again this equation has the form of equation 3.6 (p. 118). For this particular system,a2 = 030€2 '/04^Ao^4.59N2 = Ao a2= -03AE2704^ 4.60'Y2 = 04^ 4.61Alsovo2 =^= 03 ,6■62 '^ 4.62Equations 4.60 and 4.62 need to be expanded to show the dependences of 02 and vo2 on[Et2S] and [Et2SO]; again, this is a long but straightforward process, and only a sketch ofthe 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 -1K2 1)= K I AppK2 [R U]oAE2 [Et2S]2/ (KlAppl(2[Et2S]2K iApp[Et2S] [Et2S 0] + [Et2S°])^ 4.63188Similarly, from equations 4.20, 4.27, and 4.62,v02 = k2fA[Ru]4€2'(k3[Ru]0AE2'[Et2S]/(Km2[Et2S0]^[Et2S]))x(K lApprEt2S1/([Et2S0] + KlApp[Et2S]))= k3[Ru]oziE2'[Et2S] 2/4K,.2[Et2S0] + [Et2S])((CIApp) 1 [Et2S0] + [Et2S])^4.64In theory, all of the desired equilibrium and rate constants should be obtainablefrom equations 4.63 and 4.64 (the value of KIAPP could also be determined independentlyfrom the study of the first substitution reaction). In practice, these equations prove to bevery awkward to deal with numerically, but fortunately they are easily rearranged to themore tractable quadratic forms shown in equations 3.24 and 3.25 (p. 125):[Et2S] 2/132 = d i [Et2SJ 2 + d2 [Et2S] + d 3^(3.24) 4.65[Et2S]2/V02^d4rEt2S]2^d5[Et2S ]^d6 (3.25) 4.66where the parameters d,-d 6 were previously defined in chapter 3 (p. 125). An analysis ofthe dependences of [Et2S] 2/132 and [Et2S] 2/vo2 on [Et2S] at constant [Et2SOJ yields thedesired equilibrium and rate constants. Note, that if d3 and d6 are negligible relative tothe other terms in equations 4.65 and 4.66, these equations simplify to the same linearform as equations 4.49 and 4.50.1894.3 Catalytic 0 2-Oxidation of Et 2S by Ru(OEP)(Et2S)24.3.1 General Rate Law DerivationIn section 3.3 a mechanism was proposed, by which Ru(OEP)(Et 2S)2 couldcatalyze 02-oxidation of Et2S in acidic benzene. Throughout section 3.5, severalmodifications to this mechanism were suggested, in order to account for some of theexperimentally 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, isconsidered. Using the methodology provided, it is not difficult to derive rate laws for themodified mechanisms; a brief sketch of the procedures involved, together with someadditional theoretical considerations, are given in section 4.3.3.According to the assumptions summarized in section 3.5.1 (pp. 140-141), the onlyRu(OEP) species present in significant amounts during any given reaction areRu(OEP)(Et2S)2 (3) and Ru(OEP)(Et2S)(Et25.0) (2); the Ru(OEP)(Et2S0)2 species (1 and1') are assumed to accumulate only negligibly over the time period monitored, and allother Ru(OEP) species are assumed to remain in small, steady state concentrations. Therates of change in concentration of the two major Ru(OEP) species are governed by thedifferential equations:d[2]/dt = k_3[I2][Et2S0] - k3 [2]^ 4.67-d[3]/dt = d[2]/dt^ (3.38) 4.68(where 12 7,-- Ru(OEP)(Et2S)2). Again some shorthand notation will be used to make thehv2RIIII(OEP)'(Et,S )2(3) /--rc-4 (12) ; 0, coordination2RuIT(OEP)(Et 2S )2Ru(OEP)(Et2S)(02 )Et, SOI I^Ru1l(OEP) (Et,S0)2^II^Ruli(OEP) ( Et,SO XEt 2so)it( 1 ) k^(1')k '^— ' •1• 1Re(oEp)(Et2a0) (ii )Et2 S -k,-(2) Ru1i(oEp)(Ei„s)(Et,s0)^-^InternalRearrangement,&14 ,Ruli(OEP)(Et ,S)(Et,S0)Et2 S kEt, SORu iT(OEP)(Et ,S)H,0[Ruiv(OEP)(Et ,S)(PICOO)r-PhC00-k toRum (OEP)(Et ,S)(PhC00)[Ralv(OEP)(Et ,S)(PhC00)1+0H-PhCOOHEt ,Sk(I8) \ti3Et, S0=Ruiv(OEP)(Et ,S)21'^ PhCOOH6 12(17)02 (I3)2[Ruill(OEP)(Et ,S) 2 rPhC00 -(T6)^-----2H0,kd0,k92[RuII(OEP)(Et 2S)2]0, -k k (Li)2TRUM(OEP)(Et 2 S )2 r02(Is)PhCOOH(190kOXEt ,S0H,0Figure 4.2. Mechanism proposed for the 0 2-oxidation of Et2S to Et2SO, catalyzed byRu(OEP)(Et2S)2 and PhCOOH (dotted pathways imply that these processes can beneglected, or do not occur, under catalytic conditions; see the assumptions on pp. 140-141).191equations less cumbersome. Thus:13^Rull(OEP)*(Et2S)214 =4 Ru ll(OEP)+ .(Et2S)202 -15^Rum(OEP)(Et2S)2 +0216 = Rum(OEP)(Et2S)2 +PhC00 -Rum(OEP)(Et2S)(PhCOO)18^Ru ll(OEP)(Et2S)(Et2S0)The steady state equation for [1 2] will be:k14 [18] + 1(3 [2] + k.4[3] = [I2](k_3[Et2S0] + k4[Et2S])^4.69All of the reactions between k10 and k14 are unbranched, and are assumed to beirreversible; therefore, k 14 [18] = 1c 10[I6][12]. Upon substituting for k 14 [18] and rearranging,equation 4.69 becomes[I2] = (k10[16][17}^k3[2]^1(4[3])/(k_3[Et2S0] ^k4[Et2S])^4.70192Substituting for [I2] in equation 4.67 yieldsd[2]/dt = k_3[Et2S0](klofi6][I7] + k3[2] + 1(43])/(k_3[Et2S0] + k4[Et2S]) - k3[2] 4.71Rearranging 4.71 and using Km2 --.  (k_3/14) givesd[2]/dt = k ijEt2S0][I6][I7]/aEt2S01 + (1(.2)4 [Et2S])+ 1(4[3][Et2SO]/([Et2S0] + (1C2) - '[Et2S])-k3[Et2S][2]/(1C2[Et2S0] + [Et2S])^4.72Recalling that Km2 was found experimentally to be very close to 1 (table 3.2, p. 129),equation 4.72 can be simplified tod[2]/dt = kio[Et2S0][4][Idi[Et2S], + k4[Et2S0][3]/[Et2S]o-k3 [Et2S][2]/[Et2S]0,^ 4.73where [Et2S]o =-- - [Et2S] + [Et2SO]. The steady state relationships for [I 3]-[I7] are given bythe following equations:[1'3] = I./(k_s +k6[02])^4.74(where I. is the amount of light absorbed by Ru(OEP)(Et2S)2 for each turn of the catalyticcycle; I, ----- einsteins absorbed per liter per second).193k6[02][13] + kAI5] — [14](k_6, + 1(7)^4.751c7[14] = [I5](k..7 + kaPhCOOHD^ 4.76k8[PhCOOH][151 = [I6](k9 + k10[17])^4.77k9[I6] = k1o[I6M7]^ 4.78Combining equations 4.77 and 4.78 givesk8[PhC00}1][4] = 21(10[16][17]^ 4.79At the same time, combining equations 4.74, 4.75 and 4.76 gives1C6[°2]Ial(k-5 + k6[02]) + k-7[15] = [I5lik7 + k8[PhCOOH])(k.6 , + k7)/k7^4.80A series of algebraic manipulations converts this last expression to[Is] --= k61(7[02]iaNk-A7 + (k_-6 ,k8 + k71(8)[PhCOOHDOc..5 + k6[02]))^4.81which, when combined with expression 4.79, yields194k10[I6][I7] = 0.5k6k7k8[PhCOOM[O2]la+((k-61-7 + k8(k-6 , + k7)[PhC001-1])(k_s + k6[02}))^4.82Now we can substitute for k 10[I6][I7] in equation 4.73:d[2]/dt =-- 0.51c6k7k8[PhC001-1][02][Et2SOlia÷aEt2Slak-6 , k-7 + k8(k_6 , + k7)[PhCOOH])(k_5 + k6[02]))+klEt2S0][3]/[Et2SJ0 - k3 [Et2S]pit[Et2S]o^4.83Upon definingKno^1(5/ 1(6^ 4.84k_6 ,1(7/0•6 , + 101(8^ 4.85v.^0.51c7/(k_6, + k7)^ 4.86equation 4.83 can be rewritten in a somewhat more compact form:d[2]/dt = v.[PhC0011][02][Et2SO]ia+ffEt2Slo(Km3 + [02])(Km4 + [PhCOOH]))+k_4 [Et2S0][3]/[Et2S], - k3[Et2S]Pl/[Et2S]o^ 4.87195Expressions for the rate of change in [Et2SO], [Et2S] and [02] are now required.For [Et2S0]:d[Et2S0]/dt = icox[Et2S][14202] + k14[18] - k_ 3[0,2S0][I2] + k3 [2]= Ics[PhCOOH][I5] - d[2]/dt^ 4.88Substituting expression 4.81 for [I i] in equation 4.88, and taking into account thedefinitions 4.84-4.86, we can write:d[Et2S0]/dt = 2v.[PhCOOH][02]IMIC3 + [02])(1C4 + [PhCOOH]))-d[2]/dt^ 4.89Finally, combining equations 4.87 and 4.89 gives, after rearrangement:drEt2S0Vdt = vmax [PhCOOH][02]I)(1C3 + [02])(Km4 + [PhCOOH])x(2[Et2S],, - [Et2SO])/[Et2S1.-k_4 [Et2S0][3]/[Et2S]o + k3 [Et2S][2]/[Et2S].^4.90For [Et2S] and [02],-d[Et2S]/dt = d[Et2SO]/dt^ (3.40) 4.91-d[02]/dt = 0.5d[Et2S0]/dt^ (3.41) 4.92196Equations 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 asuitable expression to describe4.3.2 An Approximate Expression for I.In the system of interest, a solution contained in a spherical vessel was irradiatedby polychromatic light. The vessel was shaken at a fixed rate, and the light source wasmounted at an angle to the solution surface. In such a system, any function describing theamount of light (Ia) absorbed by a solution species is expected to have a complicatedform. Nevertheless, empirical funtions to approximate I. can be suggested, based on theform which Ia would have if a more simple apparatus had been used.Suppose, for instance, that a quiescent solution of Ru(OEP)(Et 2S)2 andRu(OEP)(Et2S)(Et2SO) was contained in a rectangular reaction vessel, and illuminated bymonochromatic light striking the vessel normal to a wall. From the exponential form ofthe Beer-Lambert law,= Lexp(-2.303(e2 1 [2] + e3' [3])^ 4.93where 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 pathlength 1. The typical units for both these quantities are (einsteins dm -2 s - '); i.e. moles ofphotons transmitted per unit area, per unit time. It follows directly from equation 4.93that the intensity of light absorbed by the solution is simply197Iabs = Io(1 - exp(-2.30302 1 [2} + E3 1 [3]))^ 4.94In studies of homogeneous reactions, it is customary to deal with units of mol t'; wetherefore define:'abs' -. . Iabs(A/V)^ 4.95where A is the surface area being irradiated ( in dm), and V is the volume of thesolution 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 solutioncontaining Ru(OEP)(Et 2S)2 and Ru(OEP)(Et2S)(Et250); the required variable is theamount of light absorbed only by Ru(OEP)(Et2S)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 onthis plane. The following relationship will hold:-dI/d1 = -(dI2/dl + dI3/dl)^ 4.96where-dI2/d1 --.== €21[2]^ 4.97198-d13/d1^€31[3]^ 4.98Equation 4.96 is simply the differential form of the Beer-Lambert law, which requiresthat the exponential decrease in light intensity, as it passes through a unit length of asolution containing several absorbing species, depends on how much the light intensitydecreases exponentially due to each indivival species. The fractional contribution to thedecrease in light intensity by Ru(OEP)(Et 2S)2 , which is equivalent to the fraction of thetotal light absorbed by Ru(OEP)(Et 2S)2 , will be given byX3^C3[3]/(62[21^E3[3])^4.99and the total amount of light a absorbed by Ru(OEP)(Et2S)2 (in units of einsteinswill be given byIe = X348 ,^ 4.100Upon defining the constants€2/€3^ 4.101c 1^I,A/V (constant only for any one particular apparatus)^4.102equation 4.100 can be written in the desired form:199Ia = ciPl( 1 - exp(-2.303(c2 1 [2] + €3'[3]))/([3] + 0[2])^4.103Now in the experiments described in section 3.5.1 it was seen that E 2 and e3 (actually theintegrated 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 experimentsdescribed, a substantial proportion of the incident light was absorbed (e.g. for the mostdilute reaction solution studied, [Ru(OEP)(Et2S)2] = 2.55x10 -5M and A525n, ",=*- 0.6 for a 1cm cell; in this situation, 75% of the 525nm incident light would be absorbed). Underthese conditions, the total amount of light absorbed by the solution will not change verymuch provided that [Ru] o remains constant. Therefore equation 4.103 should be wellapproximated byIa --z-  ci[3]( 1 - exPec2[Ru]o))/([3] + 0[2])^ 4.104wherec2^2 .303f.;^ 4.105andEar = (E2 t^E3 ')12^ 4.106Equation 4.104 describes the amount of monochromatic light which would be200absorbed by Ru(OEP)(Et 2S)2 , in a solution containing both Ru(OEP)(Et 2S)2 andRu(OEP)(Et2S)(Et250), if the solution were in a rectangular reaction vessel, with theincident light striking the vessel normal to a wall. We now consider the real apparatussetup, shown in figure 3.1 (p. 89), and consider qualitatively what changes need to bemade to equation 4.104 as the experimental setup is made more complicated. Thediscussion considers the effects of each change in the apparatus on I abs , (equations 4.94and 4.95) and X3 (equation 4.99) separately (see equation 4.100).Making the light source polychromatic will not affect the form of either labs, or X3,but the molar extinction coefficients for 2 and 3 must be replaced by their equivalentforms integrated over all of the absorbing wavelengths, as was done in the data analysisof section 3.5.1 (equation 3.52, p. 142). Neither shaking the solution nor switching froma rectangular to a spherical vessel will affect X3, but both these changes will have effectson Ith.,. Switching to a spherical vessel means that the path length is no longer constantover the reaction solution; shaking the solution makes the determination of the solutionsurface area exposed to the light very difficult or impossible, and means that scatteringeffects due to the bubbles produced by the shaking of the solution will have to becontended with.Despite the expected complicated nature of labs, in the real experimental system,one thing is certain: regardless of the experimental setup, any equation proposed todescribe Iabs , must behave the same under limiting conditions as the equation derived forthe 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 amaximum value as either [Ru]o or 1 becomes very large (i.e. when the solution becomes201infinitely concentrated, the transmittance must be 0%). The latter means that c 1 stillreflects the maximum attainable value of I., and although A is no longer a parameterwhich 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 formIt, = c 1 f[Ru]o[3]/([3] + tk[2])^ 4. 107where c 1 is a constant dependent only on the geometry of the experimental setup, thesolution stirring rate, and on the intensity of the incident light, 1,G is the ratio of the molarabsorption coefficients of Ru(OEP)(Et2S)2 and Ru(OEP)(Et2S)(Et250) integrated over allabsorbing 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(-10c2[Ru]o) + arctan(c2[Ru]o)^ (3.50) 4.108was arrived at through trial and error; it has the disadvantage that its range is from 0 to1 + (7/2) which makes the expression for the maximum value of I. somewhatcumbersome (=3irc 1/2, instead of c 1 which would be more convenient); however, theequation proved easy to work with, and has only one adjustable parameter. Now, upondefiningVm =," Vmaxel^ 4.109andkb. --. - vARti]o) [02][PhCOOH]/OKno + [02] ) (Kin4 + [PhCOOH]))^4.110202equations 4.87 and 4.90 can be written in the form of equations 3.37 and 3.39 (p.139),respectively:d[2]/dt = klEt2S0][3]/[Et2S]. - k3[Et2S]Pli[Et2S]o+ kobs[Et2SO][3]NEt2S1([3] + 0[2]))^(3.37) 4.111d[Et2SO]/dt = kobs[3](2 [Et2SL - [Et2SO])MEt2SL([3] + 0[ 2]))-k4(Et2SON3V[Et2S]o + k3 [Et2S][2]/[Et2S]O^(3.39) 4.1124.3.3. Modifications to the Proposed MechanismIn sections 3.3 and, two possible modifications to the mechanismdiscussed so far (for the 0 2-oxidation of Et2S catalyzed by Ru(OEP)(Et 2S)2) wereproposed. In one of the modifications it was postulated that Ru(OEP)(Et2S)(Et2S0) couldbe rearranging to the Ru(OEP)(Et2S)(Et250) isomer without dissociation of Et 2SO into thebulk of the solution (this "internal rearrangement" is labelled k 14 , in figure 4.2, p.190). Inthe other modification it was postulated that perhaps the initial photoactivation step (k 5 infigure 4.2) involved a direct, light-induced metal-to-porphyrin d-ir . charge transfer, ratherthan a porphyrin 7-7 * transition, as implied in figure 4.2. The procedures used to deriverate laws for the alternative mechanisms parallel those described in detail in sections2034.3.1 and 4.3.2, so only a summary is provided here. In addition, some importantfeatures of the derived rate laws are considered. Internal RearrangementIf Ru(OEP)(Et2S)(Et2SO) were isomerizing directly to Ru(OEP)(Et2S)(Et250),without intermediate dissociation of Et 2SO into the bulk solution, then the rate of changein Ru(OEP)(Et2S)(Et250) would be governed by the differential equation:d[2]/dt = k14.[ 18] + k_3 [Et2S0][I2] - k3[2]k10[4][17] + k_3 [Et2S0][I2] - k3 [2]^4.113The steady-state expression for [I2] would be[12] = (k3[2] + k4[3])/(k3[Et2SO] + 1(4[Et2s])^4.114Substituting equation 4.114 into 4.113 yields, after several steps (cf. steps 4.70-4.73):d[2]/dt = k ic,[4][I7] + k4Et2S0][3]/[Et2S]. - k3fEt2SJ[2]/fEt2S1,^4.115Substituting 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 2SOPP[Et2S]. - k3[Et2S][2]/[Et2S].^kobs[3]/([3] + b[2])^4.116204For the alternative mechanism, the differential equation governing the appearanceof Et2SO would be:d[Et2SO]/dt = 0.5k8 [PhC001-1]U5l + k3[2] - k_3[Et2S0][I2]^4.117A series of substitutions analogous to those used for the previous derivations yield theexpression:d[Et2SO]/dt = lcobs[3]/([3] + 0[2])+k3 [Et2S][2]/[Et2S]a - k4[Et2S0][3]/[Et2S]o^4.118which is the counterpart of equation 4.112.Equations 4.116 and 4.118 may appear somewhat similar to equations 4.111 and4.112, but they are fundamentally different. The difference is best seen by consideringthe initial values of the differentials d[2]/dt and d[Et 2S0]/dt for each of the mechanisms.For the dissociative mechanism,(421/dt),. 0 = 0^4.119(d[Et2SO]/dt),. 0 = Robs^4.120For the internal rearrangement mechanism,205(42}/d0t=o = kobs^ 4.121(d[Et2S0]/dt),= 0 = 'cobs^ 4.122The important difference between the first and second set of initial rate equations is thatthe internal rearrangement mechanism predicts that [2] should begin to build upimmediately, and independently from [Et2SO]. Because of this, the appearance of theintegrated [Et2SO] vs. time curves are very different for the two models. Experimentally,the original mechanism (i.e. isomerization of Ru(OEP)(Et 2S)(Et2S0) toRu(OEP)(Et2S)(Et250) via a five-coordinate intermediate) is found to fit the data muchbetter (see also the discussion in section Photoactivation Via Metal-to-Porphyrin Charge TransferThe alternative mechanism proposed in section affected the shape of thetheoretical [Et2SO] vs. time plots, but not the form of kobs . The alternative photoactivationmechanism, first illustrated in figure 3.5b, and reproduced in figure 4.3 for easyreference, affects only kobs . This allows a convenient shortcut to be employed in derivingthe form of kobs . From equation 4.120 and figure 4.3,(d[Et2S0]/dt)t. 0 = 2kobs = k2 [PhCOOH][I 5]^ 4.123therefore,Ru ii (OEP) (Et S),(3)Ru ii (OEP) .1"(Et ,S)')02 (I4)(I4') Runi(OEP)*(Et 2S),k 6 .('5)[Rum(OEP)(Et 2S)2]+02 -PhCOOHk7^kd^ HO )V[RuIII(OEP)(Et S)21 +PhC00 -(I6)2060.5 020.5 H202  kox)11. 0.5 H2Or0.5 Et2S 0.5 Et2SOFigure 4.3. Alternative mechanism for the photochemical stage of the 02-oxidation ofEt2S catalyzed by Ru(OEP)(Et 2S)2 ; see text for details.207kobs = 0.5k4PhCOOHRI 5.1^ 4.124The steady-state conditions for [I 4], [4], and [I5] are (recall that at t=0, [3] = [Ru].):[14](k..5 , + 1c6 ,) = k_61I51^ 4.125Rvlik_s + k6[02] = c i f[Ru] a^4.126[I5](k_6, + 1c7[PhCOOH]) = 1c6[02][14] + k_6114.1^ 4.127where f[Ru] 0 is the light absorption function (see equation 4.108). Combining expressions4.125-4.127 yields, after rearrangement,[IS] = ci[02]f[Ru]j(k7(1C3 + [02])( 1C4 + [PhCOOH]))where Kno is still k_5/1c6 (equation 4.84), but K in4 is now defined as:k_5 ,1(-6 ,/(k7(k_5 , + kg))Finally, substituting 4.128 into 4.124 yields:Icobs = vm [PhCOOH][O2]f[Ru]iaK m3 + [02])(Km4 + [PhCOOH]))where v„, is now defined as 0.5c 1 .4.1284.1294.130208CHAPTER 5GENERAL CONCLUSIONS ANDSUGGESTIONS FOR FURTHER STUDIESExposure to 02 or air of a benzene, toluene or methylene chloride solutioncontaining 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 correspondingsulfoxides. A 111-nmr study of this reaction in CD 2C12 for the case where RR'S = dms,indicated the presence of reaction intermediates. Attempts to identify these intermediatesled to the synthesis and characterization, by 1H-nmr, uv/vis and it spectroscopy, and CV,of a variety of Ru 11(OEP) and Rum(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 mechanismis proposed for the 02-oxidation of Ru(OEP)(RR'S)2 complexes, which can be brokendown 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 isfollowed by electron transfer from the metal to 02 ; the 02 - so formed is protonated byPhCOOH, yielding Rum(OEP)(dms)(PhC00) and H0 2 . The protonated superoxoxidedisproportionates to give 0.5 equivalents each of 0 2 and H202 , and the latter oxidizes 0.5equivalents of Et2S to Et2SO. This first stage results in the oxidation of one mole ofthioether for every two moles of Ru(OEP)(dms)2 initially oxidized. In the second stage, aRum(OEP) species (possibly Ru m(OEP)(dms)(PhCOO)), which has had its oxidation209potential lowered by coordination of an anionic ligand, is oxidized to Ru"(OEP) byanother species (possibly Re(OEP)(dms) 2 +PhC00 -), which has two neutral axialligands. During the third stage, the RuN(OEP) species is eventually converted to0=RuN(OEP)(dms), which then reacts with one equivalent of dms to produceRun(OEP)(dms)(dmso). One mole of 0=Ru iv(OEP)(dms) is produced for every twomoles of Ru(OEP)(dms) 2 initially oxidized. The net reaction results in two moles of dmsbeing oxidized to dmso for every mole of 02 consumed, with no net consumption ofPhCOOH. The basic mechanism appears to be the same for the oxidation of coordinatedEt2S or decMS, regardless of whether the reaction is performed in CH 2C12 , benzene ortoluene; however, differences in detail are observed between systems.In the presence of excess thioether, solutions of Ru(OEP)(RR'S) 2 and PhCOOH,in CH2C12 , benzene or toluene, catalyze the 02-oxidation of free thioether to sulfoxide;however, under these conditions, light of wavelength above 480 nm is required for thereaction 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 vesselare exposed to the light). The catalytic system was studied in detail for the case in whichRR'S = Et2S; again, the basic mechanism appears to be the same whether RR'S = dms,Et2S or decMS. The stoichiometry of two moles of sulfoxide produced for every mole of02 used was verified by monitoring a reaction simultaneously by gc and by oxygen-uptake experiments. The light dependence observed under catalytic conditions is believedto arise from the fact that 02 coordination to the metal is inhibited by the presence ofexcess thioether; light is then required to provide energy for an otherwise highly210unfavourable outer-sphere electron transfer from the metal to 0 2 . After the initial electrontransfer, the reaction is believed to follow the same course in both the stoichiometric andcatalytic oxidations.A detailed kinetic analysis of the gas uptake data shows that, under theexperimental 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 thevalue of the initial rate appears to be imposed by the complete absorption by the reactionsolution of the incident light by the metalloporphyrin species. The results of the kineticanalysis also suggest two other conclusions. The first conclusion is that whicheverelectronic transition is responsible for the observed photochemistry, it cannot have alifetime lower than about 104 s (corresponding to a decay rate constant of 10 8 s'), in theabsence of 02 . According to a qualitative molecular orbital picture, this suggests that thephotochemical 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 excitedelectron from the porphyrin ring to 0 2 . The second conclusion is thatRu(OEP)(Et2S)(Et250), although seen to accumulate as Et2S0 builds up with time, isoutside of the catalytic cycle (i.e. it is not an intermediate in the reaction pathway).To our knowledge, photoactivated electron transfer has not been reportedpreviously for ruthenium porphyrin systems; however, a neglected, possible lightdependence probably explains the irreproducibility encountered in studies of the 0 2-oxidation of PPh 3 catalyzed by Ru(OEP)(PPh3)2 .' A light dependence could also explainthe irreproducibility encountered in the apparently unrelated investigations of aldehydedecarbonylation catalyzed by Ru(Porp) complexes, although some data suggested that the211catalysis was a purely thermal process; 2 of note, Ru(OEP)(CO)L complexes (L = aneutral axial ligand) appear to be minor side products in both the stoichiometric andcatalytic oxidations described in this thesis. When successfully initiated, the catalyticdecarbonylation reactions were reported to be quite efficient, 2 and it may be worth re-investigating these reactions to see if they behave more consistently under steadyillumination.The possible commercial value of a catalyst which could selectively oxidizethioethers to sulfoxides was a consideration in the initial decision to investigate thereactivity of Ru(OEP)(RR'S) 2 complexes with 02 . Two general commercial applicationscan be envisioned for a catalyst which oxidizes thioethers to sulfoxides. The first is tooxidize simple thioethers such as dms, which are often waste products in industrialprocesses,' to the more valuable sulfoxides. The second commercial application would beto convert prochiral thioethers into chiral sulfoxides, which could then be used as chiralsynthetic reagents in organic synthesis.' For the oxidation of simple thioethers, thesystem described in this thesis could probably be reasonably effective if efforts weremade to optimize the geometry of the reaction apparatus for light absorption; however,theeventual decomposition of the catalyst would always be a problem. Furthermore, thecerium-based system of Riley et al. (see section 1.3) currently appears to show morepromise, despite requiring high temperatures (100° C) and 02 pressures (14 bar). 3As a model system for future developement of a chiral oxidant, theRu(OEP)(RR'S)2/PhCOOH system is fundamentally flawed in that half of the thioether isoxidized by the achiral H202 . For chiral oxidation of thioethers, a chiral Ru(Porp) systembased on the Ru(OCP)(0) 2 system previously studied in our laboratories (see section2121.2)5 could be investigated. For such a system, care would have to be taken to avoid sidereaction via the mechanism reported in this thesis.An especially intriguing direction for future study of the reaction ofRu(OEP)(RR'S)2 complexes (and possibly other Ru ((Porp) complexes) with 02 , in acidicmedia, would be to use the reaction as a probe, as part of a detailed investigation of theelectronic structure of these complexes. In particular, it would be interesting to combinean investigation of the photochemistry described in this thesis with photophysicalexperiments, such as those recently reported by Holten et al., in which the photophysicalproperties of a variety of Ru(Porp) complexes were investigated by picosecond lasertechniques.'REFERENCES FOR CHAPTER 51. 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, TheUniversity 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, 714.213APPENDIX 1QUICK BASIC PROGRAMSThis appendix lists all of the Quick Basic programs that were used for the dataanalyses discussed in chapter 3 of this thesis. In all cases the programs consist of one ormore modules which were specifically written for the tasks performed in the thesis, andseveral generic modules obtained from "Numerical Recipes In Basic" (reference 6 inchapter 3). Only the parts of the programs tailored specifically for this thesis are includedhere. A complete list of the modules taken from Numerical Recipes, along with thechapter in which the modules can be found, is included after each program.A1.1 UNFITThis is a program for fitting an experimentally derived data set (x, y, o-y) (whereay is the uncertainty in y) to a straight line, y = a + bx. The program returns the bestvalues of a and b, the value of x 2 given these values, and the goodness of fit parameterQ. In addition, the theoretical line and the experimental data points can be displayedgraphically on the screen, and the theoretical points can be saved for future inclusion in agraphical 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 FITCLSLINE INPUT "Filename:", dum$214OPEN dum$ FOR INPUT AS #1LINE INPUT #1, dum$INPUT #1, NPTDIM X(NPT), Y(NPT), SIG(NPT)LINE INPUT #1, dum$LINE INPUT #1, dum$FOR I = 1 TO NPTINPUT #1, X(I), Y(I), SIG(I)NEXT IPRINT "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 MNDAT = NPT - MDIM XDEL(NDAT), YDEL(NDAT), SIGDEL(NDAT)NDEL = M + 1FOR J = NDEL TO NPTXDEL(J - M) = X(J)YDEL(J - M) = Y(J)SIGDEL(J - M) = SIG(J)NEXT JFOR MWT = 0 TO 1CALL FIT(XDELO, YDELO, NDAT, SIGDELO, MWT, A, B, SIGA, SIGB, CHI2,Q)IF MWT = 0 THENPRINT "Ignoring standard deviation"ELSEPRINT "Including standard deviation"END IFPRINT " A = ";PRINT USING "#.#####—"; A;PRINT "^Uncertainty: ";PRINT USING "#.#####"'"; SIGAPRINT " B = ";PRINT USING "#.#####'""; B;PRINT "^Uncertainty: ";PRINT USING "#.#####"'"; SIGBPRINT " Chi-squared: ";PRINT USING "#.#####'"; CHI2PRINT " Goodness-of-fit: ";PRINT USING "#.##'""; QPRINTPRINTNEXT MWTPRINT "Do you want to see a plot of the data (y/n)"INPUT dum$215IF dum$ = "n" THEN ENDNTHEOR = 2DIM XP(NTHEOR), YP(NTHEOR)XP(1) = 0YP(1) = APRINT 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())ENDSUB PLOT (XDAT(), YDAT(), X(), YO, NDATA, NTHEOR, SIG())DOSCREEN 2CLS 2VIEW PRINT 1 TO 4LOCATE 1, 1PRINT "Enter X1,X2 (X1=X2 to stop)"INPUT Xl, X2IF X1 = X2 THEN EXIT SUBPRINT "Enter Y1,Y2"INPUT Yl, Y2CLSVIEW (50, 35)-(550, 180)WINDOW (0, 0)-(500, 145)LINE (0, 0)-(500, 145), BDX = (X2 - X1) / 500 'X Units per pixelDY = (Y2 - Y1) / 145 'Y Units per pixelFOR K = 1 TO NDATASX = INT((XDAT(K) - Xl) / DX)SY = INT((YDAT(K) - Y1) / DY)ERRY = INT(SIG(K) / DY)CIRCLE (SX, SY), 1LINE (SX, SY + ERRY)-(SX, SY - ERRY)NEXT KFOR L = 1 TO NTHEORClX = INT((X(L) - X1) / DX)C1Y = INT((Y(L) - Y1) / DY)IF L < > 1 THEN LINE (C2X, C2Y)-(C1X, ClY)C2X = C1XC2Y = C1Y216NEXT LLOOPEND SUBThe 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 thefollowing example:NPT=14X,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]217A1.2 POLFITThis is a program for fitting an experimentally derived data set (x, y, ay) (whereo-y is the uncertainty in y) to a polynomial, using the method of singular valuedecomposition. The program first returns the diagonal values of the W matrix (seechapters 2 and 14 of numerical recipes), and prompts the user for the maximum toleratedvalue of the condition number. If this value is exceeded, the appropriate w i values are setto zero; in either case, the program then returns the best values of a, b, c... in y = a +bx +cx2 +..., the value of x2 given these values, and the goodness of fit parameter Q. Inaddition, the theoretical curve and the experimental data points can be displayedgraphically on the screen, and the theoretical points can be saved for future inclusion in agraphical 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 SVDFITCLSLINE INPUT "Filename?:", dum$OPEN dum$ FOR INPUT AS #1LINE INPUT #1, dum$INPUT #1, NPTLINE INPUT #1, dum$LINE INPUT #1, dum$INPUT #1, NPOLDIM X(NPT), Y(NPT), SIG(NPT), A(NPOL), CVM(NPOL, NPOL)DIM U(NPT, NPOL), V(NPOL, NPOL), W(NPOL)LINE INPUT #1, dum$LINE INPUT #1, dum$FOR I = 1 TO NPTINPUT #1, X(I), Y(I), SIG(I)NEXT I218CALL SVDFIT(XO, Y(), SIG(), NPT, AO, NPOL, U(), V(), W(), MP, NP, CHISQ,"FPOLY", Q)CALL SVDVAR(VO, NPOL, NP, WO, CVMO, NPOL)PRINT "Polynomial fit:"FOR I = 1 TO NPOLPRINT "A("; I; ") =";PRINT USING "#.#####"'"; A(I);PRINT " +-";PRINT USING "#.#####'""; SQR(CVM(I, I))NEXT IPRINT "Chi-squared";PRINT USING "#.#####""; CHISQPRINT "Goodness of fit";PRINT USING "#.##"'", QPRINTPRINT "Do you want to see a plot of the data (y/n)"INPUT dum$IF dum$ = "y" THENDIM XP(NPT), YP(NPT)FOR J = 1 TO NPTXP(J) = X(J)YP(J) = A(1) + X(J) * (A(2) + X(J) * A(3))NEXT JCALL PLOT(XO, YO, XP(), YPO, NPT, SIG())END IFPRINT "Do you want to save the theoretical points (y/n)?"INPUT dum$IF dum$ = "y" THENINPUT "Filename?", filename$OPEN filename$ FOR OUTPUT AS #2FOR I = 1 TO NPTWRITE #2, X(I), Y(I), SIG(I), XP(I), YP(I)NEXT IEND IFENDSUB SVDFIT (X(), YO, SIG(), NDATA, AO, MA, U(), V(), W(), MP, NP, CHISQ,FUNCS$, Q)DIM B(NDATA), AFUNC(MA)FOR I = 1 TO NDATAIF FUNCS$ = "FPOLY" THEN CALL FPOLY(X(I), AFUNC(), MA)TMP = 1! / SIG(I)FOR J = 1 TO MA219U(I, J) = AFUNC(J) * TMPNEXT JB(I) = Y(I) * TMPNEXT ICALL SVDCMP(UO, NDATA, MA, MP, NP, W(), V())PRINT "DIAGONAL OF MATRIX W"FOR K = 1 TO MAPRINT USING "#.#####AAAA "; W(K)NEXT KINPUT "HOW SMALL A FRACTION OF WMAX WILL YOU ACCEPT?", TOLWMAX = 0!FOR J = 1 TO MAIF W(J) > WMAX THEN WMAX = W(J)NEXT JTHRESH = TOL * WMAXFOR J = 1 TO MAIF W(J) < THRESH THEN W(J) = 0!IF W(J) = 0! THEN PRINT "Resetting W(J)="; J; "equal to zero"NEXT JCALL SVBKSB(U(), W(), V(), NDATA, MA, MP, NP, BO, AO)CHISQ = 0!FOR I = 1 TO NDATAIF FUNCS$ = "FPOLY" THEN CALL FPOLY(X(I), AFUNCO, MA)SUM = 0!FOR J = 1 TO MASUM = SUM + A(J) * AFUNC(J)NEXT JCHISQ = CHISQ + ((Y(I) - SUM) / SIG(I)) A 2NEXT IQ = GAMMQ(.5 * (NDATA - NPOL), .5 * CHISQ)ERASE AFUNC, BEND SUBThe supprogram SVDFIT listed above was taken directly from "NumericalRecipes" with only minor modifications.The subprogram PLOT was the same one used in the program UNFIT describedearlier.220The 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 thefollowing example:NPT=9NPOL=3X,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-3DATA FOR FITTING [Et2S]"2/P(1) vs [Et2S]221A 1.3 ONEDMINThis is the iterative program which was used to find the best value for Ica,„ insection 3.5.1 of the thesis. The user provides: 1) a set of experimentally derived datapoints (t, [Et2SO], ffia,s01) (where aras01 is the uncertainty in [Et2SO] produced); 2) a setof initial conditions [Ru(OEP)(Et2S)(Et250)] o =[A] (INIT), [Ru(OEP)(Et 2S)2]0 = [B] (INIT), [Et2SO]" = [Et2SO] (INIT), [Et 2S]o =[Et2S] (INIT), to = Xl; 3) a final time X2 to stop the integrator, and an estimate of anappropriate step size for the integrator; 4) a value for the integrated extinction coefficientratio 0; 5) two initial guesses as to the value of Ic ob,. Along with the best value of kobs , theprogram 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, HDCOMMON SHARED KMAX, KOUNT, DXSAV, XP(), YP()COMMON SHARED KOBS, PSI, Et2SCISNVAR = 4DIM YSTART(NVAR), XP(200), YP(10, 200)INPUT "What is the initial time in seconds?", X1INPUT "What is the final time in seconds?", X2INPUT "[A] (INIT)?", YSTART(1)INPUT "[B] (INIT)?", YSTART(2)INPUT "[Et2SO] (INIT)?", YSTART(3)INPUT "[Et2S] (INIT)?", YSTART(4)222Et2S = YSTART(4)INPUT "Estimate PSI", PSIINPUT "Estimate the required stepsize for the integration sequence", H1PRINT "Input a filename containing raw data for comparison"INPUT DUM$OPEN DUM$ FOR INPUT AS #1LINE INPUT #1, DUM$INPUT #1, NPTDIM XDAT(NPT), YDAT(NPT), SIG(NPT)LINE INPUT #1, DUM$LINE INPUT #1, DUM$FOR I = 1 TO NPTINPUT #1, XDAT(I), YDAT(I), SIG(I)NEXT IPRINT "Input two trial values for kobs: a,b"INPUT AX, BXCALL 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 ="; BPRINT "kobs="; XMINENDFUNCTION BRENT (XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2,AX, BX, CX, DUM, TOL, XMIN, H1)ITMAX = 100CGOLD = .381966#ZEPS = 1E-10A =AXIF CX < AX THEN A =CXB = AXIF CX > AX THEN B =CXV = BXW = VX = VE = 0!FX = RKCHI2(X, XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2, H1)FV = FXFW = FXFOR ITER = 1 TO ITMAXPRINT ITERXM = .5 * (A + B)TOL1 = TOL * ABS(X) + ZEPSTOL2 = 2! * TOL1223IF ABS(X - XM) < = TOL2 - .5 * (B - A) THEN EXIT FORDONE% = -1IF ABS(E) > TOL1 THENR = (X - W) * (FX - FV)Q = (X - V) * (FX - FW)P = (X - V) * Q - (X - W) * RQ = 2! * (Q - R)IF Q > 0! THEN P = -PQ = ABS(Q)ETEMP = EE=DDUM = ABS(.5 * Q * ETEMP)IF ABS(P) < DUM AND P > Q * (A X) AND P < Q * (B - X) THEND = P / QU = X + DIF U - A < TOL2 OR B - U < TOL2 THEN D = ABS(TOL1) * SGN(XM - X)DONE% = 0END IFEND IFIF DONE% THENIF X > = XM THENE = A - XELSEE = B - XEND IFD = CGOLD * EEND IFIF ABS(D) > = TOL1 THENU = X + DELSEU = X + ABS(TOL1) * SGN(D)END IFFU = RKCHI2(U, XDATO, YDATO, SIG(), NPT, YSTARTO, NVAR, Xl, X2, H1)IF FU < = FX THENIF U > = X THENA =XELSEB = XEND IFV = WFV = FWW = XFW = FXX=UFX = FU224ELSEIF U < X THENA=UELSEB=UEND IFIF FU < = FW OR W = X THENV = WFV = FWW = UFW = FUELSEIF FU < = FV OR V = X OR V = W THENV=UFV =FUEND IFEND IFNEXT ITERIF ITER > ITMAX THEN PRINT "Brent exceed maximum iterations:: ENDXMIN = XBRENT = FXEND FUNCTIONSUB 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) / Et2SDYDX(4) = -DYDX(3)END SUBSUB HUNT (XXO, N, X, JLO)ASCND% = XX(N) > XX(1)IF JLO < = 0 OR JLO > N THENJLO =0JHI = N + 1ELSEINC = 1IF X > = XX(JLO) EQV ASCND% THEN2251 JHI = JLO + INCIF JHI > N THENJHI = N + 1ELSEIF X > = XX(JHI) EQV ASCND% THENJLO = JHIINC = INC + INCGOTO 1END IFELSEJHI = JLO2 JLO = JHI - INCIF JLO < 1 THENJLO =0ELSEIF X < XX(JLO) EQV ASCND% THENJHI = JLOINC = INC + INCGOTO 2END IFEND IFEND IFDOIF JHI - JLO = 1 THEN EXIT SUBJM = INT((JHI + JLO) / 2)IF X > XX(JM) EQV ASCND% THENJLO = JMELSEJHI = JMEND IFLOOPEND SUBSUB MNBRAK (XDATO, YDATO, SIG(), NPT, YSTARTO, NVAR, Xl, X2, AX, BX,CX, DUM, H1)GOLD = 1.618034GLIMIT = 100!TINY = 1E-20FA = 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 THENDUM = AXAX = BXBX = DUMDUM = FB226FB = FAFA = DUMEND IFCX = BX + GOLD * (BX - AX)FC = RKCHI2(CX, XDATO, YDAT(), SIGO, NPT, YSTART(), NVAR, Xl, X2, H1)DOIF FB < FC THEN EXIT DODONE% = -1R = (BX - AX) * (FB - FC)Q = (BX - CX) * (FB - FA)DUM = Q - RIF ABS(DUM) < TINY THEN DUM = TINYU = BX - ((BX - CX) * Q - (BX - AX) * R) / (2! * DUM)ULIM = BX + GLIMIT * (CX - BX)IF (BX - U) * (U - CX) > 0! THENFU = RKCHI2(U, XDATO, YDATO, SIG(), NPT, YSTARTO, NVAR, Xl, X2,H1)IF FU < FC THENAX = BXFA = FBBX = UFB = FUEXIT SUBELSEIF FU > FB THENCX = UFC = FUEXIT SUBEND IFU = CX + GOLD * (CX - BX)FU = RKCHI2(U, XDATO, YDATO, SIG(), NPT, YSTARTO, NVAR, Xl, X2,H1 )ELSEIF (CX - U) * (U - ULIM) > 0! THENFU = RKCHI2(U, XDATO, YDATO, SIG(), NPT, YSTARTO, NVAR, Xl, X2,H1)IF FU < FC THENBX = CXCX = UU = CX + GOLD * (CX - BX)FB = FCFC = FUFU = RKCHI2(U, XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2,H1)END IFELSEIF (U - ULIM) * (ULIM - CX) > = 0! THENU = ULIM227FU = RKCHI2(U, XDATO, YDATO, SIG(), NPT, YSTARTO, NVAR, Xl, X2,H1)ELSEU = CX + GOLD * (CX - BX)FU = RKCHI2(U, XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2,H1)END IFIF DONE% THENAX = BXBX = CXCX = UFA = FBFB = FCFC = FUELSEDONE% = 0END IFLOOP WHILE NOT DONE%END SUBFUNCTION RKCHI2 (W, XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl, X2,H1)KOBS = WDIM YCOPY(NVAR)FOR K = 1 TO NVARYCOPY(K) = YSTART(K)NEXT KEPS = .0001KMAX = 200HMIN = 0DXSAV = 1CALL ODEINT(YSTARTO, NVAR, Xl, X2, EPS, H1, HMIN, NOK, NBAD, DUM,RKQC)FOR K = 1 TO NVARYSTART(K) = YCOPY(K)NEXT KDIM YINT(NPT), YTHEOR(KOUNT), XTHEOR(KOUNT), XTABL(4), YTABL(4)FOR I = 1 TO KOUNTYTHEOR(I) = YP(3, I)XTHEOR(I) = XP(I)NEXT IJLO = 0KPASS = KOUNT228FOR I = 1 TO NPTCALL HUNT(XTHEORO, KPASS, XDAT(I), JLO)FOR K = 1 TO 4IF JLO < = KOUNT - 2 THENXTABL(K) = XP(JLO - 2 + K)YTABL(K) = YTHEOR(JLO - 2 + K)ELSEXTABL(K) = XP(JLO - 3 + K)YTABL(K) = YTHEOR(JLO - 3 + K)END IFNEXT KCALL RATINT(XTABLO, YTABL(), 4, XDAT(I), Y, DY)YINT(I) = YJLO = INT(JLO + KOUNT / NPT)NEXT ICHI2 = 0FOR J = 1 TO NPTCHI2 = CHI2 + ((YDAT(J) - YINT(J)) / SIG(J)) A 2NEXT JRKCHI2 = CHI2ERASE YINT, YTHEOR, YTABL, XTHEOR, XTABLEND FUNCTIONOf the subprograms and functions listed above, the following were taken directlyfrom "Numerical Recipes" with only minor modifications:BRENT, MNBRAK, (Chapter 10);HUNT (Chapter 3).229The 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 formatillustrated by the following example:NPT=12X^Y^SIG (Y)821,.0030894,.00041200,.0042814,.00041615,.0056192,.00042031,.0067806,.00042516,.0083214,.00042972,.0094714,.00043436,.010583,.00043835,.011614,.00044229,.0124036,.00045000,.0142396,.00045790,.015424,.00046261,.016413,.0004A1.4 TWODMINThis program is exactly analogous to ONEDMIN, but in this case tk is treated asan adjustable parameter, and the program iteratively seeks the values of both k ob , and 1,t/for which X2 is a minimum. Three initial guesses as to the value of the set (k ob„lk) are fed230into the program, and three (k ot,„1//) values for which x2 differs by less than 1% arereturned.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(), YPOCOMMON SHARED KOBS, PSI, Et2SCLSNVAR = 4NP = 2MP = 3FTOL = .0001DIM YSTART(NVAR), XP(200), YP(10, 200), P(MP, NP), X(NP), Y(MP)INPUT "What is the initial time in seconds?", X1INPUT "What is the final time in seconds?", X2INPUT "[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", HiNDIM = NPPRINT "Input a filename containing raw data for comparison"INPUT DUM$OPEN DUM$ FOR INPUT AS #1LINE INPUT #1, DUM$INPUT #1, NPTDIM XDAT(NPT), YDAT(NPT), SIG(NPT)LINE INPUT #1, DUM$231LINE INPUT #1, DUM$FOR I = 1 TO NPTINPUT #1, XDAT(I), YDAT(I), SIG(I)NEXT IFOR I = 1 TO MPFOR J = 1 TO NPX(J) = P(I, J)NEXT JY(I) = AMOEB(XO, NP, XDATO, YDATO, SIG(), NPT, YSTARTO, NVAR, Xl,X2, H1)PRINT Y(I)NEXT ICALL AMOEBA(PO, Y(), MP, NP, NDIM, FTOL, DUM, ITER, XDATO, YDATO,SIGO, NPT, YSTARTO, NVAR, Xl, X2, H1)PRINT "Iterations:"; ITERPRINTPRINT "Vertices of final 2-D simplex and"PRINT "function values at the vertices:"PRINTPRINT " I X(I) Y(I) CHISQUARE"PRINTFOR I = 1 TO MPPRINT USING "###"; I;FOR J = 1 TO NPPRINT USING "##.#####""; P(I, J);NEXT JPRINT USING "##.#####''"; Y(I)NEXT IPRINTENDFUNCTION AMOEB (X(), NP, XDATO, YDATO, SIG(), NPT, YSTARTO, NVAR,Xl, X2, H1)IF X(1) < = 0 OR X(2) < = .1 OR X(2) > 1 THENAMOEB = 10000ELSEAMOEB = RKCHI2(X(1), X(2), XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR,Xl, X2, H1)END IFEND FUNCTION232SUB AMOEBA (P0, Y0, MP, NP, NDIM, FTOL, DUM, ITER, XDATO, YDATO,SIG(), NPT, YSTART(), NVAR, Xl, X2, H1)ALPHA = 1!BETA = .5GAMMA = 2!ITMAX = 500DIM PR(NDIM), PRR(NDIM), PBAR(NDIM)MPTS = NDIM + 1ITER = 0DOILO = 1IF Y(1) > Y(2) THENIHI = 1INHI = 2ELSEIHI = 2INHI = 1END IFFOR I = 1 TO MPTSIF Y(I) < Y(ILO) THEN ILO = IIF Y(I) > Y(IHI) THENINHI = IHIIHI = IELSEIF Y(I) > Y(INHI) THENIF I < > IHI THEN INHI = IEND IFNEXT IRTOL = 2! * ABS(Y(IHI) - Y(ILO)) / (ABS(Y(IHI)) + ABS(Y(ILO)))IF RTOL < FTOL THEN ERASE PBAR, PRR, PR: EXIT SUBIF ITER = ITMAX THEN PRINT "Amoeba exceeding maximum iterations.": EXITSUBITER = ITER + 1FOR J = 1 TO NDIMPBAR(J) = 0!NEXT JFOR I = 1 TO MPTSIF I < > IHI THENFOR J = 1 TO NDIMPBAR(J) = PBAR(J) + P(I, J)NEXT JEND IFNEXT IFOR J = 1 TO NDIMPBAR(J) = PBAR(J) / NDIMPR(J) = (1! + ALPHA) * PBAR(J) - ALPHA * P(IHI, J)233NEXT JYPR = AMOEB(PRO, NDIM, XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR,Xl, X2, H1)PRINT "YPR= ", YPRIF YPR < = Y(ILO) THENFOR J = 1 TO NDIMPRR(J) = GAMMA * PR(J) + (1! - GAMMA) * PBAR(J)NEXT JYPRR = AMOEB(PRRO, NDIM, XDATO, YDATO, SIGO, NPT, YSTARTO,NVAR, Xl, X2, H1)PRINT "YPRR= ", YPRRIF YPRR < Y(ILO) THENFOR J = 1 TO NDIMP(IHI, J) = PRR(J)NEXT JY(IHI) = YPRRELSEFOR J = 1 TO NDIMP(IHI, J) = PR(J)NEXT JY(IHI) = YPREND IFELSEIF YPR > = Y(INHI) THENIF YPR < Y(IHI) THENFOR J = 1 TO NDIMP(IHI, J) = PR(J)NEXT JY(IHI) = YPREND IFFOR J = 1 TO NDIMPRR(J) = BETA * P(IHI, J) + (1! - BETA) * PBAR(J)NEXT JYPRR = AMOEB(PRRO, NDIM, XDATO, YDATO, SIGO, NPT, YSTARTO,NVAR, Xl, X2, H1)PRINT "YPRR= ", YPRRIF YPRR < Y(IHI) THENFOR J = 1 TO NDIMP(IHI, J) = PRR(J)NEXT JY(IHI) = YPRRELSEFOR I = 1 TO MPTSIF I < > ILO THENFOR J = 1 TO NDIMPR(J) = .5 * (13(I, J) + P(ILO, J))234P(I, J) = PR(J)NEXT JY(I) = AMOEB(PRO, NDIM, XDATO, YDATO, SIGO, NPT, YSTARTO,NVAR, Xl, X2, H1)PRINT "Y("; I; ")=", Y(I)END IFNEXT IEND IFELSEFOR J = 1 TO NDIMP(IHI, J) = PR(J)NEXT JY(IHI) = YPREND IFPRINT ITERLOOPEND SUBSUB 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) / Et2SDYDX(4) = -DYDX(3)END SUBSUB HUNT (XXO, N, X, JLO)ASCND% = XX(N) > XX(1)IF JLO < = 0 OR JLO > N THENJLO =0JHI = N + 1ELSEINC = 1IF X > = XX(JLO) EQV ASCND% THEN1 JHI = JLO + INCIF JHI > N THENJHI = N + 1ELSEIF X > = XX(JHI) EQV ASCND% THENJLO = JHIINC = INC + INC235GOTO 1END IFELSEJHI = JLO2 JLO = JHI -INCIF JLO < 1 THENJLO = 0ELSEIF X < XX(JLO) EQV ASCND% THENJHI = JLOINC = INC + INCGOTO 2END IFEND IFEND IFDOIF JHI - JLO = 1 THEN EXIT SUBJM = INT((JHI + JLO) / 2)IF X > XX(JM) EQV ASCND% THENJLO = JMELSEJHI = JMEND IFLOOPEND SUBFUNCTION RKCHI2 (W, Z, XDATO, YDATO, SIGO, NPT, YSTARTO, NVAR, Xl,X2, H1)KOBS = WPSI = ZDIM YCOPY(NVAR)FOR K = 1 TO NVARYCOPY(K) = YSTART(K)NEXT KEPS = .0001KMAX = 200HMIN = 0DXSAV = 1CALL ODEINT(YSTARTO, NVAR, Xl, X2, EPS, H1, HMIN, NOK, NBAD, DUM,RKQC)FOR K = 1 TO NVARYSTART(K) = YCOPY(K)NEXT KDIM YINT(NPT), YTHEOR(KOUNT), XTHEOR(KOUNT), XTABL(4), YTABL(4)236FOR I = 1 TO KOUNTYTHEOR(I) = YP(3, I)XTHEOR(I) = XP(I)NEXT IJLO = 0KPASS = KOUNTFOR I = 1 TO NPTCALL HUNT(XTHEOR(), KPASS, XDAT(I), JLO)FOR K = 1 TO 4IF JLO < = KOUNT - 2 THENXTABL(K) = XP(JLO - 2 + K)YTABL(K) = YTHEOR(JLO - 2 + K)ELSEXTABL(K) = XP(JLO - 3 + K)YTABL(K) = YTHEOR(JLO - 3 + K)END IFNEXT KCALL RATINT(XTABLO, YTABLO, 4, XDAT(I), Y, DY)YINT(I) = YJLO = INT(JLO + KOUNT / NPT)NEXT ICHI2 = 0FOR J = 1 TO NPTCHI2 = CHI2 + ((YDAT(J) - YINT(J)) / SIG(J)) A 2NEXT JRKCHI2 = CHI2ERASE YINT, YTHEOR, YTABL, XTHEOR, XTABLEND FUNCTIONOf the subprograms and functions listed above, the following were taken directlyfrom "Numerical Recipes" with only minor modifications:AMOEBA (Chapter 10);HUNT (Chapter 3).237The 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, [Et2SO], arEbsol) experimental data file should be in the same format as thatrequired by the ONEDMIN program.A1.5 ODEGRPHThis is a program which can be used to display graphically the results of anumerical 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, [Et2SO], 0-- rEt2s0);conditions [Ru(OEP)(Et2S)(Et250)]. = [A] (INIT), [Ru(OEP)(Et 2S)2]. = [B] (INIT),[Et2SO]a = [Et2SO] (INIT), [Et2S]. = [Et2S] (INIT), to = Xl; 3) a final time X2 to stopthe integrator, and an estimate of an appropriate step size for the integrator; 4) a valuefor the integrated extinction coefficient ratio ik; 5) a value for k obs . Note that this programdoes not find the best values of kob, as do the previous two; this program simplyintegrates equations 3.37-3.40 once, using the kob, and b values provided. However, theprogram allows any one of the generated concentration vs. time data pairs to be displayedgraphically on the screen; in the case of [Et2SO] vs. t, the experimentally derived data set2) a set of initial238will be displayed along with the theoretical curve. Also, the program provides theopportunity of saving the theoretical [Et2SO] vs. t data set, for later inclusion in agraphical 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(), YPOCOMMON SHARED KOBS, PSI, Et2SDOCLSDIM XP(200), YP(10, 200)NVAR = 4DIM YSTART(NVAR)DIM YCOPY(NVAR)INPUT "What is the initial time in seconds?", X1INPUT "What is the final time in seconds?", X2INPUT "[A] (INIT)?", YSTART(1)INPUT "[B] (INIT)?", YSTART(2)INPUT "[Et2SO] (INIT)?", YSTART(3)INPUT "[Et2S] (INIT)?", YSTART(4)FOR K = 1 TO NVARYCOPY(K) = YSTART(K)NEXT KPRINT "Input a filename containing raw data for comparison"INPUT DUM$OPEN DUM$ FOR INPUT AS #1LINE INPUT #1, DUM$INPUT #1, NPTDIM XDAT(NPT), YDAT(NPT), SIG(NPT)LINE INPUT #1, DUM$LINE INPUT #1, DUM$FOR I = 1 TO NPTINPUT #1, XDAT(I), YDAT(I), SIG(I)NEXT IDOCALL RKPLOT(YSTARTO, YCOPYO, Xl, X2, XDATO, YDATO, SIG(), NPT,239NVAR)PRINT "Do you want to do further analysis on this data set (y/n)?"INPUT DUM$IF DUM$ = "n" THEN EXIT DOLOOPPRINT "Any other data you wish to analyse (y/n)?"INPUT DUM$IF DUM$ = "n" THEN ENDERASE XP, YP, XDAT, YDAT, SIG, YSTART, YCOPYCLOSE #1LOOPENDSUB 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) / Et2SDYDX(4) = -DYDX(3)END SUBSUB RKPLOT (YSTARTO, YCOPYO, Xl, X2, XDATO, YDATO, SIGO, NPT,NVAR)DODOINPUT "Estimate kobs", KOBSINPUT "Estimate PSI", PSIEt2S = YSTART(4)EPS = .0001INPUT "Estimate the required stepsize", H1HMIN = 0!KMAX = 200DXSAV = (X2 - Xl) / (X2 - X1)CALL ODEINT(YSTARTO, NVAR, Xl, X2, EPS, H1, HMIN, NOK, NBAD,DUM, RKQC)PRINT "Successful steps:^"; NOKPRINT "Bad steps:^"; NBADPRINT "Stored intermediate values:"; KOUNTPRINT "Press return to continue"INPUT DUM$PRINT "^t^[A]^[B]^[Et2S0]^[Et2S]^,,FOR I = 1 TO KOUNT240PRINT USING "####.# "; XP(I);PRINT USING "#.####"' "; YP(1, I); YP(2, I); YP(3, I); YP(4, I)NEXT IFOR K = 1 TO NVARYSTART(K) = YCOPY(K)NEXT KPRINT "Do you wish to try another value of kobs (y/n)?"INPUT FLAG$IF FLAG$ = "n" THEN EXIT DOLOOPPRINT "Do you wish to see a plot of the data (y/n)?"INPUT FLAG$DOIF FLAG$ = "n" THEN EXIT DOPRINT "Which variable? (Input as a number 1-4)"INPUT VAR#DIM YTHEOR(KOUNT)FOR I = 1 TO KOUNTYTHEOR(I) = YP(VAR#, I)NEXT ICALL PLOT(XDATO, YDATO, XP(), YTHEOR(), NPT, KOUNT, SIG())SCREEN 0PRINT "Do you wish to save the calculated data set (y/n)?"INPUT FLAG$IF FLAG$ = "y" THENINPUT "Document to be saved:", DUM$OPEN DUM$ FOR OUTPUT AS #2FOR I = 1 TO KOUNTWRITE #2, XP(I), YTHEOR(I)NEXT ICLOSE #2END IFPRINT "Do you wish to try another variable? (y/n)"INPUT FLAG$ERASE YTHEORLOOPPRINT "Do you wish to plot another value of kobs (y/n)?"INPUT FLAG$IF FLAG$ = "n" THEN EXIT DOLOOPEND SUBThe subprogram PLOT was the same one used in the program UNFIT describedearlier.241The following modules were incorporated, directly and without any modification,from "Numerical Recipes In Basic" into the program:ODEINT, RKQC, RK4 (Chapter 15).The (t, [Et2SO], cr[Ekso) experimental data file should be in the same format as thatrequired by the ONEDMIN program.242APPENDIX 2RESULTS OF STOPPED-FLOWEXPERIMENTSA2.1 Experiments Carried Out Using Light of 400.5 nm WavelengthThe two tables that follow give the numerical values of the parameters a t , (3 1 'y i , usedto obtain the data points in figures 3.15 and 3.16. Following each table are the relativeabsorbance vs. time raw data plots (corrected for a non-level baseline; see section A2.3) towhich the equationA = al + flie-(yit)was fitted, to obtain each set of a t , fi t , 7 1 values. For each experiment, the relativeabsorbance change was monitored over a period of 100 ms; the first four points of everyexperiment appear to be within the dead time of the instrument, and were neglected in thefit. The initial concentration of Ru(OEP)(Et2SO)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% dilutionin the stopped-flow reaction chamber).243A2.1.1 Experiments Carried Out Using a Constant [Et 2SO] of 1.18 ± 0.03 mMRelative uncertainty in [Et2S] 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 48.2A2.1.1.2 1.19x10 -0.050 0.142 48.3A2.1.1.3 2.97x10-4 -0.024 0.277 55.0A2.1.1.4 5.93x104 -0.152 0.392 67.4A2.1.1.5 7.42x10 -0.123 0.434 72.6A2.1.1.6 1.48x10-3 -0.171 0.529 88.1A2.1.1.7 1.85x10-3 -0.154 0.558 92.3A2.1.1.8 3.71x10-3 -0.148 0.607 108A2.1.1.9 9.27x10-3 -0.153 0.633 123A2.1.1.10 1.85x10-2 -0.169 0.633 130A2.1.1.11 3.71x10-2 -0.174 0.636 134A2.1.1.12 5.56x102 -0.179 0.644 133A2.1.1.13 0.111 -0.176 0.639 137A2.1.1.14 0.231 -0.176 0.643 139■0.01—, 0.05 -z0,2 0.03 -0cI) 0.01 -0.04^0.05^0.06Time (s)0.07 0.090.08 0.100.02 0.030.01^0.02 0.03^0.04^0.05(s)0.06Time (s)Time (s)0.08 0.09 0 . 10A2. 0.09 0.102450.200.16 -G 0.12 -0.08 -0L.,,n 0.04 -¢0.00 -45.-0.04 -a)-0.08 --0.12 -A2A.1.4-0A6 ^0.00 0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08^0.09^0.10Time (s)0.28 -0.22 -V0g 0.16 -.02 0.10 -A0.04- 0.02-0.08 -A2.1.1.5-0.14 ^0.00■^1^1^1^10.05^0.06^0.07^0.08^0.09Time (s)0.01^0.02^0.03^0.04 0.100.28 -c 0.20 -c.., 0.12 -v)0.04--0.12 -A2. ^0.00I^I^I^I^r^r0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08^0.09Time (s)i.1)) 0.28 -00)0.20-L.0rn0.12 -a)0.04 -cocd-0.04 --0.12 -A2.1.1.9-0.202460.380.30 -cu0.22 -to.oc.u) 0.14 -0.06 -Z-0.02-0.10 --0.18 ^0.00^0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08Time (s) 0.09^0.100.38 -0) 0.30 -2 0.22 -00.14-V.-> 0.06 -7:5'17) -0.02-0.10 -A2A.L80.10-0.18 ^0.0070.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08^0.09Time (s)0.00^0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08^0.09^0.10Time (s)2470 440.36-m0.28 -^ A2.¢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 0.10Time (s)0.440.36 -,c.), 0.28 -cis0.20 -0L.,(,)0.12 -a)0.04air713 --0.12 -A2.1.1.11 -0.20 --0.00 0.01^0.02 0.03^0.04^0.05^0.06^0.07^0.08^0.09 0.10Time (s)0.440.36z)  0.28 -0as-a 0.20 -00.12 -ar0.04Tuc4-0.04 --0.12 -A2.1.1.12-0.200.00I^ I^ I^ I^ I^ I0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08^0.09Time (s)0.102480.440.36 -1.,41) 0.28 -a. 0.20-042 0.120.04 -mTuco-0.04 --0.12 -A2.1.1.13-0.20 - ,^I^I^I^I^I^i^I0.00^0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08Time (s)0.440.360.09^0.1004) 0.28 -^ A2. 0.12 -a)0.04 -co-0.04 --0.12 --0.20 ,^1^,^I^I^I^I^I^I0.00^0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08^0.09^0.10Time (s)249A2.1.2 Experiments Carried Out Using a Constant [Et2SO] of 17.7 ± 0.2 mMRelative uncertainty in [Et2S] for each experiment ....- 1-2%.400 data points were collected in the 0-100 ms time range.Graph # [Et2S] (M) cri 01 71 (s4)A2.1.2.1 5.93x104 -0.034 0.057 39.2A2.1.2.2 7.42x10 -0.023 0.069 38.3A2.1.2.3 1.48x10-3 -0.049 0.121 42.3A2.1.2.4 1.85x10-3 -0.079 0.143 43.1A2.1.2.5 3.71x10-3 -0.097 0.232 51.6A2.1.2.6 9.27x10-3 -0.128 0.403 64.7A2.1.2.7 1.86x10-2 -0.088 0.539 82.7A2.1.2.8 3.71x10-2 -0.188 0.597 93.6A2.1.2.9 5.57x10-2 -0.176 0.617 103A2.1.2.10 0.111 -0.179 0.654 113A2.1.2.11 0.232 -0.198 0.677 122A2.1.2.12 0.464 -0.178 0.662 1260.01 0.02 0.03 0.04^0.05^0.06Time (s)2500 .010F. 0.00 -0COI-0.01 -d-0.03 -0.04^0.05^0.06Time (s)0.01 0.030.02 0.08 0.08 0.09 0.100.05 ^0.04 -0.03 -tQ 0.02-0A0.01cis0.007.)s:4-0.01-0.02 -- -0A 0.0300.01 -a)0.01^0.02^0.03^0.04^0.05^0.06Time (s)-0.03 --0.050.00 0.080.07 0.100.092514.)U0.02 -i.ct2 0.00" ) -0.02-0.04 --0.08 ^0.00^0.01^0.02^0.03^0.04^0.05^0.06Time (s)0.07^0.08^0.09 -A2.1.2.6U0.14 -ca0.08a) 0.02-a-)-0.04-0.10 --0.16 ,^I^I^I^I0.00^0.01^0.02^0.03^0.04^0.05^0.06Time (s)0.07 0.08 0.09 0.10C.)16 0.06tel0.02--0.06 --0.10 ^0.00^0.01^0.02^0.03^0.04^0.05^0.06Time (s)0.07 0.08 0.09 0.100.440.38a) 0.32 -0C0.26 -A0.20 -Aa) 0.14ccs 0.08 -T.)C4 0.02 --0.04 -252A2.1.2.7-0.10^ 4~••■•■■•^0.00^0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08^0.09Time (s)0.100.400.30 -00.20L00.10 -a)0.00 --0.10 -A2.1.2.8-0.20 ^0.00I^I^I^I^I^ I^I0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08^0.09^0.10Time (s)0.400.30 -000.2000.10 -a)z 0.00 --0.10 -A2.1.2.9Inwp■mmi...1111.10.^-0.20 1^^, 1^ ,^,^,0.00^0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08^0.09Time (s)0.100.38 -a.)c)• 0.28 -as• 0.18 -ma) 0.08 -73-0.02rx-0.12A2.1.2.12 - 0.22   2530.40 -0.30 -0.20  -0.10 -0.00 -- 0.10 -A2.1.2.10- 0.200.00 0.01 0.02^0.03^0.04^0.05^0.06Time (s)0.07 0.08 0.09 0.100.44 -0.34 -a)UC 0.24 -msc.0.14 -cn>a) 0.04 -eses17)-0.06 -- 0.16 -A2.1.2.11- 0.26 ^0.00^0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08^0.09^0.10Time (s)0.00^0.01^0.02^0.03^0.04^0.05^0.06^0.07^0.08^0.09^0.10Time (s)254A2.2 Experiments Carried Out Using Light of 402.8 nm WavelengthThe table that follows gives the numerical values of the parameters a2 , 02 72 , used toobtain the data points in figure 3.18. Following the table are the relative absorbance vs. timeraw data plots (corrected for a non-level baseline; see section A2.3) to which the equationA = a2 + 132e-(72t)was fitted, to obtain each set of a2 , 132, 72 values. For each experiment, the relativeabsorbance change was monitored over a period of 100 s. The initial concentration ofRu(OEP)(Et2SO)2 in each case was (3.44 + 0.07)x10-6 M.255A2.2.1 Experiments Carried Out Using a Constant [Et 2SO] of 1.18 ± 0.03 mMRelative uncertainty in [Et2S] 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 0.47aA2.2.1.2 1.85x10' 0.0073 0.0404 0.251A2.2.1.3 3.71x10-3 -0.059 0.0870 0.183A2.2.1.4 9.27x10-3 -0.093 0.181 0.104A2.2.1.5 1.86x10-2 -0.127 0.289 0.0706A2.2.1.6 3.71x10-2 -0.086 0.391 0.0549A2.2.1.7 5.56x10-2 -0.139 0.441 0.0489A2.2.1.8 0.111 -0.180 0.513 0.0432A2.2.1.9 0.231 -0.185 0.556 0.0414a) The calculated uncertainites in these values are about 10%; for the remaining 02 and 'Y2values, the calculated uncertainties were about 1 %.0.00^40.00^60.00^100.00Time (s)0.01 -a)roO-.0-ra—0.03 -ro—0.05 -- 0.070.00 60.00^100.00256 0.04A2.2.1.10^ab^008°6 6800^00o B$4,^a, .00 0 6,O 0 276^°^a?•^0^0c :a. O.^%0 0  0 o TO o *0^00,^o°% o o^ 059 %o  tr.%^0.,0 ^?moo OS 9^*('V • 6"---51 0 ,L"--°----U, 0°^'0^°^ °°<,^op. .° CO^ 0 o00 ^° '4 ^:ofto^00.030.00^20.00^40.00 60.00^80.00 100.00Time (s)Time (s)-0.120.00 20.00 100.0040.00^60.00 80.002570.080g 0.03 -04:1d -0.02 -Tuc4 -0.07 -0.15 -0.10 -A2.2.1.5Aco• 0.05 -c.0• 0.00-a)0 -0.05 -a-0.10 -16.1■4•11amelowileMINIIIMMONERONWIMINO)10A2.2.1.6•11Time (s)-0.150.00^20.00^40.00^60.00^80.00^100.00Time (s)0.300.25 -a)o 0.20 -aro0.15 -o)0.10 -N• 0.05 -aC4 0.00 --0.05 --0.10 ^0.00 20.00 40.00^60.00 80.00 100.00Time (s)0.00 20.00 40.00^60.00 80.00 100.0040.00^60.00Time (s)80.00 100.000.30 -a)0.20 -m0.G1 0.10  -ce)a)0.00 -Vrxco- 0.10 -- 0.200.300.25 -U0.15 -s.C/• 0.10 --tt• 0.05 -0.00 -73- . 0 5 --0.10 -2580.20 - A2.2.1.7- 0.15 ^0.00 20.00^40.00^60.00^80.00^100.00Time (s)Time (s)A2.3 Blank Experiments0.04259Blank -A0.020.01 -431bOIS.t.Ob 6f/t45,6%C'Z'Dgbc.001%0.00 -0.01 0.02 0.03-^0.05^0.06Time (s)0.07^0.08^0.09 0.10Blank --0.01 -•^ °^44,444SN493107094: s..^e^40t9 40^° ste<4et9°- 4e,Ake1111%°,84'9'^°% otoi0.00 --0.020.00 0.01^0.02^0.03 0.04^0.05^0.06 0. 07 0. 08 0.09 0.10Time (s)260APPENDIX 3RESULTS OF OXYGEN UPTAKEEXPERIMENTSA3.1 First Data SetThe three tables that follow give the numerical values of the data points shown infigures 3.23 and 3.25. Following each table are the [Et2SO] vs. time raw data plots whichgave rise to each data point in figures 3.23 and 3.25.261A3.1.1 [Ru], Dependence Studies[PhCOOH] = 24.4 + 0.1 mM[02] = 7.63 ± 0.07 mM[Et2S] = 0.742 + 0.006 MShaking rate = 164 + 10 cycles/minSolution volume = 10.0 + 0.1 mLRelative uncertainty in [Ru] o -.- 1%Graph #^[Ru]. (M)^kobsx106^x2^ QA3.1.1.1 2.55x105 1.26 8.0 0.34A3.1.1.2 5.10x10-5 2.26 19 0.071A3.1.1.3 1.02x10-4 3.41 17 0.11A3.1.1.4 2.04x10-4 4.48 6.2 0.90A3.1.1.5 2.43x10-4 4.68 11 0.29A3.1.1.6 4.08x104 5.72 10 0.30A3.1.1.7 6.15x10 6.42 36 2x104A3.1.1.8 8.37x104 7.91 25 0.014A3.1.1.9 1.04x10-3 8.14 34 3x104A3.1.1.10 1.21x10-3 8.38 33 9x102620.0000.04 ^0.03 —F, 0.02 —c\t...,43,_.0.01 —0.00060002000 6000t (s)263t (s)t (s)2000^ 4000^ 6000t (s)00 07 -0.06 -0.05 -m-E 0.04 -E';'^0.03 -0.02 -0.01 -0.002640.07 ^0.06 -0.05 -0.04-C."cnj'2 0.03 -C40.02 -0.01 -0.00A3.1.1.92000^ 4000^ 6000t (s)2650.070.06 -0.05 ---i'0.04 -0cn\'7 0.03 -w0.02 -0.01 -0.000 2000 4000t (s)6000266A3.1.2 [PhCOOH] Dependence Studies[Ru]. = 0.408 + 0.004 mM[02] = 7.63 ± 0.07 mM[Et2S] = 0.742 + 0.006 MShaking rate = 164 + 10 cycles/minSolution volume = 10.0 + 0.1 mLRelative uncertainty in [PhCOOH] = 0.5-1 %Graph #^[PhCOOH]^kobsx 106^x2^Q(M)A3.1.2.1 8.35x104 1.24 14 0.30A3.1.2.2 1.25x10-3 1.25 16 0.15A3.1.2.3 2.09x10-3 1.55 25 0.020A3.1.2.4 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 3.5x104A3.1.2.7 1.75x10-2 4.98 30 1.8x10'A3.1.2.8 2.11x10-2 5.16 2.2 1.0A3.1.2.9 2.44x10-2 5.72 9.5 0.30267600040000.040.03 -0.01 -0.00 ^0 2000t (s)t (s)2684000 60000.050.04 -i 0.03 -0U)N-1-J41 0.02 -0.01 -0.00 ^ ■0 2000t (s)t (s)269t (s)A3.1.3 [02] Dependence Studies[Ru]. = 0.408 ± 0.004 mM[PhCOOH] = 24.4 + 0.1 mM270[Et2S] = 0.742 + 0.006 MShaking rate = 164 + 10 cycles/minSolution volume = 10.0 + 0.1 mLRelative uncertainty in [02] --. 1%Graph # [02] (M) kthsx 1 06 x2 QA3.1.3.1 1.76x10-3 1.72 3.5 0.98A3.1.3.2 2.18x10-3 1.71 2.2 0.99A3.1.3.3 2.65x10-3 2.69 3.6 0.96A3.1.3.4 3.64x10-3 3.26 15 0.17A3.1.3.5 4.90x10-3 4.05 7.2 0.78A3.1.3.6 5.13x10-3 4.10 6.1 0.87A3.1.3.7 6.32x10-3 4.82 9.9 0.45A3.1.3.8 7.63x 10 3 5.16 9.5 0.30A3.1.3.9 8.44x10-3 5.93 16 0.192710.020 0 0 1cnC\0.00t (s)t (s)0.030 2000 4000 6000t (s)0.04 -0.03 -0.002720^2000^ 4000^ 6000t (s)0.00040002000 6000t (s)2000 4000 60000 04 -0.03 -7:70.02 -0.01 -0.0000.05 ^0.04 -0.01 -t (s)273274A3.2 Second Data SetThe two tables that follow give the numerical values of the data points shown infigures 3.24 and 3.25. Following each table are the [Et2S0] vs. time raw data plots whichgave rise to each data point in figures 3.24 and 3.25.A3.2.1 [Ru]. Dependence Studies[PhCOOH] = 24.4 + 0.1 mM[02] = 7.63 + 0.07 mM[Et2S] = 0.742 + 0.006 MShaking rate = 164 + 10 cycles/minSolution volume = 10.0 + 0.1 mLRelative uncertainty in [Ru] o .--- 1%Graph # [Ru]a (M) k03x106 X2 QA3.2.1.1 2.53x10-5 1.23 9.7 0.72A3.2.1.2 5.06x10' 1.71 8.2 0.88A3.2.1.3 1.01x10 1.86 14 0.18A3.2.1.4 1.01x10 2.29 15 0.45A3.2.1.5 2.02x10" 3.23 7.9 0.95A3.2.1.6 2.28x104 3.18 29 0.023A3.2.1.7 4.05x104 3.79 6.6 0.95A3.2.1.8 1.18x10-3 4.80 125 02752760.050.04 -0.01 -0.00080001^ 12000^4000 6000t (s)2770.05 -0.04 -0.01 -0.00 I^ r^ i0^ 2000 4000 6000t (s)8000278A3.2.2 [PhCOOH] Dependence Studies[Ru] o = 0.202 + 0.002 mM[02] = 7.63 + 0.07 mM[Et2S] = 0.742 + 0.006 MShaking rate = 164 + 10 cycles/minSolution volume = 10.0 + 0.1 mLRelative uncertainty in [PhCOOH] ...-- 0.5-1 %Graph # [PhCOOH](M)kobsx1 06 x2 QA3.2.2.1 1.21x10-3 0.786 2.9 0.99A3.2.2.2 2.31x10-3 1.18 9.6 0.39A3.2.2.3 4.59x10-3 1.71 6.7 0.88A3.2.2.4 4.99x10-3 1.58 40 1.6x104A3.2.2.5 1.03x10-2 2.38 4.2 0.95A3.2.2.6 1.50x10-2 2.55 0.89 1.0A3.2.2.7 2.44x10-2 3.23 7.9 0.95A3.2.2.8 4.79x10-2 3.20 21 0.100 2000 4000^6000t (s)2791^ i4000 6000t (s)1E4CIDN2800 030.02 -N0.01 -0.00t ( s )0^ 2000^ 4000^ 6000t (s)2810.04 ^0.03 —c:7 0.02 —cvi;.10.010.00080002000^ 4000^ 6000t (s)282A3.3 Additional Data SetsThe two tables that follow give the numerical values of the data points for someexperiments not discussed in the body of the thesis. The first gives the results of a series ofexperiments in which the reaction vessel shaking rate was varied from one experiment to thenext. The second table lists the results of a series of experiments in which the volume of thereaction solution was varied from one experiment to the next. Following each table are the[Et2SO] 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[Et2S] = 0.742 + 0.006 MSolution volume = 10.0 + 0.1 mLRelative uncertainty in the shaking rate = 5-8%Graph # ShakingRatekthsx106 x2 QA3.3.1.1 133 3.04x10' 11.8 0.62A3.3.1.2 164 3.23x10-6 7.9 0.95A3.3.1.3 186 2.61x10' 22 0.102830.04 ^0.03 -5.) 0.02 -N0.01 -0.0000.040.03 -0.02 -N0.01 -0.0000.04 ^0.03 -2000^ 4000^ 6000t (s)2000 4000t (s)6000A3.3.1.3A3.3.1.2mo 0.02 -N0.01 -0.000 2000 4000t (s)6000284A3.3.2 Dependence of the Reaction Rates on the Volume of the Reaction Mixture[Ru],, = 0.408 ± 0.004 mM[02] = 7.63 ± 0.07 mM[PhCOOH] = 24.4 ± 0.1 mM[Et2S] = 0.742 ± 0.006 MShaking rate = 164 ± 10 cycles/minRelative uncertainty in the solution volume .-- 0.5-2%Graph #^Solution^kobsx10°^x2^QVolume(mL)A3.3.2.1 10.0 8.14 34 3.5x104A3.3.2.2 5.00 8.64 3.8 0.97A3.3.2.3 2.00 13.3 14 0.334000 6000' 0.04 -0V)Nalj0.02 -0.000 2000t (s)60000.020.000^ 2000^ 4000t (s)0.08 -0.07 ^0.06 -0.05 -0.04 -0U)0.03 -c.40.02 -0.01 -0.002850^2000^4000^ 6000t (s)0.06 -A3.3.2.2


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