, whereas the physical domain of integration is only from cp = 0 + ir. Thus it Is correct to compute induced shift ratios for any given A, but one should not compare absolute shifts computed from different choices for A. - 134 -Finally, the possibility of rapid random jumps between n equally likely values of may be simulated by use of the periodic weight function, [5] P()d = (l\/TT)cos2I(n\/2)((J) - y)]d)d = a6(<|\u00bb - ) + b6((j) - <|) ) + . ..+f6(4> - )d , where a,b,...,f represent the probability of finding the complex with $-value $ t respectively. Numerical integration (when necessary) was carried out by low-order Gauss-Legendre quadrature (i.e., 6, 8, or 10 point) and in most cases checked against higher order formulas to verify its validity. The Appendix contains a complete listing of the computer programs used in the analysis of complex conformation according to the above models. Only the programs for completely free rotation and that for a rigidly locked complex are listed. The programs used with a Gaussian weight factor are similar to that for free rotation,requiring only a change in weight function from Eq. [4]. - 135 -Results and Discussion Determinations of molecular geometry from chemical shift ratios appear to be best illustrated by contour plots of the type shown in Figs. 23-28. The contours are simply paths of constant normalized variance (\"R-value\", agreement factor) between observed and calculated shift ratios, as a function of possible positions of the lanthanide-donor atom distance (R) , the angle (\u00a32) between the europium-donor bond and the bond between atom #2 and the donor atom, and the azimuthal angle () shown in Fig. 21A. A small normalized variance (< 0.04) thus indicates very good agreement between observed and calculated shift ratios. The first substrate considered was the monofunctional donor, l,2:5,6-di-0_-isopropylidene-a-D-glucofuranose 1. Me. O \u2014 C H 2 M e ' i D Me * Only those protons directly bonded to the rigid furanose ring were Rigid in the sense that the lsopropylldene ring substituent prevents the furanose ring from adopting a l l but a few possible conformers in the pseudorotation cycle. For the purpose of this present study, a single rigid conformer has been assumed. - 136 -used to derive the complex geometry. The co-ordinates for these protons can be accurately defined whereas use of the other protons would necessitate a much more detailed analysis which allowed for internal rotation within the substrate itself. This particular molecule was chosen to represent the model where there was unlikely to be any rotation about the C^-donor atom bond as a result of the intramolecular steric hinderance. This was only an intuitive assumption based on visual inspection of a Dreiding model of JL and will be tested by comparing the results from a l l three models for internal rotation. Table 13 lists the values of the shift ratios which were used to determine the geometry of the furanose ring. These ratios are calculated from the appropriate A -values listed in Table 12, Chapter II. The stoichiometry for this complex can be accurately determined to be 1:1. Several attempts were made to f i t the observed shift ratios to those calculated, with the assumption that there was no internal rotation about the C^-donor atom bond, for several reasonable conformations of the furanose ring. All conformations tested had bond lengths and bond angles in accord with X-ray and neutron diffraction data for related 86 furanose ring systems. A number of different values for the dihedral angles, which were estimated from X-ray data and n.m.r. coupling constant data, were tested (e.g. the near zero coupling for H-2, H-3 is indicative (Karplus) of a H C C H dihedral angle near 90\u00b0). - 137 -Table 13. Induced chemical shift ratios for association of four substrates with lanthanide n.m.r. shift reagents. Substrate A -ratios J3 Shift Reagent Solvent Aniline, 16 o\/m=4.79 o\/p=4.00 Eu(dpm)3 CDC13 Pyridine, 17 o\/m=3.05 o\/p=3.22 Eu(dpm)3 CDC13 1,2:5,6-di-O-isopropyl'-. H-3\/H-2=2. 59 idene-a-D-glucofuranose, . ~ lc H-3\/H-1-3.52 H-3\/H-4=1.82 Eu(dpm)3 CDC13 5-hydroxy-l,2,3,4,7,7- H-5\/H-6(exo)=1.40 hexachloronorborn-2-ene, lib H-5\/H-6(endo)=2.90 Eu(fod). CC1, Shift ratios were determined from bound chemical shifts which were obtained from plots of [S]c versus (1\/6), as explained in Chapter II. For 16, 17, and 1, binding was unequivocally shown to be 1:1. For binding of 11_ to Eu(fod)3, the binding was too strong to measure, and the listed shift ratios correspond to the induced shifts for an [L]0\/[S] ratio of 0.3. The shift ratios for 11 are in good agreement with those in ref. 44 for the unsubstituted alcohol. The H-5 proton was not used in the analysis because of the possibility of internal rotation about the C-4 - C-5 bond which would complicate the analysis. - 138 -The conformation which finally allowed for a successful geometric f i t to be obtained has bond lengths, bond angles, and dihedral angles as shown in Table 14. This conformation is signified as from the pseudo-3 rotation cycle and differs only very slightly from the conformer arrived at from high resolution n.m.r. studies. It should be emphasized that, although a l l likely conformations were investigated, this method does not test whether the conformation used is the best possible one, only that this conformation is preferred over other proposed conformations. The data in Table 14 are then input to the program COORD which produces a set of cartesian co-ordinates for the atoms shown with oxygen at the origin. These cartesian co-ordinates for the protons, H-l, H-2, H-3 and H-4 as well as the corresponding shift ratios (Table 13) are then put into the appropriate geometry program. Fig. 23A,B shows the contours which are obtained, under the assumption that there is no internal rotation about the carbon-donor bond. Two features are evident. First, for some choices of , there are no \"good\" fits (i.e. having normalized variance, R, smaller than 0.04). Second, among the range of ^-values for which good fits are obtained, some -values lead to unreasonably short europium-oxygen bond distances. Based on these results, i f JL is rigid with respect to internal rotation about the carbon-donor bond, then the most o likely position of the europium is R = 2.2 A, Q = 1 1 4\u00b0, and = 1 1 6\u00b0. It is significant that these parameters appear to correspond with an The numbering scheme here is as shown on the structure, i t is not numbered in the conventional manner. For the purpose of these geometry calculations, atom #1 is always the donor atom. - 139 -Table 14. Bond, distances, bond angles and dihedral angles used to calculate a set of cartesian co-ordinates from COORD for 1,2:5,6-di-O-isopropylidene-a-D-glucofuranose. Numbering scheme is as shown below with atom #1, the oxygen of the hydroxyl group. 1-2 Bond Distance = 1.40 A; 2-3 Bond Distance = 1.523 A; 123 Bond Angle = 115.7\u00b0. Atoms Bond Distances(A) Bond Angle(deg.) Dihedral Angle (deg.) A B C D CD BCD ABCD 12 3 4 2 3 4 5 3 4 5 6 12 3 8 3 4 5 9 4 5 6 10 5 6 2 7 1.450 1.427 1.523 1.083 1.083 1.083 1.083 105.8 109.3 105.8 109.0 109.0 109.0 109.0 105.0 15.0 345.0 210.0 225.0 240.0 150.0 Dihedral angle of CD relative to AB, measured clockwise along the direction B to C. - 140 -~1 I 1 1 1 1 1 1 1\u2014 1.84 2.00 2.16 2.32 2.48 R(&) \"1 1 1 1 1 I 1 1 1 1 1 1.84 2.00 2.16 2.32 2.48 R(&) ure 23A. Contours of normalized variance (\"R-value\" agreement factor) between observed and calculated induced chemical shift ratios as a function of possible positions of the lanthanide atom relative to the donor atom of the substrate for jL. It has been assumed that there is no internal rotation about the bond from carbon to donor oxygen. - 141 -ure 23B. Contours of normalized variance (\"R-value\" agreement factor) between observed and calculated induced chemical shift ratios as a function of possible positions of the lanfhanide atom relative to the donor atom of the substrate for 1_, It has been assumed that there is no internal rotation about the bond from carbon to donor oxygen. - 142 -orientation of Eu(dpm)^:1 which has the metal in a sterically favourable position. The position of the metal is also in accord with the observed shift for H-5 being greater than H-3. Fig. 24A,B shows the effect of varying degrees of internal motion on the agreement between observed and calculated ratios for 1^. Beginning (as in Fig. 23) with a static molecular frame, we now allow for a Gaussian distribution of (((-values, centered at the most likely (f>-value of 116\u00b0 , with a root-mean-square width of either 14\u00b0 (\"narrow Gaussian\" in Fig. 24A) or 40\u00b0 (\"wide Gaussian\" in Fig. 24B). It is clear that this greater latitude in internal rotational position produces less reasonable f i t s , with respect both to agreement with experiment (normalized variance) and also intuition (too-short values for Eu-0 bond distance). In fact, the contour plot for the assumption of completely free internal rotation about the carbon-donor bond (Fig. 24B) shows that free rotation is simply not possible in this complex. Thus we have demonstrated that the l:Eu(dpm)3 complex is relatively rigid and thus the geometry of the complex may be determined with confidence. The above model (that of a rigid complex) can hardly be expected to hold for a substrate such as aniline, 3-6_, where there should be l i t t l e preference for the shift reagent to be rigidly attached at any one value of (j>. This presumption is reasonable in view of the rather large bond distance for europium-nitrogen bonds. X-ray determinations o of this distance put i t in the range of ca. 2.65 A. Table 13 lists the values of the shift ratios which were used to - 143 -gure 24A. Contours of normalized variance as a function of lanthanide position for 1. For the \"static plot\", there is no internal rotation about the carbon-donor bond. For the \"narrow Gaussian\"., -values are first weighted by the factor, (A\/ \/rr) exp I-A2 Q) 2] d, and then integrated over al l $ (with A = \/W) b efore comparing observed with calculated shift ratios (see Theory). - 144 -R(S) Figure 24B. Contours of normalized variance as a function of lanthanide ' position for 3^. For the \"wide Gaussian\", ^-values are first weighted by the factor, (A\/Vrr) exp[-A2(<)>-<)>0)2]d, and then integrated over a l l (with A = 1) before comparing observed with calculated shift ratios (see Theory). For the \"free rotation\" plot, <}>-values are averaged over a l l -values of 0\u00b0 and 180\u00b0. - 149 -the vicinity of 4> = 6 6\u00b0 , and the f i t at = 90\u00b0 was very poor. This o leads to the conclusion that the complex is rigid, with R = 2.55 A, \u00a31 = 12 4\u00b0, and (}) = 6 6\u00b0 . The problem with this conclusion is that the experiment shows a single resonance for both o and m protons on opposite sides of the aromatic ring! Thus, the symmetry of aniline must be maintained in the complexed state. Here then is a case where the agreement with experimental shift ratios for three protons is excellent, the Eu-N bond distance which results is reasonable, but the \"determined\" geometry is wrong. Since the \"static\" f i t s at -values of 0\u00b0 and 18 0\u00b0, although in agreement with experimental shift ratios, are unreasonable from a point of view of steric hindrance which would be a maximum in this position. Thus in conclusion, only the free rotation model produces chemically meaningful results for the aniline:Eu(dpm) complex. So far a distinct chemically meaningful f i t has been obtained after treating each molecule with several possible models for internal ft When a l l five protons were included in a static model at the (only possible) -value giving an excellent \"static\" f i t at Figure 27. Contours of normalized variance as a function of lanthanide position for 11. Internal rotation about the C-0 bond is assumed to be completely free (unhindered). - 154 -2 . 2 2 . 4 2 . 6 2 . 8 3 . 0 R ( & ) G A U S S I A N eft = 2 3 6 \u00b0 2 . 2 2 . 4 2 . 6 2 . 8 3 . 0 R ( A ) Figure 28. Contours of normalized variance as a function of lanthanide position for _11. Top: no internal rotation about C-0 bond. Middle: Gaussian distribution in -<*)0) 2]dcf) with A = 1, centered at = 236\u00b0. Bottom: Gaussian of the same width, but centered at 0 = 248\u00b0. - 155 -equally good fits could be obtained; so that virtually no information about R and can be derived from the experiment. For substrate 11, the bound conformation probably exhibits some internal rotation, with the Eu more often opposed than adjacent to the apical chlorines. This result would seem to have quite a severe consequence on the results reported elsewhere for related compounds where a claim to a single unique static f i t has been made. The.results for the substituted bicycloheptenol, JA, provide one final point of interest. Although the method of fitting shift ratios from the best number of individual conformations is not determinative as to Eu-0 distance or even Eu-O-C angle, there is a dependence on (see Fig. 28) which shows for the present compound a definite minimum at ca. 2 5 0\u00b0, the orientation expected for the exo-hydroxyl position on the grounds of minimal intramolecular steric interaction. In confirmation of this claim, comparison of shift ratios for _11 with 44 those for the exo- and endo-bicycloheptanol shows that the shift ratios for _11 match nicely with those for exo-bicycloheptanol, but do not match the rather different values for endo-bicycloheptanol. This assignment of configuration at C-2 (numbering scheme as shown in Table 16) could not have been made on the basis of coupling constant data. For the analysis of complex conformation in the systems discussed up to now, i t has been necessary to first define a particular (most reasonable) configuration of the substrate whose co-ordinates were then calculated using the computer program COORD. These cartesian co-ordinates and the observed shift ratios were then put into the appropriate geometry program for internal rotation and several metal co-ordination schemes were examined. - 156 -The molecule, pyridine, 17_, appeared at first sight to present a rather well defined rigid system on which to perform a geometry calculation according to the above procedure. Bond lengths and 87a bond angles were available from a number of X-ray and microwave studies^k'C and could be used to generate a set of cartesian co-ordinates using the computer program COORD. The directional lone pair of the nitrogen donor group left l i t t l e doubt as to which model for internal rotation was most likely - namely a rigidly locked complex where only internal rotation about the Eu-N bond was possible, which would not affect either r or 6 in Eq. II]. In addition, X-ray data for Eu(dpm)3(py)2 were available which reported an average Eu-N bond ; o distance of 2.65 A. Even though this value was for an eight co-ordinate lanthanide complex whereas our present analysis was for a seven co-ordinate lanthanide complex, (vide infra), there seemed l i t t l e doubt as to what the value for the Eu-N bond distance determined from the present system of analysis could be. Table 13 lists the values of the shift ratios which were used to determine the geometry of the pyridine:Eu(dpm)^ complex. These ratios were calculated from the appropriate A -values listed in Table 12, B Chapter II. The binding constant was in the range where accurate determination was possible and thus the stoichiometry can be accurately determined to be 1:1. Using the computer program for a rigidly locked complex, several attempts were made to f i t the observed shift ratios with those calculated for several reasonable conformations of the * 71 Selbin . has reported the preparation and properties of the stable Eu(dpm)\u201e(py) complex and other seven co-ordinate lanthanide complexes. - 157 -pyridine ring. No_ fits were obtained over any reasonable Eu-N bond 0 distance (2.2 to 3.5 A); even when the geometry of the pyridine ring was defined using X-ray data for transition metal complexes with AAA 8 8 pyridine. The inability to f i t the observed shift ratios was particularly disconcerting, especially when one considers the well-defined nature of this system. There are three possibilities which may contribute to the above result. They are, in order of ascending importance: (i) the principle magnetic axis may be other than along the Eu-N bond, (ii) the possibility of a contact contribution to the induced shift -if present, this would be most probable for the o-protons , and, ( i i i ) the geometry of the substrate bound in the complex may be different than that for the free substrate in solution. We s t i l l allow for rapid internal rotation about the Eu-N bond which, as discussed in the theory, ensures effective axial symmetry. Also, i t can hardly be assumed at this juncture that a contact contribution is present in the induced shift, even in view of the aromatic character of this 89 system. This brings us to the third possibility about which we are unable to make any definite comments and which i f correct, would inhibit the success of the present system of analysis unless fortuitously the required conformation for pyridine was chosen. A specific computer program was written to attempt to resolve the problems encountered with pyridine. This program will not be listed and although written specifically for pyridine, i t would be applicable, in a slightly modified form, for any planar system. * It should be emphasized, however, that for geometry determinations, protons with small r and wide angle 6 will be the most sensitive to configurational changes. - 158 -The only molecular dimension which is input to this program is \u00b0 88 the C-3 - H-3 bond distance, which is taken as 1.02 A. In addition, a minimum value for the Eu - H-3 distance, and as before, the observed shift ratios are input. It is assumed (and not unexpectedly), therefore, that the Eu atom lies in the plane of the pyridine ring and along the axis. The computer then varies the Eu - H-3 distance in increments o of 0.06 A to a maximum possible value which would correspond to a c 2 Eu-N bond distance of 3.5 A. At each increment the quantity, [(3cos 6^ -3 l ) \/1^ ] * is calculated for H-l and H-2 and the ratio compared with the observed (Table 13). The output of this program is a series of plots to which one manually fits a structure of pyridine, assuming C-C bond o o lengths of 1.40 A and C-H bond distances between 1.02 and 1.08 A. The geometry of pyridine which resulted from such a treatment is shown below. - 159 -The significant difference in this structure with any tried in the previous treatment, is the position of the o-protons which are displaced towards the point of complexation with the shift reagent. This result may reflect a possible stabilized structure with these hydrogens participating in H-bonding with the (dpm) ligand of the lanthanide complex. Although this change in geometry of the pyridine ring is not large, i t was enough to prevent any fits being obtained for the several proposed geometries when treated in the regular manner. o o The resulting Eu-N bond distance, R = 2.67 A+ 0.1 A (fi = 118\u00b0 +2\u00b0) is in excellent agreement with the reported X-ray value for R o of 2.65 A. The method of analysis used above can be applied, in principle, to molecules which are not planar but the display of the results would best be viewed in 3-D, using graphical displays of the sort used by 2 2b R.J.P. Williams. No attempt was made to develop our technique to this degree. The results for pyridine provide one final point of interest. We have stated that one of the distinct aspects necessary, before any attempt can be made to determine molecular geometry, is the experimental determination of reliable values for the bound chemical shifts, for each proton involved. Other less precise ways for determining this parameter were discussed in Chapter II, but i t was not until the data Using this calculated geometry, a set of cartesian co-ordinates was generated and these plus observed shift ratios were put into the regular geometry program for the static case (Appendix C). An excellent f i t was obtained (expected) thus confirming the above treatment. - 160 -for pyridine had been collected and reduced as a plot of IS ]Q versus (1\/6) that the vital importance of this particular aspect became apparent. In Table 17 are listed the A -values for the protons of pyridine a 90 91 determined by ourselves and those from twoother independent groups. ' It can be seen that the values for this parameter differ significantly from one group to another. It is particularly interesting that the 90 limiting shifts of Group I (for {S] of 0.5 M) are larger than the 91 limiting shifts from Group II (for [S]q of 0.15 M). This is consistent with a probable dependence of the slope of a plot of 6 versus 44 IL] \/IS] (method used to determine A^-values by groups I and II ) on IS] as discussed in Chapter II. This dependence of the slope on IS3 suggests that the binding constant is small enough to affect the bound shift determinations and in fact we have measured the binding constant and found i t to be 76 liter mole 1 and thus from our data can accurately determine the stoichiometry to be 1:1. Of particular significance in Table 17 is the variation in shift ratios among Ihe various measurements. Other than ourselves, only Group II has made use of the shift ratios to determine the complex geometry and thus the geometry of the pyridine ring. Using the ratios as shown, they found the best agreement with calculated shift ratios o was with a Eu-N bond distance of 4.0 + .4 A. This calculated value for the Eu-N bond distance was based on measurements taken from a molecular model and not from a detailed computer analysis. However, the results from a detailed computer analysis using the ratios reported by Group II were even less encouraging. The best \" f i t s \" between calculated and - 161 -Table 17. Induced chemical shift data for association of pyridine with Eu(dpm)3 : three independent determinations. Group - Pyridine A -Values,^ p. . p.m. A_-Ratios 15 Solvent 0 28.7 o\/m = 2.90 CDC13 I3 m 9.9 o\/p = 3.12 P 9.2 o 25.9 o\/m = 2.88 CC1. 4 IIb m 9.0 o\/p = 3.16 P 8.2 o 23.8 o\/m = 3.05 CDC13 IIIC m 7.8 o\/p = 3.22 P 7.4 a b From ref. 90. From ref. 91. Our own work. For (a) and (b), this parameter was determined by linearly extrapolating [L]Q [L]o a plot of 6 versus , to a f -. ratio of 1.0 (see ref. 44). LbJo LbJo For (c), the A^-values were obtained from a plot of [S] versus (1\/6) ij o as explained in Chapter II. - 162 -experimental shift ratios were obtained with a Eu-N bond distance of o ca. 3.5 A and with the Eu some 40\u00b0 out of the plane of the ring. It is d i f f i c u l t to find any chemical evidence which would substantiate either of these values and there is obviously l i t t l e interest in doing so in view of the excellent and chemically meaningful results presented previously. This chapter has provided a number of models for derivation of molecular conformation in the presence of internal rotational motion by use of lanthanide shift reagents. A l l four molecules studied were ri g i d except at the point of attachment to the lanthanide and so provided the simplest type of problem for the analysis. The results show that determination of molecular geometry is straightforward and gives chemically reasonable results only in cases where: (i) the entire complex is relatively rigid as with _1 and J_7_ and, ( i i ) there i s completely free internal rotation as with _16. For _16_ and 1_1 i t was shown that the presence of internal rotational motion, even when present only at the site of attachment to the lanthanide, can lead to either erroneous or un-determinative results respectively for attempts to find the \"best\" single (static) conformation of the bound complex. These results clearly demonstrate the d i f f i c u l t i e s , even for r i g i d substrates, which may be encountered when attempting to determine the bound conformations of substrates bound to lanthanide shift reagents. Thus, there is need for considerable caution (and a variety of motional models) in any attempt to treat polyfunctional and non-rigid substrates or both. - 163 -GENERAL CONCLUSIONS The foregoing investigations warrant a few general conclusions to bring the work presented in this thesis into perspective with present and certainly the future application of lanthanide shift reagents to organic n.m.r. spectroscopy. More specific conclusions have been presented within the Chapters and will not be reiterated The primary theme and objective throughout this thesis has been to develop the necessary chemical and theoretical understanding for the ultimate use of lanthanide shift reagents to the determination of molecular conformation in solution. As a whole, therefore, this thesis represents the successful progression of our understanding and evaluation of the applications of lanthanide shift reagents to organic n.m.r. spectroscopy. We have described numerous experimental optimizations and in addition have presented a detailed theoretical analysis of the lanthanide-substrate equilibrium which has permitted, for the first time, the chemical aspects of this equilibrium to be fully understood. In addition, this latter understanding has provided the basis on which rests present and future applications of lanthanide shift reagents to the determination of molecular structure. In Chapter III, we have successfully described in detail this particular aspect, as it pertains to a series of rigid organic substrates. We have demonstrated that geometry determinations are possible but not simple and considerable caution is advised in future applications to polyfunctional and\/or non-13 rigid systems. In this connection, the use of C shift ratios in - 164 -conjunction with shift ratios, the use of broadening reagents, chemical derivatization and more detailed computer programing will assist in overcoming some of the problems which will be encountered when attempting to determine solution conformations of these more complex molecules. In conclusion, i t is the belief of this author that lanthanide shift reagents have become and will continue to be a routine and integral part of organic n.m.r. spectroscopy. - 165 -EXPERIMENTAL The Experimental for this thesis has been divided into two parts. A. Techniques and experimental methods, synthesis and\/or purification of compounds, for Chapter I. B. Techniques and experimental methods, synthesis and\/or purification of compounds not previously described in part A, for Chapters II and III. The reason for this partitioning of the Experimental is two-1 13 fold. (i) All H and C n.m.r. measurements discussed in Chapter I were made with a modified Varian HA-100 spectrometer, operating in the frequency-swept mode with a probe temperature of 32.0\u00b0C. Whereas, al l n.m.r. measurements reported in Chapters II and III were made on a Varian XL-100 spectrometer, operating in the frequency-swept mode with a probe temperature of 40.0\u00b0C. (ii) In Chapter I, chemical shift changes induced by various Ln(dpm)3 complexes were measured as a function of the change in the concentration of the lanthanide shift reagent. In Chapters II and III on the other hand, the concentration of the lanthanide shift reagent was maintained constant (ca. 0.006 M) and the substrate concentration was varied. - 166 -For both parts A and B, extreme precautions were taken to exclude moisture at a l l stages of the experiments. A. General Methods (a) All n.m.r, measurements were made with a modified Varian HA-100 spectrometer, operating in the frequency-swept mode with a probe temperature of 32.0\u00b0C. For experiments using the europium, thulium, and gadolinium reagents, 5_, 6_, 9_, deuterochlorof orm solutions were used, with internal tetramethylsilane (TMS) as the reference signal for the field-frequency lock. Experiments with the praseodymium reagent, 7_> were made with chloroform solutions and the chloroform resonance was used to provide a lock signal; some TMS was added to provide a chemical shift reference. (b) An account of the modifications necessary for the measurement 1 13 2 13 of H-( C) INDOR spectra has been described elsewhere. C chemical shifts are reported in p.p.m. relative to TMS. (c) When applicable, analyses of the n.m.r. spectra were made with a modified version of the LA0CN3 program and an I.B.M. 360-67 computer. (d) Melting points were performed on a Thomas-Hoover capillary m.p. apparatus and are corrected for thermometer error. (e) Deuterochloroform (99.8%) from Merck Sharp and Dohme, Montreal, was stored over Linde molecular sieve (4A), which had been * Modifications were performed by R.B. Malcolm of the Department of Chemistry, U.B.C. - 167 -heated In an oven at 110\u00b0C for 24 hours, to both dry i t and remove traces of acid which decompose the lanthanide complex. Carbon tetrachloride (A.R. Grade) was distilled and stored over NaOH pellets prior to use. Ethanol-free chloroform was obtained by standing A.R. Grade chloroform over granular, self-indicating silica gel. (f) A sample of the lanthanide reagent was vacuum sublimed immediately prior to an experiment. The lanthanide was dissolved in either deuterochloroform, chloroform, or carbon tetrachloride (ca. 0.04 g\/ml). Aliquots of this standard solution were added via a 0.10 ml syringe to a solution of the carbohydrate (ca. 0.18 g\/ml). After purification and\/or sublimation, a l l further handling of the lanthanide reagent and carbohydrate was carried out in a glove bag flushed with dry nitrogen. (g) The preparation of a l l solutions was conducted under dry nitrogen in a glove bag using apparatus that had been baked at 110\u00b0C immediately prior to use. Synthesis and Purification of Compounds (a) The carbohydrate derivatives, _1, 2^, and 3_, were stock samples which were recrystallized twice from CHCl^-hexane 1:2 v\/v. Crystals were then dried in vacuum at the temperature of boiling methylene chloride for 12-20 hours, immediately prior to use. M.p.s were determined as follows: 1 103-105\u00b0C 2 73.5-74.8\u00b0C 3 57.5-58.5\u00b0C - 168 -The n.m.r. parameters were in entire accord with the assigned structures. (b) 2,2-Dimethyl-l-propanol (neo-pentanol), 8^ , was purchased from Matheson Coleman and Bell and was purified by distillation from calcium hydride. The material had a b.p. of 114\u00b0C. (c) Tris (dipivalomethanato) europium (III), 5_, was prepared from ft europium oxide (99.99%) following the method of Eisentraut and 16 Sievers. Yield was greater than 95%. The material from the reaction was stored in a vacuum desiccator containing phosphorus pentoxide. A small sample was vacuum sublimed at 140\u00b0C at 0.1 mm Hg or lower immediately prior to an experiment. In the above synthesis, the europium oxide is dissolved in an excess of 15.4 M HNO^ to prepare the hydrated europium(III) nitrate - Eu(NO^)-xH^O. Care must be taken at this stage to ensure all excess HNO^ is removed with the help of a steam bath or preferably using a rotary evaporator. Any excess acid remaining at this step will cause a decomposition of the final product - Eu(dpm)3. The thulium reagent, 6_, the praseodymium reagent, ]_, and tie gadolinium reagent, 9_ were prepared by the same method, ft starting with the corresponding nitrate salt. 2,2,6,6-Tetramethyl-3,5-heptanedione (dpm) was purchased from Eastman Organic Chemicals. (d) 3-0-Acetyl-l,2:5,6-di-O-isopropylidene-a-D-allofuranose, k_, was prepared from 1,2:5,6-di-O-isopropylidene-a-D-allofuranose, 2, as 92 described in the literature, using excess acetic anhydride in dry pyridine. Product was recrystallized twice from ethanol-water mixture and then vacuum dried for 48 hours at the b.p. of methylene chloride. Obtained from Alfa Inorganics, Inc. - 1 6 9 -The yield was approximately 70% and had a m.p. of 73.5-74\u00b0C. (e) 5-Hydroxy-l,2,3,4,7,7-hexachloronorborn-2-ene, 11, was prepared from the hydrolysis of the adduct of vinyl acetate with 93 hexachlorocyclopentadiene following the procedure of E.K. Fields. This procedure was deviated from in that the alcohol adduct JUL was extracted from the water with CHCl^ which was subsequently evaporated off under reduced pressure to give a syrup. This was then treated twice with decolourizing charcoal and the resulting crystals recrystallized from n-heptane. Product was further purified by vacuum sublimation immediately prior to use and had a m.p. of 153.5-154.0\u00b0C. B. General Methods (a) All n.m.r. measurements were made with a Varian XL-100 operating in the frequency-swept mode with a probe temperature of 40.0\u00b0C. Tetramethylsilane (TMS) was used as the internal reference signal for the field-frequency lock for the experiments using deuterochloroform, deuterobenzene or carbon tetrachloride as solvents. Experiments with chloroform or benzene solutions used the chloroform resonance or the benzene resonance respectively to provide a lock signal; some TMS was added to provide a chemical shift reference. (b) Deuterobenzene (99.8%) from Merck Sharp and Dohme, Montreal, and benzene (A.R. Grade) were stored over Linde molecular sieve (4A), which had been heated in an oven at 110\u00b0C for 24 hours prior to use. Other solvents were purified and\/or dried as described in part A. - 170 -(c) The preparation of a l l solutions was conducted under dry nitrogen in a glove bag using apparatus that had been baked at 110\u00b0C immediately prior to use. (d) All plots of the experimental data were made with a Hewlett-Packard Calculator (model 9100B) and a Hewlett-Packard Calculator Plotter (model 9125A). (e) Method 1. Constant [S] , Varying [L] Q i 2 o A series of standard solutions, each containing a known amount of the substrate (ca. 0.6, 0.2, 0.08, 0.04 M) was prepared. One particular standard solution was then selected and 1.0 ml of this solution was used to dissolve a known quantity of the lanthanide reagent (ca. 0.015 g, 0.02 M of Ln(dpm>3; ca. 0.190 g, 0.175 M of Ln(fod)3). The spectrum of this mixture then gave the maximum shift. Further spectra were run after each successive addition of a 0.10 ml aliquot of the standard substrate solution. In each case the observed shift decreased. (f) Method 2. Constant [L] , Varying [ S] Q J. a 0 The lanthanide reagent (ca. 0.042 g, 0.012 M of Ln(dpm)3; ca. 0.070 g, 0.012 M of Eu(fod)3) was dissolved in 4.8 ml of solvent and 0.2 ml tetramethylsilane in a 5.0 ml volumetric flask. The substrate was separately dissolved in 5.0 ml of the same solvent. Aliquots (0.50 ml) of the lanthanide solution were then added to each of a series of 5-10 graduated 1.0 ml flasks. To each of these flasks was now added varying amounts of the stock solution of substrate; e.g., vial 1, 0.5 ml; vial 2, 0.4 ml; etc. The content of each flask was then made up to 1.0 ml by further addition of solvent. Each solution - 171 -was then placed in a separate n.m.r. tube which was capped and stored in a thermostatted water bath prior to measurement. (g) Appendix B, C and D contain a listing of the computer programs used to determine the complex conformation. Details, for the understanding and possible use of these programs, are provided in the form of comment statements which have been appropriately situated throughout the programs. A brief discussion of the necessary input data for each of these programs will be presented at the beginning of each Appendix. Synthesis and Purification of Compounds (a) Tris(2,2-dimethyl-6,6,7,7,8,8,8-heptafluoro-3,5-octanedionato)-europium(III), 13, was prepared from europium oxide (99.99%) following 94 the method of Springer et a l . Yield was greater than 95%. The complex was recrystalllzed twice from methylene chloride and was thereafter stored in a vacuum desiccator containing phosphorus pentoxide. This is important because i t has been reported\"^ that the anhydrous fod complex absorbs one mol equiv of water when allowed to stand unprotected in a moist atmosphere. All further manipulations were carried out in a glove bag which had been flushed several times with dry nitrogen. (b) n-Propylamine, 12, from Eastman Organic Chemicals was purified by distillation from KOH pellets into a sealed receiver also containing KOH pellets. The material had a b.p. of 49.0\u00b0C. (c) Bicyclo[2.2.1]heptan-2-one(norcamphor), 14, from Aldrich Chemical Company was vacuum distilled at 120\u00b0C into a receiver contain-ing KOH pellets. The material had a m.p. of 94-95\u00b0C. - 172 -(d) n-Propanol, 15_, was purified by distillation from calcium hydride. The material had a b.p. of 98.7\u00b0C. (e) Aniline (reagent grade), 16, from British Drug Houses Ltd. 95 was purified as follows. 10.0 ml was distilled from a small amount of zinc dust and a 4.0 ml fraction collected from the middle: b.p. pf 183\u00b0C. (f) Pyridine, 17_, was purified by refluxing over KOH pellets for ca. 1 hour and then distilling into a sealed receiver also containing KOH pellets. The material had a b.p. of 114.2\u00b0C. (g) 2,2-Dimethyl-3-butanone, 18, from Aldrich Chemical Company was purified by distillation from MgSO^ into a sealed receiver also containing MgSO^ . The material had a b.p. of 106-107\u00b0C. (h) The carbohydrate derivatives, 19_, 2(), and 21^, existed as pure stock samples in the laboratory. Crystals were dried in vacuum at the temperature of boiling methylene chloride for 12-20 hours, immediately prior to use. The n.m.r. parameters were in entire accord with the assigned structures. (i) Acenaphthenone, 22_, was a stock sample which was vacuum sublimed at 85\u00b0C at 0.3 mm Hg immediately prior to use: m.p. of 118-119.5\u00b0C. (i) The dimethylaminocyclophosphonitriles, 23_ to _27, were obtained from N.L. Paddock and J.N. Wingfield, Department of Chemistry, U.B.C. The stable complex which was obtained by reacting Eu(fod)^ (1.0 mole equivalents) with 1.0 moles of NgPgtNMe^g was prepared by the following method. 0.255 grams of Eu(fod)\u201e was added to a solution of 0.292 grams N P (NMe )1 f i in anhydrous carbon tetrachloride. The - 173 -flask was sealed and the solution stirred at room temperature for 80 hours. Solvent was removed by vacuum distillation to give a white solid which melted to a paste at 606C in a water bath. A l l attempts to purify the product by recrystallization and by eluting the product down an alumina column failed, giving only the pure nonamer, m.p. 232-234\u00b0C. The n.m.r. spectrum shown in Fig. 19C was thus recorded for the crude product. - 174 -APPENDIX A Calculation of and 6^ from R, Q, and . Referring to Figures 21A and 21B, i t is convenient to deal with the following quantities: r^ = distance vector between lanthanide atom and i'th proton of substrate; R = lanthanide-donor atom distance vector; R' = lanthanide - x-axis distance vector; ~r^ = distance vector from donor atom (origin) and i'th proton Ithis vector is not shown in the figure]; 0^ = angle between R and r^; ft = angle between R and the x-axis; <|> = angle between R' and y-axis (a measure of the angle of internal rotation of the lanthanide-donor bond axis about the bond axis from the donor atom to atom #2). 2 It is expedient to compute cos 0^ directly from the dot product of R _^ and r^: 2 V * 2 Eq [1] cos 0. = {-\u2014=\u2014\u2014} |r.||R| One can now write, 3cos20 - 1 3(r-t)2 ~ \\t\\2 |r |2 Eq 12] ^ 3 - A 2 = \u2014 | r\u00b1|3 | t |2 \\r.\\5 but r. = R - r.' , l i ' - 175 -and r ' = x. i + y. j + z. k, where x., y., z. are i 1 7i J 1 l J\u00b1 l co-ordinates of the i'th proton, R = |R|cosfi i + |R|sinfi coscj) j + |R|sinfi sin<(> k. Substitution into Eq. [2] followed by some rearrangement gives the final result: 3cos26i - 1 2|R|2 - 4|R|Q + 3Q2 - \\P\u00b1\\2 P ] 1^13 = ( | r l | 2 + | R | 2 - 2|f|Q)5\/2 12 2 ^ 2 2 where r. = x. + y. + z. , 1 l1 l \u2022'i l ' and Q = x^ cosfi + y^ sinfi costf) + z^ sinfi sin<|>, - 176 -APPENDIX B This computer program, COORD, written in Fortran was used to calculate the atomic cartesian co-ordinates for molecules given bond lengths, bond angles and dihedral angles. These values must be obtained from X-ray or microwave studies of the molecule or related molecules. Comment statements, appropriately spaced throughout the program explain the operational procedures of the program and the format required to read in the necessary data. The substrate atoms are numbered consecutively and i f the calculated cartesian co-ordinates are required for input data to the geometry programs (Appendices C and D), atom #1 must be assigned to the donor atom. - 177 -C THIS PROGRAM AS STANDS MILL TAKE DP TO 24 ATOMS PER MOLECULE C C C C THIS PROGRAMME CALCULATES THE COORDINATES IH A 3 DIMENSIONAL C SPACE GIVEN THE BOND LENGTHS, BOND ANGLES, AND DIHEDRAL C THIS IS AN ADAPTATION OP PROGRAM COORD WBITTEN ORIGINALLY BY DBWAR C THE FIRST CARD HAS THE NAME OF THE MOLECULE (OB OTHER HEADING) C IS THE FIRST 36 COLUMNS C C C NOAT IS THE NUMBER OF ATOMS. B12 IS THE EOND DISTANCE FROM ATOM C 1 TO ATOM 2, R23 IS THE BOND DISTANCE FROM ATOM 2 TO 3 , ETC. TH123 C IS THE 123 BOND ANGLE C C C C C c DIMENSION X (24) , Y (24) , Z (21) , R (21,24) , NAME (9) CALL PLOTS C IKQ IS THE NUMBER OF MOLECULES FOR WHICH THE PROGRAM HILL CALCULATE C THE COORDINATES FOR IKQ=1 DO 1111 LOVEU = 1,IKQ 45 READ 900 , (NAME (I) ,1=1,9) 900 FORMAT ( 9A4) WRITE(6,950) (NAME(I),1= 1 ,9) 950 FORMAT(1H1,9A4) REAL(5,901)NOAT, R12;H23,TH123 901 FORMAT( I2,2F7.4,F14.7) WRITE(6,952)R12,R23rTH123 ,NOAT 952 FORMAT (7H R12 = F7.4, 10H R23 = F7.4,10H TH123 = ,1PE10.3,5X, 117HNUMBER OF ATOMS= ,12) 3 THETA=TH123*3.1415926536\/180. CCOS=COS (THETA) SSIN=SIN (THETA) 4 DO 51 1=1,3 X (I)=0.0 Y (I)=0.0 51 Z (1)^0.0 X (2) = R12 X(3)=R12~R23*CC0S Y(3)=R23*SSIN DO 5 I = 4, NOAT 5 X(I) - 10000.0 WRITE(6,953) 953 FORMAT (88H0 NA NB NC ND ILAZY RCD 1 THBCD PHABCD\/) C C C ATOHS NA, NB, NC, HAVE KNOWN COORDINATES AND ARE NOT COLLINEAR. C THBCD IS THE BCD BOND ANGLE IN DEGREES AND PHABCD IS THE DIHEDRAL C ANGLE OF CD RELATIVE TO AB, MEASURED CLOCKWISE ALONG THE DIRECTION C B TO C. ILAZY ALLOWS AUTOMATIC CALCULATION OF ANGLES IN NORMAL C TETRAHEDRAL AND PLANAR SYSTEMS. 2LAZY = 0,1,2,3,4,5 ; TETRAHEERAL C WITH DIHEDRAL ANGLES OF 0,60*120,180,240, AND 310 DEGREES C RESPECTIVELY. ILAZY= 6,7 ; PLANAR CIS, TRANS RESPECTIVELY. - 178 -C ILAZY=8 ; ATOMS B,C,D ARE COLLINEAR. ILAZY = 9 ; DATA HILL SUPPLY C ANGLES. C DO 52 I=4,NOAT READ(5,902) NA,NB,NC,ND, ILAZY,RCD,THBCD,PHABCD 902 FORMAT(412,2X*I1,F7.4, 2F14.7 ) C C CBECK TO SEE THAT COORDINATES OF ATOM NA,NB, AND NC HAVE BEEN C CALCULATED C 7 IF (X(NA) \u2022 X(!SB) \u2022 X (NC) - 7000.0) 8, 50, 50 8 WRITB(6,954)NA,NB,NC,ND, ILAZY,RCE,THBCD,PHABCD 954 FORMAT (3X,12, 3X,12,3X,12,3X,12, 18X,11,7X,F7.4,8X,E14.7,4X, 1E14.7) IF (ILAZY - 8)\/ 79, 78, 79 78 RBC=SQRT ( (X (NC)-X (HE) ) **2* (Y (NC)-Y (NB)) **2+ (Z (NC)-Z (NB) ) **2) X(ND) = X(NC) + (X(NC) - X (NB)) *RCD\/RBC Y(ND) = Y(NQ \u2022 (Y(NC) - Y (NB) ) *RCD\/RBC Z(ND) = Z(NC) + (Z(8C) - Z (NB)) *RCD\/RBC GO TO 52 C C C MOVE ATOM HC TO THE ORIGIN C 79 XA = X (NA) - X (NC) YA = Y (NA) - Y (NC) ZA = Z (NA) - Z (NC) XB = X (NB) - X (NC) YB = Y(NB)| - Y(NC) ZB = Z (NB) - Z (NC) C C ROTATE ABOUT Z AXIS TO MAKE YB=0, XB IS POSITIVE. IF XYB IS TOO C SMALL, ROTATE FIRST 90 DEGREES ABOUT Y AXIS C XYB=SQRT(XB**2+YB**2) K = 1 IF (XYB - 0.1) 9, 10, 10 9 K = 0 XPA = ZA ZPA = -Xli XA = XPA ZA = ZPA XPE = ZB ZPE = -XI3 XB =XPB ZB = ZPB XYB=SQRir (XB*\u00bb2*YB**2) 10 COSTH = XB\/XYB SINTH = YB\/XYB XPA - XA*C0STH \u2022 YA*SINTH YPA = YA*COSTH - XA*SINTH C C ROTATE ABOUT Y AXIS TO MAKR ZB VANISH C 11 RBC=SQHT (XB**2 + YB**2 + ZB**2) SINPH = ZB\/RBC COSPH=SQRT (1.-SINPH**2) XQA = XP A*COSPH \u2022 ZA*SINPH ZQA = ZA*COSPH - XPA*SINPH - 179 -C ROTATE ABOUT X AXIS TO MAKE ZA=0 , YA POSITIVE 12 YZA=SQRT (YPA**2+ZQA**2) COSKH = YPA\/YZA SINKH = ZQA\/YZA IF (ILAZY - 1) 13, 14, 15 13 COSD = 1.0 SIND = 0 C C COORDINATE A, (XQA,YZA,0); B,(RBC,0,0); C, (0,0,0); NONE ARE NEGATIVE C COORDINATES OF C NOW CALCULATED IN NEW FRAME C GO TO 21 14 COSD = 0.5 SINE=0.5*SQRT(3.) GO TO 21 15 IF (ILAZY - 3) 16, 17, 18 16 COSD = -0.5 SIND=0.5*SQRT(3.) GO TO 21 17 COSD = -1.0 SIND = 0 GO TO 21 18 IF (ILAZY - 5) 19, 20, 22 19 COSD = -0.5 SIND=-0.5*SQRT (3.) GO TO 21 20 COSD = 0.5 SINE=-0.5*SQRT(3.) 21 COSA = -1.0\/3.0 SINA=(2.\/3.)*SQRT(2.) GO TO 2 9 22 IF (ILAZY - 7) 23, 24, 26 23 COSD = 1.0 SINE = 0 GO TO 25 24 COSE = -1.0 SIND = 0 25 COSA = -0.5 SINA=0.5*SQRT (3.) GO TO 29 26 IF (ILAZY - 9) 27, 28, 28 27 CONTINUE GO TO 29 28 THBCD=THECE*3.1415926536\/180o PHABCD=PHABCD*3.1415926536\/180. SINA=SIN (THBCD) COSA=COS(THBCD) SINE=SIN (PHABCD) COSE=COS (PHABCD) 29 CONTINUE XD = RCD*COSA YD = BCD*SINA*COSE ZD = BCD*SINA*SIND C C TRANSFORM COORDINATES OF D BACK TO ORIGINAL SYSTEM C 30 YPD = YD*COSKH - 2D*SINKH ZPD = ZD*COSKH \u2022 YD*SINKH XPD = XD*COSPH - ZPD*SINPH ZQD = ZPE*COSPH \u2022 XE*SINPH - 180 -31 32 52 C C XQD = XPD*COSTH - YPD*SINTH YQD = YPD*COSTH + XPD*SINTH IF (K - 1) 31, 32, 31 XBD = -ZQC ZRD = XQD XQD = XRD ZQD = ZRD X (NC) Y (ND) Z(NE) = XQD = YQD = ZQD X (NC) Y (NC) Z (NC) CONTINUE 69 PRINT 69 FORMAT(\/\/\/ 94H THE ABOVE FEW LINES ARE JUST A REHASH OF THE INPU 1T INFO. IN CASE ONE LACKS SELF-CONFIDENCE \/ 32H NA=ATOM A 2, N1 = ATOM 1 , ETC. \/ 96H COORDINATES FOR ATOMS A,B, AND C ARE 3 KNOWN, EACH CARD THEN SOVBS FOR THE POSITION OF ATOM D \/ 4 95H RCD= DISTANCE FROM ATOM C TO ATOM D : THBCD= ANGLE DEFINED 5 BY ATOMS B,C,D; C EEING THE APEX: \/ 50HPHABCD= DIHE 6DRAL ANGLE OF THE ABC AND BCD PLANES ) C C 955 956 881 41 88 957 C C C c c C ) X-COORDINATE Y-COORDINAT C C WRITE(6,950) (NAME (I) ,1=1,9 WRITE (6,955) FORMAT (78H0NO. OF ATOM 1E Z-COORDINATE\/) DO 41 1=1,NOAT WRITE (6,956) I, X (I) , Y (I) ,Z (I) FORMAT (1H ,5X,I2,15X,F10.7,11X,F10.7,11X,F10.7) PUNCH 881 , X(I), Y ( I ) , Z(I) FORMAT(3 (1PE10.3)) CONTINUE CO 88 1=1,NOAT DO 88 J=1,NOAT R (I, J)=SQRT ( (X (I)-X (J)) **2+ (Y (I) -Y (J) ) **2* (Z (I) -Z (J) ) **2) WRITE (6,950) (NAME (I) ,1=1,9 ) WHITE (6,957) FORMAT(1H0,21HINTERATOMIC DISTANCES,\/\/) THE NEXT TWENTY OR SO STATEMENTS FORM A PRINT LOOP WHICH DOES NO MORE THAN PRINT OUT THE ELEMENTS OR MATRIX R , THE INTERATOMIC DISTANCES MATRIX. NC= NUMBER OF COLUMNS IN PRINT OUT. PLEASE NOTE FORMAT111 BEFORE BECOMING ORIGINALo LET'S LET NC =10. NC= 10 KK=0 NCM1= NC-1 NICE =0 DO 105 IZ=1,NOAT, NC JOY = IZ+ NCM1 IF(JOY.GT. NOAT) JOY=NOAT THE NEXT STATEMENT MAKES SURE YOU DON'T HAVE A DATA SET STRATIFIED BETWEEN TWO PAGES. (I.E. 52 LINES\/PAGE MAX.) NICE = NICE* NOAT IF(NICE-52) 106,107,107 107 LIKE= 0 NICE = 0 GO TO 108 106 LIKE =1 - 181 -108 CONTINUE IF (LIKE *KK-1) 102,103, 103 101 FORMAT (1H1) 102 PRINT 101 103 PRINT 104 , (MUCK, MUCK=IZ,JOY) 104 FORMAT(1H0,\/10I10) 109 DO 112 IRS=1,NOAT 112 PRINT111, IRS, (R (IRS,ICS) , ICS-IZ,JOY) 111 FORMAT (1H I2,2X,10 (1PE10.3)) 105 CONTINUE C CAII TRAIL (NOAT, X,Y,Z) 1111 CONTINUE GO TO 665 50 WRITE (6,958) 958 FORMAT(1 HO,38HCCORDS.OF 1 REFERENCE ATOM UNAVAILABLE) 665 CONTINUE CALL PLOTND STOP END SUBROUTINE TRAIL (NOAT, X,Y,Z) C C TRAIL PLOTS OUT THE POINTS IN 2: (WITH A 3D FLAVOR) C NOAT IS THE NUMBER OF ATOMS TC BE PLOTTED C X,Y,Z ARE THE COLUMN MATRICES CONTAINING THE ATOMIC COORDINATES C N IS THE NUMBER OF DIMENSIONS X,Y, AND Z ARE GIVEN IN THE MAIN C CAN HANDLE UP TO NOAT =24 C DIMENSION X (24),Y(24),Z (24),ZP (24), YP (24) , HT (24) XMAXI = 0. XMINI = 0. CALL PAT(X, XMAXI, XMINI, NOAT) QP = XMAXI- XMINI DO 79 MP= 1,NOAT ZP(MP) = -X(MP)*0.5 + Z(MP) YP(KP) = -X (HP) *0\u201e5 \u2022 Y(HP) 79 HT (MP) = (X(MP) -XMINI) \/QP *0\u201e56 \u2022 0.14 CALI SCALE (ZP,NOAT, 10., YMIN\u201e DY, 1) CALL SCALE (YP,NOAT, 10., XMIN5 DX, 1) DO 779 MP=1,NOAT ZZZ=MP 779 CALL SYMECL (YP (MP), ZP(HP), HT (MP), 01, 0., -1) CALL PLOT (12. ,0. ,-3) RETURN END SUBROUTINE PAT(X, XMAXI* XMINI,NOAT) C C X IS A VECTOR OF NOAT DIMENSIONS OF WHICH THE LARGEST AND C SMALLEST VALUES ARE TO BE FOUND. N IS THE DIMENSION OF THE TOTAL C RESIDING SPACE OF WHICH NOAT MAY BE ONLY A SUBSPACE C XMINI AND XMAXI WILL EE RETURNEE AS THE MAXIMUM AND MINIMUM VALUES C OF X C DIMENSION X(24) XMAXI = X (1) CO 3 J=2,NOAT IF (XMAXI-X (J)) 2,2,3 2 XMAXI= X(J) - 182 -3 CONTINUE XMINI = X (1) DO 1 J=2,NOAT IF (XMINI-X (J) ) 4,4,5 5 XMINI = X(J) 4 CONTINUE RETURN END - 183 -APPENDIX C This computer program was used to determine complex conformation for a rigidly locked complex (Eq. [3], Chapter III). Input data to this program includes: the i n i t i a l value for the Eu-donor atom bond distance (R) , bond angle (ft), dihedral angle (<})), and the range over which these values are to be varied5 the experimentally observed shift ratios; the cartesian co-ordinates for each atom considered. Numerous comment statements are appropriately spaced throughout the program to assist in explaining the specific computations carried out in this program. - 184 -DIMENSION X ( 2 4 ) , Y ( 2 4 ) , Z (24) , DX (24) , DY (24) , DZ(24) , DIST (24) 1 ,DOT (24) ,SD (6) ,UNCER(6) , RATIO (6) , WT (6) DIMENSION ZZ (24,24) ,THEDAA (24) , RR(24) DIMENSION NAME (6) PI ~ 3.141593 C C THIS PROGRAM IS FOR A RIGIDLY LOCKED COMPLEX C TAKE NOTE OF CO-ORDINATE CONVENTION C READ 700,(NAME(I) , 1=1,6) PRINT 701 , (NAME ( I ) , 1=1,6) 700 FORMAT (6A4) 701 FORMAT(1H 1, 6A4) READ 1, NUMHYD 1 FORMAT (II) C C NUJ = NUMHYD-1 C NUMHYD IS THE NUMBER OF HYDROGENS WHICH SHIFT RATIOS ARE TO BE C CALCULATED THEORETICALLY AND FITTED TO EXPERIMENTAL VALUES C C READ 101, NTHEDA,NPHI, NRAD, BTHEDA, DPHI, DR 101 FORMAT ( 3(12) , 3 (E10.3) ) C C C AIL INPUT ANGLES AND INCREMENTS ARE IN DEGREES C DISTANCES I . E . RINT AND DR ARE IN ANGSTROMS C NTHEDA = NUMBER OF INCREMENTS OF THEDA TO BE CONSIDERED (<21) C NPHI = NUMBER OF INCREMENTS OF PHI TO BE CONSIDERED (<21) C NRAD = NUMBER OF INCREMENTS OF BOND DISTANCES TO BE CONSIDERED C DTHEDA = SIZE OF INCREMENT OF THEDA TO BE CONSIDERED C DPHI = SIZE OF INCREMENT OF PHI TO BE CONSIDERED C DR = SIZE OF INCREMENT OF BOND TO BE CONSIDERED C NOTE: NTHEDA*DTHBDA-1= RANGE CF VALUES OF THEDA SCANNED, SAME FOR C OTHER VALUES C C READ 102, THEDAI, P H I I , RINT 102 FORMAT(3(E10.3)) C C C THESE ARE THE INITIAL VALUES FOR THEDA, PHI AND BOND DISTANCE C RESPECTIVELY C PRINT 337 337 FORMAT(1H1, 9HVARIABLE ,5X13HINITIAL VALUE, 5X21HINCREMENTAL INCRE U S E ,5X21HNUMBER OF INCREMENTS \/) PRINT 338 ,RINT,DR,NRAD,THEDAI,BTHEDA,NTHEDA,PHII ,DPHI, NPHI 338 FORMAT (2X, 9HBOND DIST , 5 X F 5 . 2 , 1 8 X F 5 . 3 , 18X12 \/ 1 1X5HTHEDA ,8XF6 .1 ,2X3HDEG,15XF5 .2 , 3HDEG , 15X13 \/ 2 1X5HPHI , 8 X F 6 . 1 , 2 X 3 H D E G , 1 5 X F 5 \u201e 2 , 3HDEG , 15X13 \/ ) THECAI = THEDAI*PI \/180 . PHII = PHII *P I \/180 . DTHEDA = DTHEDA*PI\/180. DPHI = DPI1I*PI\/180. C PRINT 612 612 FORMAT(\/\/99HSTOP A MOMENT; DO THESE NUMBERS BELOW LOCK AT ALL FAMI - 185 -1LIAB? IF NOT WE HAD BETTER QUIT HERE! ) C C C C C AA = 0.0 C AA IS A PARAMETER TO BE USED LATER ON IN NORMALIZING ERROR MEASURE DO 661 MM=1,NUJ READ 2, RATIO (MM) , UNCER (MM) , WT (MM) AA = RATIO (MM)*RATIO (MM)* WT (MM) * A A PRINT 2, RATIO (MM) , UNCER (MM) ,WT(MM) C WT DEFINES THE WEIGHTS ASSIGNED TO EACH RATIO FOR FINDING THE LEAST C DISTANCE VALUES. N . E . SUM OF THE WEIGHTS = 1. 2 FORMAT (3 ( E10.3)) 661 CONTINUE C C THE RATIOS ARE THE EXPERIMENTALLY DETERMINED SHIFT RATIOS FOR ATOM C ONE \/ATOM 2; ATOM 1 \/ ATOM 3; ATOM 2 \/ ATOM 3 : IF NUMHYD = 3 C IN THAT ORDER * \u00ab \u2022 \u2022 \u00bb \u2022 ? ? ? C C IF NUMHYD = 4 THEN RATIOS ARE 1\/2; 1\/3; 1\/4; 2\/ C UNCER GIVES THE UNCERTAINTIES IN EACH RESPECTIVE SHIFT RATIO. I . E . , C IF THE CALCULATED RATIO IS WITHIN UNCER OF THE EXPERIMENTAL RATIO, C THEN THE POINT WILL WARRANT FURTHER CONSIDERATION C C C C THIS STATEMENT READS IN THE VALUES OF THE X , Y , AND Z CO-ORDINATES C FOR EACH ATOM (MUST BE COMPUTED ELSEWHERE, I . E . COORD ETC.) DO 3 1=1,NUMHYD READ 29,X (I) , Y (I) , Z (I) PRINT 29, X (I) , Y (I) , Z (I) 29 FORMAT(3 ( E10.3)) 3 CONTINUE C C PRINT 333 333 FORMAT (1H1 , 1 X , 1 2HDISTANCE-ANG ,5X,9HTHEDA-DEG ,6X 1,3HPHI ,10X, 7HEPSILON \/ \/ ) C C PHI = FHII DO 23 LP =1,NPHI HI = 180. *PHI \/ P I R = RINT DO 21 LR = 1, NRAD T H E E ft = TliEDAI DO 22 LT=1,NTHEDA HEDA = 180 . * THE DA\/PI XE = R*COS (THEDA) YE = R*SIN (THEDA)* COS (PHI) ZE = R* SIN (THEDA) *SIN (PHI) C NOTE N . B . THE ATOM TO WHICH EU IS \"BONDED\" TO IS ASSUMED TO C HAVE MOLECULAR COORDINATES ( 0 , 0 , 0 ) . BE SURE YOUR DATA POINTS ARE C RELATIVE TO THIS REFERENCE POINT DO 8 L=1,NUMHYD C C C THIS NEXT PORTION GIVES THE POSITION VECTORS TO EACH ATOM WITH - 186 -C VECTORS READ SET AT THE EU ATOM C DX (L) = (XE - X (L) ) DY (L) = (YE - Y (L) ) DZ (L) = (ZE - Z (L) ) C C DIST GIVES THE ABSOLUTE VALUE FOR EACH OF THESE ATOMIC POSITION C VECTORS. C DOT GIVES THE SCALAR PRODUCT OF EACH POSITION VECTOR DOTTED WITH TH C EU-COMPLEX BOND VECTOR. C DIST(L) = SQRT (DX (L) *DX (L) + DY (L) *DY (L) \u2022 D Z ( L ) * D Z ( L ) ) DOT (L) = ( XE *DX(L) + YE *EY (L) + ZE *DZ (L) ) \/ (DIST (L) *R) 8 CONTINUE DO 108 KB=2,NUMHYD SD(KB-1) = (3.*DOT(1 )*DOT(1 ) - 1 . ) *BIST(KB) * * 3 \/ 1 ((DIST(1 ) * * 3 ) * (3.*DOT(KB) *DOT (KB) - 1 . )) SD(KB-1) = SD(KB-1) \u2022 SB 108 CONTINUE EPS = 0. DO 62 IG=1,NUJ 62 EPS = WT(IG) * ( (RATIO (IG) - SD ( IG) ) * *2 ) + EPS EPSQ = SQRT ( EPS\/AA) PRINT 33, R , H E D A , HI , EPSQ 33 FORMAT ( 2X, F 5 . 2 , 10X,F6 .1 , 10XF6.1 , 10X,1PE10.3 ) 67 CONTINUE ZZ (LR,LT) = EPSQ THEEAA(LT) = HECA 22 THEDA = THEDA+ DTHEDA SR (LR) = R 21 R= R+ DR C C C PLOTTING INSERTION C C CALL SCALE ( RR , L 0 , 10 . , XMIN, DX,1) CALL SCALE (THEDAA, I T , 10 . , Y?UN,DY, 1) CALL AXIS( 0 . , 0.,12HBOND DISTo , - 1 0 , 1 0 \u201e , 0 . , XMIN, DX) CALL AXIS( 0 . , 0 . , 10HBOND ANGLE , 10, 1 0 . , 9 0 . , YMIN, DY) CALL NUMBER (2. , 10 .2 , 0 .14 , HI , 0 . , -1) CALL SYMBOL(4. , 10 .2 , 0 .14 , 17HCOMPOUND NAME , 0 . , 17) C PLOT THE CONTOURS CN = 0.02 CALL CNTOUR (RR, LR, THEDAA, L T , Z Z , 24, CN, 3 . , CN ) CN = 0.04 DO 200 1=1,7 CALL CNTOUR(RR, LR, THEDAA, L T , Z Z , 24, CN, 3 . , CN ) 200 CN= CN + 0.04 CALL P L O T ( 1 2 . , 0 . , -3) 23 PHI = PHI + DPHI CALL PLOTND STOP END - 187 -APPENDIX D This computer program, also written in Fortran, was used to determine complex conformation when there is free internal rotation about the carbon-donor atom bond of the complex (Eq. [2], Chapter III). Input data to this program includes: the in i t i a l value for the Eu-donor atom bond distance (R), the bond angle (f2) , and the range over which these parameters are to be varied; the experimentally observed shift ratios; the cartesian co-ordinates for each atom considered. To assist in the use and understanding of this program, several comment statements are appropriately situated throughout the program. - 188 -EXTERNAL C02AVE COMMON X ( 2 4 ) , Y(24) , Z ( 2 4 ) , R, THEDA, N, ETA DIMENSION AVE (24) ,ONCER (10) , RATIO(10) , S D (10) , HT ( 10) DIMENSION ZZ (24,24) ,THEDAA (24) , RR(24) DIMENSION NAME (6) READ 700,(NAME(I) , 1=1,6) PRINT 701 , (NAME (I) , 1=1,6) 700 FORMAT (6A4) 701 FORMAT (1H1, 6A4) C C THIS PROGRAM IS FOR FREE OR ESSENTIALLY FREE INTERNAL ROTATION C BE SORE TO TAKE NOTE OF CO-ORDINATE AND ROTATION CONVENTIONS C PI = 3.141593 C CALL PLOTS READ 1, NOMHYD 1 FORMAT(11) C NUMHYD IS THE NUMBER OF HYDROGENS WHICH SHIFT RATIOS ARE TO BE C CALCULATED THEORETICALLY AND FITTED TO EXPERIMENTAL VALUES NUJ = NUMHYD -1 C READ 101, NTHEDA,NETA, NRAD, DTHEDA, DETA, DR 101 FORMAT ( 3(12) , 3 (E10.3) ) C ALL INPUT ANGLES AND INCREMENTS ARE IN DEGREES C DISTANCES I . E . RINT AND DR ARE IN ANGSTROMS C NTHEDA = NUMBER OF INCREMENTS OF THEDA TO BE CONSIDERED (<21) C NRAD = NUMBER OF INCREMENTS OF BOND DISTANCES TO EE CONSIDERED C DTHEDA = SIZE OF INCREMENT OF THEDA TO BE CONSIDERED C DR SIZE OF INCREMENT OF BOND TO BE CONSIDERED C NOTE: NTHEDA*DTHEDA-1= RANGE OF VALUES OF THEDA SCANNED, SAME FOR C OTHER VALUES C READ 102, THEDAI, ETAI ,RINT C THESE ARE THE INITIAL VALUES FOR THEDA, PHI AND BOND DISTANCE C RESPECTIVELY 102 FORMAT(3(E10.3)) C PRINT 337 337 FORMAT(1H1, 9HVARIABLE ,5X13HINITIAL VALUE, 5X21HINCREMENTAL INCRE 1ASE ,5X21HNUMBER OF INCREMENTS \/) PRINT 338,RINT,DR,NRAD,THEDAI,DTHEDA,NTHEDA 338 FORMAT(2X, 9HBOND DIST , 5 X F 5 . 2 , 1 8 X F 5 . 3 , 18X12 \/ 1 1X5HTHEDA ,8XF6 .1 ,2X3HDEG,15XF5 .2 , 3HDEG , 15X13 \/ ) THEDAI = THEDAI*PI \/180. DTHEDA = DTHEDA*PI\/180. ETAI = ETAI*PI \/180. DETA = DETA*PI \/180 . C PRINT 612 612 FORMAT (\/\/99HSTOP A MOMENT; DO THESE NUMBERS BELOW LOOK AT ALL FAMI 1LIAR? IF NOT WE HAD BETTER QUIT HERE! ) C C C c c R = RINT AA = 0.0 - 189 -C AA IS A PARAMETER TO BE USED LATER ON IN NORMALIZING ERROR MEASURE DO 661 MM=1,NUJ READ 2, RATIO (MM), UNCER(MM),WT(MM) C WT DEFINES THE WEIGHTS ASSIGNED TO EACH RATIO FOR FINDING THE LEAST C DISTANCE VALUES. N . B . SUM OF THE WEIGHTS = 1. AA = RATIO(MM)*RATIO (MM)* WT (MM) \u2022 AA PRINT 2, RATIO (MM) , UNCER (MM) ,WT(MM) 2 FORMAT (3 ( E10.3)) 661 CONTINUE C C THE RATIOS ARE THE EXPERIMENTALLY DETERMINED SHIFT RATIOS FOR ATOM C ONE \/ATOM 2; ATOM 1 \/ ATOM 3; ETC. C IN THAT O R D E R \" \" \" ? ? ? C C IF NUMHYD = 6 THEN RATIOS ARE 1\/2; 1\/3; 1\/4; 1\/5; 1\/6. C UNCER GIVES THE UNCERTAINTIES IN EACH RESPECTIVE SHIFT RATIO I . E . , C IF THE CALCULATED RATIO IS WITHIN UNCER OF THE EXPERIMENTAL RATIO, C THEN THE POINT WILL WARRANT FURTHER CONSIDERATION C C C THIS STATEMENT READS IN THE VALUES OF THE X , Y , AND Z CO-ORDINATES FO C EACH ATOM (MUST BE COMPUTED ELSEWHERE, I . E . COORD ETC.) CO 3 1=1,NUMHYD READ 29,X (I) , Y (I) , Z (I) PRINT 29, X (I) , Y (I) , Z (I) 29 FORMAT (3 ( E10.3)) 3 CONTINUE C C PRINT 333 333 FORMAT (1H1 ,1X,12HDISTANCE-ANG ,5X,9HTHEDA-DEG ,6X 1 , 16X ,7HEPSILON \/ \/ ) C c DO 21 LR = 1, NRAD THEDA = THEDAI DO 22 LT=1,NTHEDA HEDA = 180 . * THEDA\/PI C C C ETA = ETAI DO 23 LN =1,NETA TA= E T A * 1 8 0 . \/ P I C C STEP TO CARRY OUT THE NUMERICAL INTEGRATION C A IS THE LOWER BOUND OF INTEGRATION, B THE UPPER C PLEASE USE NORMALIZED WEIGTING FUNCTIONS W . R . T . PHI DO 72 N=1,NUMHYD A=0. B= 2 . * P I 72 AVE (N) = FGAU08(A,E,C02AVE) \/ (B-A) C 8 POINT GAUSS-LEGENDRE QUADRATURE WAS USED TO CARRY OUT NUMERICAL C INTEGRATION C STANDARD SUBROUTINE U . B . C . C PRINT 73, (AVE(LS) , LS= 1,NUMHYD) 73 FORMAT ( 10 (1X,1PE11 .4 ) ) - 190 -DO 108 KB=2,NUMHYD SD(KB-1) = AVE(1) \/ A V E (KB) 108 CONTINUE EPS = 0. DO 553 IG=1,NUJ EPS = WT (IG) * ( (RATIO (IG) - SD (IG) ) * *2) \u2022 EPS 553 CONTINUE EPSQ = SQRT ( EPS\/AA) PRINT 33, R,HEDA, TA, EPSQ 33 FORMAT ( 2 X , F 5 . 2 , 2 ( 1 0 X , F 6 . 1 ) , 10X,1PE10.3 ) 67 CONTINUE Z Z ( L R , I T ) = EPSQ 23 ETA = ETA+DETA THEDAA(LT) = HEDA 22 THEDA = THEDA* DTHEDA RR(LR) = R 21 R= R+ DR C C C PLOTTING INSERTION C C CALL SCALE{ RR , L R , 1 0 . , XMIN, DX,1) CALL SCALE (THEDAA, L T , 10 . , YMIN,DY, 1) CALL AXIS( 0 . , 0.,10HBOND DIST. , - 1 0 , 1 0 . , 0 . , XMIN, DX) CALL AXIS ( 0 . , 0 . , 10HBOND ANGLE , 10, 10 . , 9 0 . , YMIN, DY) CALL SYMBOLS* . , 10 .2 , 0 . 14 , 17HC0MP0UND NAME , 0 . , 17) C PLOT THE CONTOURS,CNTOUR IS A STANDARD SUBROUTINE AT U . B . C . CN = 0.05 DO 200 1=1,6 CALL CNTOUR(RR, LR, THEDAA, L T , Z Z , 24, CN, 3 . , CN ) 200 CN= CN + 0.05 CALL PLOTND STOP END FUNCTION C02AVE (PHI) COMMON X ( 2 ^ ) , Y ( 2 4 ) , Z ( 2 4 ) \u201e R, THEDA,N, ETA PI = 3. 141593 Q = (R*R + X(N)*X(N) + Y(N)*Y(N) \u2022 Z (N) *Z(N) - 2 . * R * 1 (X (N) *COS (THEDA) \u2022 SIN (THEDA) * (Y (N) *COS (PHI) \u2022 Z (N) *SIN (PHI) ) ) ) C02AVE= ( 3 . * (R-(X (N) * COS (THEDA) \u2022 SIN (THEDA) * ( Y (N) *COS (PHI) 1 + Z ( N ) * SIN (PHI)))) * *2 - Q ) \/ 2 (Q** (2.5) ) C TO DO A GAUSSIAN WEIGHT ABOUT PHI NOUGHT, SIMPLY ADD A GAUSSIAN C WEIGHT FACTOR, EQ(4) , TIMES THE QUANTITY ABOVE RETURN END - 191 -REFERENCES 1. F.A. Bovey. Nuclear magnetic resonance spectroscopy. Academic Press, New York (1969). 2. (a) P.R. Steiner. Ph.D. Thesis. University of British Columbia (1971), and references therein; (b) R. Burton, L.D. Hall and P.R. Steiner, Can. J. Chem. 49, 588 (1971). 3. F.A.L. Anet, J. Amer. Chem. Soc. \u00a34, 1053 (1962). 4. (a) J. Manville. 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