GENERAL DISCUSSION Dr. R. A. More O'Ferrall (University College Dublin) said :The initial formation of a tetrahedral carbanion in the ionisation of nitromethane would seem to imply that the main activating effect of the nitro group is inductive or electrostatic. Why then does hydrogen exchange occur so much more readily than in a tetramethyl-+ ammonium ion?l A (CH&N substituent is unable to conjugate but since it is a positive monopole its inductive effect should be greater than that of the dipolar NO2 group. Prof. F. G. Bordwell (Northwestern University) said The rate of exchange for the tetramethylammonium ion may be much slower than the actual rate of carbanion formation because of internal return. The large kH/kDratios observed for nitro- alkanes indicate that internal return is not a problem in this instance.Furthermore we believe that the effect of the nitro group on the formation of the "essentially pyramidal "nitro carbanion is not purely electrostatic in nature but instead involves conjugation. Even a pyramidal anion should overlap to some degree with the n-system of the nitro group; such overlap should be appreciable in intermediate 2 if as we have suggested some rehydridization and solvent reorganization has occurred in its formation. Dr. W. J. Albery (Oxford University) said First I would like to ernphasise the similarity between the diazo systems discussed earlier and the nitro system i B-+ H -C -NO2$B---H 1 \ 0- W. von E. Doering and A. K. Hoffman J. Amer. Chem. SOC.,1955,77 521.*W. J. Albery A. N. Campbell-Crawford and J. S.Curran J.C.S. Perkin 11 1972 2206. 132 GENERAL DISCUSSION Secondly while we may write a tetrahedral intermediate such as (2) we do not intend to imply that the system moves all the way to (2). If one believes the Marcus theory it may be shown that the most favourable path for reaction is when the thermodynamic driving force for the proton transfer (AG;’ in Marcus terminology and AGO’ in Kreevoy’s notation ’) is equal to zero. Thus in both cases the amount of lone pair development in (2) should be such that the pK of the organic substrate roughly corresponds to the pK of the cataly~t.~ Prof. A. J. Kresge (University of Toronto)said The anomalous Bronsted exponents observed in nitroalkane ionization imply that negative charge builds up on the a-carbon atom in the proton transfer transition state of this reaction and explanation of this unexpected behaviour therefore reduces essentially to justifying the greater negative charge density at this atom in this transition state than in the stable nitronate- ion reaction product.Bordwell’s justification postulates a new reaction intermediate a second anionic species from which the proton has been transferred completely but in which the electron pair left behind has not yet moved to a more stable location. This explanation would seem to have electrons moving more slowly than protons. It is possible however to avoid this difficulty by assuming that complete electroe reorganization requires a completely formed carbon-nitrogen double bond ; in the proton transfer transition state this double bond is only partly formed and a portion of the negative charge generated in the substrate therefore must remain localized on its a-carbon atom.4 This explanation provides a mechanism whereby electron delocalization may lag behind proton transfer in a sin& reaction step and thereby removes the need for inventing a new reaction intermediate.Prof. F. G. Bordwell (Northwestern University) said The conversion of 2 to 3 involves not only “ movement of electrons to a more stable location ” but as pointed out in the paper partial rehybridization (movement of atoms) partial solvent reorganization (movement of molecules) and breaking of the strong BH . . . C-H-bond.Each of these factors is believed to contribute to the activation barrier between 2 and 3. Intermediate 2 is stabilized by solvation forces and strong H-bonding. Prof. F. G. Bordwell (Northwestern University) said Bell pointed out in his lecture that compounds which differ appreciably in structure often do not fall on the same Brijnsted plot. Nitroethane and 1,l-dinitroethane are likely to fall in this category. A study in our laboratory (J. E. Bartmess unpublished results) has shown that for a series of substituted nitroethanes of the type G(CH,),CH2N02 p* = 1.2 for equilibrium acidities in 50 % (vlv) MeOH-H20 (p* E 1.0 estimated for H20). Data of Sitzmann Adolph and Kamlet give p* = 3.60 for equilibrium acidities of a comparable series of 1,1-dinitroethanes G(CH2),CH(N02)2in water.This means that the negative charge in the dinitro anions must be concentrated to a much greater degree on carbon (and nitrogen) then is true in the mononitro anions. This is contrary to what might have been expected on the basis of the relative acidities in the two series. The data point to the presence of strong steric inhibition of resonance which renders difficult a straight-forward interpretation of solvent effects. R. A. Marcus paper at this Symposium. A. I. Hassid M. M. Kreevoy and T. Laing paper at this Symposium. W. J. Albery A. N. Campbell-Crawford and J. S. Curran J.C.S. Perkin 11 1972 2206. A. J. Kresge Canad. J. Chem. 1974 52 1897. M. H. Davies J.C.S. Perkin II 1974 1018. M. E. Sitzmann H. G. Adolph and M.J. Kamlet J. Amer. Chem. Soc. 1968,90,2815. GENERAL DISCUSSION Dr. B. G. Cox (University of Stirling) said The reactions of nitroethane and 1,l dinitroethane with acetate (and hydroxide) ions have been quoted as examples of reactions showing a Bronsted coefficient greater than unity. Our results simply show that in accordance with expectations based on the relative solvation of the mono- and dinitroalkane anions the Bronsted coefficient decreases (and becomes “normal ” i.e. 0 < p < 1) as the DMSO content of the solvent increases. With reference to the results quoted by Bordwell an alternative explanation of them may be given again in terms of the different solvation of the anions. Thus the much stronger interactions with protic solvents of the mono nitro alkane anions would be expected to reduce the p* values of the nitroethane series relative to the 1,l dinitroethanes.The p* values should be much closer and perhaps even reversed in dipolar aprotic solvents or in the gas phase. Dr. B. R. Eggins (N. Ireland Polytechnic) said I think it is a pity that Cox has not extended his experiments in DMSO +water mixtures to very high mole fractions of DMSO including very dry DMSO and to very low fractions of DMSO. We have observed some unexpected effects in the oxidative dephosphorylation of hydroquinone phosphates. The relative rates of P-0 and C-0 bond fission during the oxidation of durohydroquinone monophosphate in mixtures of alcohols and water was found to be relatively constant at 39f2 % in methanol ethanol and propan-1-01 up to 0.8 mole fraction of alcohol which is similar to the results found by Kirby and Varvoglis and by Bunton Fendler and Fendler for the hydrolysis of p-nitrophenylphosphate.It is probable that the rate of proton transfer is a key step in determining these relative rates.5 However in solutions of mole fraction of alcohol greater than 0.8 the rate ratios decreased sharply. This decrease was also observed with propan-2-01 and trifluoroethanol. Our suggested explanation for this effect is that it is due to the change in the structure of solvent water as the diamond lattice can be completely broken down when four molecules of another suitable solvent can solvate each water molecule.6 The fast proton transfer which is possible by proton jump transfer in structured water does not occur when the structure is lost.As further evidence for this hypothesis the effect is partially reversed when very dry methanol is used and there as an increase in the percentage P-0 bond fission. This may be due to the restoration of linear structure to methanol which can allow limited proton jump transfer. While not wishing to deride the enormous value that linear free energy relation- ships have provided in correlating kinetic and thermodynamic data and showing up structural effects in reactions I feel that in attempting to explain anomalies in Bronsted plots such as curvature and p values greater than unity it is necessary to consider other factors more fully. By their very nature linear free energy relation- ships are energy difference plots and are intended to eliminate factors which are assumed to be constant throughout a reaction series.However this means that the effects due to changes in such factors are masked. I suggest that in Cox’s work and that of others involving mixed solvents changes of solvent structure should not be ignored. R. P. Bell and R. L. Tranter Proc. Roy. Soc. A 1974 337 517. B. R. Eggins and D. W. Hutchinson unpublished results referred to in V. M. Clark and D. W. Hutchinson,Prog. Org. Chem. 1968,7 100. A. J. Kirby and A. G. Varvoglis J. Amer. Chem. SOC., 1967 89,415. C. A. Bunton E. J. Fendler and J. H. Fendler J. Amer. Chem. Soc. 1967 89 1221. W. W. Butcher and F. H. Westheimer J. Amer. Chem. Soc. 1955 77 2420.F. Franks and D. J. G. Ives Quart. Rev. 1966,20 1. GENERAL DISCUSSION Prof. J. B. Wyne (University of Calgary) said I would like to comment on the papers of both Cox and Gibson and of Saunders and his co-workers. In both of these studies aqueous organic binary solvent mixtures were employed in order to effect variation of the bulk properties of the solvent medium but little or no comment is made regarding the important and sometimes highly complex variations in these systems at the molecular interaction level. Cox and Gibson report that the rates of proton transfer from nitroalkanes change in the opposite direction as the mole fraction of organic cosolvent is increased in water +dimethylsulphoxide (DMSO) compared with water +2,2,2-trifluoroethaiiel (TFE).They rationalise this behaviour in terms of the large difference in the interaction of water with anions of high charge density. In our recent examination of the heats of solution of quaternary ammonium salts in aqueous binary mixtures we have measured the AHs of tetramethylammonium chloride in both water +DMSO and water +TFE mixtures. The results shown in fig. 1 clearly establish that there are not only large differences in the solvent-ion interactions in these two systems but the heats of solution actually change in the opposite direction as observed by Cox and Gibson for the rates of proton transfer. AH of Mc,,NCI in Voii3us Aqueous Orgunic E.lix!ures ot 25°C FIG.1. These authors also note that anomalies in the Bronsted coefficient are character- istically associated with the high water content end of the solvent mixture range.This of course is the region in which the added organic cosolvent has its maximum effect on the unique "structuredness " of water. The AHs data in fig. 1 reflects this structural influence in the 0.0 to 0.1 mole fraction organic cosolvent region and in the case of water -I-TFE mixtures the AHs against mole fraction dependence actually changes sign. Again in the elegant and exhaustive kinetic study of carbon-13 isotope effects on proton transfer Saunders and his co-workers have employed dimethylsulphoxide + GENERAL DISCUSSION water mixtures. Re-examination of the plots in fig. 1 and 4 of their paper indicate that in all cases reasonable curves can be drawn through the experimental points indicating extrema at approximately 0.33 mole fraction dimethylsulphoxide.This is the same composition as has been frequently observed to characterise the extremum behaviour in many other phenomena in DMSO +water mixtures including excess heats and volumes of mixing and activation energies for various hydrolyses in these solvent mixtures. Parker and others have agreed that at this composition the unique structural features of water can be assumed to have been completely destroyed by the organic cosolvent and that a loose 2 1 H20:DMSO complex characterises the solvent system. While it is correct to say that this extremum behaviour in aqueous organic media is not normally found in free-energy ((AG log k etc.) composition) plots due to enthalpy/entropy compensation (Lumry’s Law) plots of the ratio of free energy terms as is the case in fig.1 and 4 in Saunders’ paper could well exhibit such behaviour. In any event the occurrence of extrema in the isotope effect against solvent composition plots at the same mole fraction as has been ascribed to the formation of a particular DMSO+water complex and as is observed with many other properties deserves some attention. It is also known that small additions of DMSO (among many other organic cosolvents) to water has a very marked effect on the so-called “structure ” of water. This is an important point in explaining the observed difference in isotope effect between 100 % and 95 % water which surprised Saunders and his co-workers.Very substantial changes in ionic heats of solution occur between pure water and 0.05 mole fraction DMSO. Accordingly it is not surprising that the kinetic isotope effect for proton transfer presumably via some form of Grotthus chain mechanism should undergo considerable change as the structure of the solvent water is effected by initial additions of organic cosolvent . Dr. B. G. Cox (University of Stirling) said In replying to Hyne and Eggins I would like to emphasise that a major point of our paper is that the effect of solvent variation on the rates of the proton transfer reactions studied is not simply related to (and may be opposite to) the effect on the corresponding equilibria. This shows that solvent effects whether they arise from “structural ” effects or H-bonding interactions etc.do not in general vary monotonically with the extent of proton transfer during the reactions and hence will influence observed p values. We have studied the reactions reported in mixed solvents with the mole fraction of the organic component varying between 0.06 and 0.85 and found no extremain the variation of rates with solvent composition. We feel that in DMSO+H20 water mixtures in particular the very large rate increases observed (>lo3) on transfer from water to the mixtures can most simply be interpreted in terms of the desolvation fo the anion bases (OAc- F- R,CNO;). Prof. W. H. Saunders (Uaiversity of Rochester) said :We assumed in interpreting our results that addition of dimethyl sulphoxide to aqueous hydroxide changes rates and isotope effects mainly by increasing the basicity of both reactant hydroxide ion and hydroxide ion in the transition state.We cannot exclude the possibility that other solvent effects enter in but there is in our opinion no definite evidence for such effects. As Hyne points out free energies need not reflect extrema in enthalpies. Our isotope effects reflect differences in free energies of activation. Since the rate for the light isotopic species changes monotonically with solvent composition it is hard to see why a solvent effect unaccompanied by a change in the extent of proton transfer would not change the rate for the heavy isotopic species in a parallel manner. GENERAL DISCUSSION The H-function for the medium does correlate well with rate which rises mono- tonically with increasing concentration of dimethyl sulphoxide and shows no pecularities in either high-water of 2 1 water dimethyl sulphoxide regions.Turning to several specific points raised by Hyne the minima in the carbon isotope effects (fig. 1) are shallow and difficult to locate but do not appear to occur at the same solvent composition. Neither do the more easily located maxima in kH/kD (fig. 4) so that clear evidence for specific solvent effects in the 2 1 water dimethyl sulphoxide region is lacking. As for the possible relation between changes in water structure and the scatter of carbon isotope effects for the sulphonium salt in 95-100 % water the slowness of the reactions and our failure to control sample sizes closely enough could explain the scatter.Consequently I do not feel justified in yielding to the temptation to attribute the scatter to specific solvent effects. Dr. W. J. Albery (Oxford University) said In presenting his paper Marcus com- pared electron and proton transfers and emphasised that while electrons may tunnel through distances of up to 1 nm a simple proton transfer takes place over a much shorter distance. For this reason he expected that the solvent oscillation which facilitates electron transfer may be less important in proton transfer. However while this argument may be true for simple proton transfers as soon as one has a carbon base with a n system then the movement of charge out of for instance the diazo or nitro group may provide sufficient leverage for solvent oscillations to be significant for these systems.This would explain why these systems have substantial Wand Wp terms. Prof. R. P. Bell (University of Stirling) said It seems to me rather artificial to speak of the effect of the isotopic mass of carbon upon the tunnelling of hydrogen since in the transition state the system can be represented by a single reduced mass moving along the reaction coordinate. It would be of interest to know how much this reduced mass depends upon the extent of H-transfer and also how much it varies as the system moves away from the transition state. The latter variation could be significant when the tunnel correction is considerable. Prof. W. H. Saunders (University of Rochester) said It is of course just a way of looking at a process which cannot really be dissected in this fashion but it is not entirely without mechanistic merit.A large tunnel correction requires a reaction coordinate frequency of fairly large absolute magnitude and fairly large isotopic sensitivity. The dependence of frequency on reduced mass suggests that motion of hydrogen must contribute substantially to the reaction coordinate for the first condition to be satisfied. Furthermore the model calculations on the E2 reaction give a sizable tunnel correction to the P-carbon isotope effect a considerably smaller one to the a-carbon isotope effect and essentially none at all to the leaving-group isotope effect even for 14Nagainst 5N.Thus conditions favourable to a significant tunnel correction to a heavy-atom isotope effect seem to include direct coupling of hydrogen motion to the heavy-atom motion.On the other hand it must be admitted that the sensitivity of the reaction coordinate frequency to isotopic substitution at carbon will be least when the reduced mass is closest to the mass of hydrogen a condition which will hold when the C-H and 0-H stretching force constants are nearly equal. A simple triatomic model yields a negligible tunnel correction under these circumstances. The E2 model does better because the reaction coordinate always involves more heavy-atom motion. The isotopic sensitivity of the reaction-coordinate frequency rises for less symmetrical GENERAL DISCUSSION transition states since the extreme reaction coordinates for the triatomic model can be regarded as approach of 0to CH and retreat of OH from C respectively.Prof. P. Zuman (Clarkson College) said Differences between the dependence of H-function (obtained for dissociation of anilines or indoles) and J-function (obtained for addition of OH-ions to benzaldehydes) on DMSOlwater ratio indicates that H-is not a simple function of OH-hydration. Change of H-function with DMSO concentration should thus not be used as a measure of OH-hydration. Prof. W. H. Saunders (University of Rochester) said E. S. Lewis’ proposal that steric hindrance promotes tunnelling suggests that a larger tunnel effect ought to be observed with triethylamine and tributylamine than with quinuclidine which has the alkyl groups on nitrogen “tied back ”.Yet Caldin’s data in table 2 indicate the tunnel effect is largest with quinuclidine. Please comment on this departure from the expected order. Prof. E. F. Caldin (University of Kent) said The tunnelling correction (QH) at 25°C in toluene for the reactions of 4-nitrophenylnitromethane decreases in the order quinuclidine > tri-n-butylamine > triethylamine. The curvature of the bar- rier decreases in the same order; this is because the barrier height decreases while the width varies little. The higher barrier for tri-n-butylamine compared with triethylamine can be interpreted in terms of steric hindrance either (1) by the original idea that the effect of bulky groups is to increase the repulsive forces between reactant molecules or (2) by E.s. Lewis’ recent suggestion that their effect is to hinder solvation of the transition state thus reducing the effects of coupling of the proton transfer with motions of heavy solvent molecules which would otherwise increase the effective mass and SO reduce the tunnelling correction. To account for the still higher barrier height for quinuclidine in these terms it is necessary to suppose that exclusion of solvent on the side remote from the proton is important ; the cage structure of the quinuclidine molecule makes it impossible for the solvent to approach the nitrogen atom in the reaction complex (C . .H . .N-from this side whereas 3 with the other amines there is much less hindran~e.~ Dr.W. J. Albery (Oxford University) said Accepting Caldin’s analysis I would like to ask how much coupling does mfI = 1.3 represent? Could it be that tunnelling is SO easily quenched by even a little heavy atom motion that the Franck Condon separation of H+ and solvent motion is still a good approximation? Prof. E. F. Caldin (University of Kent) said In reply to Albery one way of quantifying the extent of coupling in proton-transfer represented by an effective mass of 1.3 a.m.u. (rather than 1.0 a.m.u.) is to calculate the effect on the tunnelling correction Q,which is the ratio of the rate constant to that which would be observed with the same potential-energy barrier if there were no tunnelling (i.e. if the proton could be treated as a particle rather than a wave).We use Bell’s equations and simplify by taking only the first term and by assuming AH” = 0. Then Q = +u/(sin 3u) ; u = hv,/kT; v = Et/nb (2m).f. 1 L. H. Funderburk and E. S. Lewis J. Amer. Chern. Soc. 1964 $6,2531. 2 E. s. Lewis in Proton-transfer Reactions ed. E. F. Caldin and V. Gold (Chapman and Hall London 19751 p. 333. 3 E. F. Caldin and S. Mateo J.C.S. Furaduy I 1976,72 112. GENERAL DISCUSSION Let Q refer to rn = 1 a.m.u. and Q’ to m = 1.3 a.m.u. and suppose the barrier dimensions E and 2b are constant. Then taking the value of u as for acetonitrile (4.3) we find Q/Q’ = 1.4. Thus coupling of solvent motions with proton transfer to the extent that increases the effective mass to 1.3 a.m.u. does not reduce Q by a factor comparable with Q,which for several of the solvents in our work is over 20 at 25°C (see ref.(l) of our paper).For toluene for instance QHat 25°C is 28 and would be reduced to 20. Most of the reduction in QH(and therefore in kH/kD) on passing from toluene to acetonitrile for instance (for which QH = 2.6 at 25°C) is due to the decrease of curvature of the barrier (v = 1 420 cm-l for toluene 956 cm-1 for acetonitrile) which in turn is due to the decrease in barrier height (EH= 8.60 for toluene 5.85 kcal n101-~ for acetonit- rile). This decrease in EHis attributable to increased solvation of the transition state whether due to electrostriction or to specific interactions. Prof. R. P. Bell (University of Stirling) said It is worthwhile emphasizing that the calculated barrier dimensions in tables 1 and 2 involve the assumption m,-mH = 1.This is a somewhat arbitrary assumption though it does follow from a highly simplified electrostatic model of the coupling between proton motion and solvent rotation; however I do not think that any refinement of this treatment is likely to lead to essentially different results. Dr. W. J. Albery (Oxford Unirersity) and Prof. PI. M. Kreevoy (Uuiveusity of Minnesota) (communicated) We would like to offer an explanation for the variation in EHwith solvent observed by Caldin and Wilson. In the more polar solvents specific solvent-solute interactions can stabilize the transition states in which there is already some charge separation. This leads to a reduction in EH,the barrier to the actual proton transfer (see table I of Caldin’s paper).In terms of the Marcus theory this corresponds to a reduction in AG’ but at the expense of an increase in W‘. Since only AG# is susceptible to tunnelling the barrier height calculated from the manifestations of tunnelling goes down dramatically even though the reaction A FIG.1.-Effect of changing the solvent from a non polar solvent A to a polar solvent B on thc truncated parabolic energy barrier to proton transfer. On the left are shown the corresponding free energy terms of the Marcus theory ; W*must be small for the non polar solvent A but can be much larger for the polar solvent B. GENERAL DISCUSSION does not become much faster. The situation is shown schematically in fig.1 in which following Caldin's argument we have kept the barrier width constant. This explanation accommodates very nicely the general observation that tunnelling corrections are small in polar solvents even when the large primary isotope effect suggest that the effective mass in the reaction coordinate must be close to the mass of the proton. The flat squat barrier of curve B will only lead to a small tunnelling correction. The pattern shown in fig. 1 can also explain the rather puzzling insensitivity of the fractionation factor for the proton in flight to the symmetry of the transition state found for instance in the diazo system. Some results for catalysis by L30+ are collected in the table. An advantage of using L30+ is that in all the cases except one one can also measure the degree of proton transfer (aL30+)from the secondary solvent isotope effect ; for diphenyl-diazo-methane we can see from fig.1 of Kreevoy's paper that a must be small. The results in table 4 of Kreevoy's paper show that for other acids than L30+ again -0.25 despite the large difference in reactivity TABLE O 1.-VALUES OF ~ L + ~AND dl FOR R1R2CN2 R1 RZ log(k/M-1 s-1) a aL30+ dl b IHC coo- 4.8 0.30 0.24 Me COOEt 1.3 0.29 0.22 CaSe C6H5 -0.1 t0.2 0.20 Me COMe -0.1 0.27 0.22 COOEtf COO- -1.7 0.36 0.27 a Rate constant for H+ catalysed reaction ; b Fractionation factor for proton in flight ; C M. M. Kreevoy and D. E. Konasewich J. Phys. Chem. 1970,74,4464 ; d W. J. Albery and A. N. Campbell-Crawford J.C.S. Perkiti ZI 1972 2190; e Ref.(1); f W. J. Albery C. W. Conway and J. A. Hail J.C.S. Perkin II 1976 473. and transition state symmetry for the 4 different acids. The same pattern and values of 41are found for other aliphatic diazo compounds.2 As discussed above this system has very large W'terms and quite small AGf terms. It corresponds therefore more closely to a very flat cirve B in fig. 1. This therefore means that there will be very little contribution from tunnelling to a maximum in the primary isotope effect (minimum in 41>.Furthermore the Westheimer contribution to the maximum will be small because first the fractionation factor for the proton after the W' process may be reduced from that in the reactant and second systems with small values of A require less unequal force constants to shift the Bronsted coefficients.Thus we may expect systems with large values of W' and small values of 1 not to show a pronounced maximum in the primary kinetic isotope effect as the symmetry of the transition state is changed. Prof. E. F. Caldin (University of Kent) said It is now recognised that the transfer of a proton and the resulting solvent reorganisation are not necessarily synchronous (cf. the papers by Bordwell Marcus Kreevoy et al. and Caldin and Wilson and ref. (23) of the last-named paper). For reactions where they are markedly out of step the general question arises which comes first ? Does the proton-transfer occur first and the resulting charge-separation force the polar solvent molecules to rotate ? Or does the proton-transfer occur only when the random motions of solvent molecules A.I. Hassid M. M. Kreevoy and T. Laing paper at this Symposium. W. J. Albery A. N. Campbell-Crawford and R. W. Stevenson J.C.S. Perkin II 1972 2198. F. €3. Westheimer Chem. Rev. 1961 61 265. GENERAL DISCUSSION lead to a configuration suitable to the transition state? Is there any general method of predicting the result or of determining it experimentally? This question is distinct from the question of coupling in which one process gives rise to a force that brings about the other. Rotation of solvent molecules takes a much longer time than the passage of a proton across an energy-barrier but could be coupled with it in the sense that the charge-separation associated with the proton- transfer could lead to a torque on polar solvent molecules which would produce rotation.It is also necessary to distinguish on the molecular level between processes that are “fast ” in the sense that the process requires a relatively short time (e.g. a vibration compared to a rotation) and those that are “fast ” in the sense that the process occurs frequently so that the associated rate is high. The rotation of solvent molecules though “slower ” than proton-transfer in the first sense may (or may not) be “faster ” in the second. Prof. R. A. Marcus (Uniuersity of Illinois) said In answer to Caldin’s interesting query regarding slow and fast coordinates I would like to present a picture or two which also serves to supplement Albery’s remarks.We consider first the nature of the potential energy profile. The profile depends of course on the coordinate being used as abscissa. For example if in the skewed-axis figure of my paper (fig. 1 there) the potential energy were plotted along the valley of the reactants over the saddle- point and along the valley of the products the barrier would be an Eckart-like one i.e. a roughly bell-shaped curve. If instead the potential energy were plotted against some collective solvent orientational coordinate allowing the proton to vibrate but not to transfer the profile would be as in fig. l(a)of this comment labelled reactants while if the protonic binding were that of the products the profile would instead be the curve labelled products in fig. l(a).The effect of a proton transfer on these profiles is indicated by the dotted-line profiles in fig. l(a) which allow for a protonic motion which always adjusts itself (adiabatically) to changes in the solvent coordinates rather than not being allowed to transfer. The splitting A&in fig. l(a) is related to the frequency of proton jumping v by the relation A&-hv,. When the proton jumps very readily (e.g. v -1014 s-l) A&is large perhaps roughly the size of a vibrational quantum for a hydrogenic motion. Fig. l(a) applies to a thermoneutral system. For a fairly exothermic reaction these profiles would instead be as in fig. l(b) while for a fairly endothermic one they would be as in fig. l(c). Thus turning to Caldin’s question in fig. l(b) where the U b C I FIG.1.-Profiles of potential energy for proton transfers versus some generalized solvation coordinate for the cases of (a) thermoneutral (b) exothermic and (c) endothermic reaction.The splitting AE reflects the proton jumping frequency -Ac/h at the cited value of this solvation coordinate. The proton jump occurs mid-way in largely prior to and largely after the solvation reorganization as indicated in cases (a),(b)and (c) respectively. S 10-6 142 GENERAL DISCUSSION “ intersection ” of the parabolas occurs early the protonic jump precedes the slow solvent molecules’ reorientations while in fig. l(c) the reverse is true. In fig. I(a) the slow reorientation partly precedes and partly follows the proton jump. Similar remarks apply when profiles are plotted against other slow coordinates.Incidentally in fig. 1 of this comment the protonic tunnelling is not a tunnelling through the barrier there. Rather it is reflected in the magnitude of v, i.e. in A&. Dr. W. J. Albery (Oxford University) said In considering the role of the solvent and the timing of its motion with respect to atom transfer I believe it is helpful to consider fig. 1 which shows a reaction involving proton transfer and a change in the solvation with a transition state that is intermediate on both co-ordinates (cf. fig. 1 p. 141 above).’ The effect of the torque exerted by the charge separation on the polar solvent molecules will be included in the calculation of the free energy surface and will be responsible in part for the shape of the profile along the proton transfer co-ordinate.The relaxation of the solvent after the proton transfer can be seen at the back of the diagram. Thus this type of “ coupling ” is described by the shape of the surface. As discussed earlier the most favourable path for the proton transfer will be when ApK for the actual proton transfer is not too far from zero. Movement along the solvation co-ordinate achieves this condition. However movement along this co-ordinate is slower than movement along the proton transfer co-ordinate. The translational and rotational diffusion of the solvent will have a lower velocity than the actual proton transfer. Note that one is concerned with the velocity of motion (cm s-l) rather than the velocity of reaction (M s-’).The latter is a function as well of the population of the different species. One could describe the system in terms of rate constants for motion along the different co-ordinates. However a more plausible model is to treat motion along the solvent co-ordinate as a diffusion process. Neutron diffraction data show that diffusion coefficients measured under macroscopic conditions continue to be a good description of motion down to times as short as 10-l2 s. We can write for the steady state where along the solvation co-ordinate AG --glx. RT In this equation k(x) is a function of the displacement along the solvation co- ordinate. If k(x) = 0 then there will be zero flux and one obtains the normal thermodynamic distribution for c c/c = exp( -g’x) = exp( -AGIRT).Analytical solutions for the flux can be obtained if one assumes that k(x) is zero for x < x1and then has a finite value. The form of the solutions their dependence on D or k,3 and whether the diffusion or the kinetic process is rate determining have been di~cussed.~ If the kinetic process is rate determining then the transition state is at + and the solvent is pre-equilibrated to the value at x,. If k(x) is large the diffusion process along x that is the solvent reorganization can be rate determining. W. J. Albery Reaction Transition States (ed. J. Dubois) (Gordon and Breach London 1972) p. 224. W. J. Albery Proton-Transfer Reactions (Chapman and Hall London 1975) p. 307. J. W. White Ber. Bunsenges. Phys.Chem. 1971 75 379. W. J. Albery Proton-Transfer Reactions (Chapman and Hall London 1975) p. 303 et seq. GENERAL DISCUSSION Solvation -FIG.1.-Diffusion/kinetic model of a proton transfer where the alteration of the solvent is shown by the square circle and diamond. The ApK of the AH S system varies as shown and proton transfer is most likely to occur when ApK = 0. The route through X where the solvent "lags " the proton transfer is less favourable than the route through f. Motion along the solution co-ordinate is assumed to obey a modified diffusion equation. Free energy differences corresponding to the Marcus parameters are shown except that the contribution to Wr from the formation of the encounter complex cannot be shown on the diagram.Solvation FIG.2.-Diffusion kinetic model for an asymmetric proton transfer where AG for the reaction is positive going from left to right and negative going from right to left. In the first case there is a large Wr term and solvent motion precedes the proton transfer. In the second case there is a small Wr term and solvent motion follows the Droton transfer. 144 GENERAL DISCUSSION Whatever the exact form of the solvation the flux can be described as the product of the concentration at x = 0 and a rate constant. Thus this analysis can be carried out for a succession of steps where the faster subsequent processes provide the rate constant "k " for the particular slower process being considered as a diffusion. Remember that by "faster " we do not niean the usual kineticist's distinction between fast and slow steps but rather we are concerned with the actual velocity of motion or the time taken for a single particle to complete that step of the reaction.In these terms the slower the process the earlier it has to take place. There will not be time for it to take place later as the particular molecule accelerates to its destruction. Thus for a typical reaction in solution we have the sequence Encounter + Ionic Atmosphere * Solvation + Atom transfer. Debye-Hiickel theory works for salt effects. Similarly there is no solvent lag because those reactants that are peculiarly solvated for the transition state are the ones that react. Reactants with normal reactant solvation do not react because for them the barrier through X (in fig.1) is larger than that through the transition state. The surface in fig. 1 is drawn for a reaction where AG = 0 and shows therefore a symmetrical transition state. For "uphill " transfers we obtain the surface shown in fig. 2. Here there has to be more solvent re-organization before ApK for the actual proton transfer becomes close to zero. Hence for the uphill case solvent re-organization largely precedes the proton transfer and W' is large. The "down-hill "case can be considered as the reverse of fig. 2. For this case there is little solvent re-organization before the proton transfers.