J . Phys. Chem. 1986, 90, 3156-3159
3756
(a)provide a useful guide to those rate processes in which diffusion must be included. The rates of proton transfer ( k 2 )from various methylarene cation radicals follow a general Brernsted relationship with the series of substituted pyridine bases included in Figure 8. For the deprotonation of a particular methylarene cation radical by different pyridine bases, the driving force can be expressed in terms of the acidity constant pKaBof the pyridine base (conjugate acid). The Marcus equations reformulated in this manner (eq 29) yields a consistent value of the intrinsic barrier of proton transfer from various ArCH," to different pyridines. The unified correlation of activation free energies for proton transfer in Figure 9 provides the work terms w,and wp. The magnitudes of these (inner-sphere) work terms are such as to strongly influence the evaluation of the acidity constant pKaAof the methylarene cation radical-a situation which strongly contrasts with that for outer-sphere electron transfer from uncharged ArCH,. The magnitude of the deuterium kinetic isotope effect can be interpreted in terms of a transition state in which proton transfer from the methylarene cation radical
has only progressed partially. The limited hydrogen bonding to the base in the activated complex is supported by the small steric effects of ortho-substituted pyridines. Such an early transition state is consistent with the magnitude of the B r ~ n s t e dslope as interpreted by the Marcus formulation of proton transfer.
Acknowledgment. We thank the National Science Foundation and the R. A. Welch Foundation for financial support. Registry NO. Me&,, 87-85-4;Me5C6H,700-12-9; 1,2,3,5-Me&,H~, 527-53-7; 1 ,2,3,4-Me4C,H2,488-23-3; 1 ,2,4,5-Me4C6H2, 95-93-2; 1,2,4Me3C6H3,95-63-6;1,2,3-M&,H3,526-73-8;1,3,5-Me$&,, 108-67-8; 1,3-Me2C6H4, 108-38-3; 1,2-Me2C6H4, 95-47-6;I ,4-Me2C&, 106-42-3; PhMe, 108-88-3; (5-H-~hen)~Fe'+, 13479-49-7; (5-C1-phen),Fe3+, 22327-23-7; (5-N02-phen),Fe3+, 22327-24-8;2-fluoropyridine,372-48-5; 2-chloropyridine, 109-09-1 ; 3-cyanopyridine, 100-54-9;4-cyanopyridine, 100-48-1 ; 3-chloropyridine,626-60-8; 3-fluoropyridine,372-47-4;pyridine, 110-86-1; 2-methylpyridine, 109-06-8;4-methylpyridine, 108-89-4; 4-methoxypyridine,620-08-6; 2,6-dimethylpyridine, 108-48-5; 2,6-ditert-butylpyridine, 585-48-8; 2,4,6-trimethylpyridine, 108-75-8; D2, 7782-39-0.
Application of the Marcus Equation to Methyl Transfers' Edward S . Lewis Department of Chemistry, Rice University, Houston, Texas 77251 (Received: January 15, 1986)
The transfer of methyl between two nucleophiles is used as an example of the application of the Marcus equation to group transfers. The direct measurement of equilibria and identity rates allows prediction of unsymmetrical reaction rates over a wide range, which are in good agreement with experiment. Some of the identity rates, measured to test the equation, contain previously unknown information about the charge distribution in the transition state. The quadratic Marcus term is shown to be negligible (by virtue of the rather high intrinsic barriers for methyl transfer); as a consequence, the effect of the leaving group can be separated from that of the attacking nucleophile, leading to a useful scale of nucleophilic and leaving group character. In some cases the quadratic term may become important, but it is unlikely that an experimental distinction can be made between various nonlinear rate-equilibrium relations which behave the same with equilibrium constants near unity.
Introduction This paper is concerned with the uses of the Marcus equation by organic chemists. The impact in organic chemistry is as a way of thinking, rather than merely a method to calculate reaction rates. Initially organic chemists did not take much notice of electron-transfer reactions, the origin of the Marcus equation.2 However, electron-transfer processes have since become such a familiar part of organic chemistry that the acronym SET (single electron transfer) is now in accepted use. Nevertheless, electron transfer was considered a narrow area of interest and the Marcus equation was not widely used. The extension of the equation to proton transfers by Marcus3 and other^,^.^ to hydrogen atom transfers (using a somewhat different analytical form) also by M a r c ~ sand , ~ later to methyl transfer by Albery and Kreevoy6 and in the gas phase by Pellerite and Brauman' has brought this approach to the SN2reaction, a center of mechanistic organic chemistry. The essential new addition of the Marcus treatment is the idea of an intrinsic barrier, the average of the two identity barriers, which is considered separately from the thermodynamic driving force. In this way it allowed an understanding of the fact that all proton-transfer rates do not fall on the same Bronsted plot when (1) This paper is Methyl Transfers, 12; paper 11 is ref 24. (2) Marcus, R. A. J . Pfiys. Cfiem.1956, 24,966. Throughout this paper reference is made to the Marcus equation rather than Marcus theory. This is deliberate because the applications covered are remote enough from the original derivations to remove much semblance of theoretical justification; it is used here primarily as a plausible empirical relation. (3) Marcus, R. A. J . Pfiys. Chem. 1968, 72, 891. (4) Kreevoy, M. M.; Oh, S.-W. J . Am. Chem. SOC.1973, 95, 4805 (5) Kresge, A.J. Chem. SOC.Reu. 1974, 2, 475. (6) Albery, W. J.; Kreevoy, M. M. Ado. Phys. Org. Chem. 1978, 16, 87. (7) Pellerite. M. J.; Brauman, J. I. J . Am. Chem. SOC.1980, 102, 5993.
0022-3654/86/2090-3756$01.50/0
log k is plotted against log K for the same reaction rather than against pK,, because the intrinsic barriers differ. It also allows an understanding of curvature in Bronsted plots; curvature is an essential feature of the Marcus equation as well as the widely accepted ideas such as the Hammond postulate,8 the variable transition state, and the reactivity-selectivity principle. These curvatures, it must be stated, are more often talked about than seen in unequivocal experimental results.9 The analytical separation of the thermodynamics from some independent purely kinetic factor, now expressible as the intrinsic barrier, is particularly attractive to those aware of the absence of generality of rate-equilibrium relations, while at the same time seeing many of these. The application of this idea is only beginning to find interested users.
Methyl Transfer Reactions The Fit to the Marcus Equation. Methyl-transfer reactions were first considered as an appropriate subject for consideration using the Marcus equation by Albery and Kreevof who assembled data from the literature on a number of reactions of nucleophiles with methyl halides in predominantly aqueous media. Thermodynamic data from several sources were combined with this, the applicability of the Marcus equation was assumed, and a series of identity barriers was fitted. The result was a plausible and internally consistent set of numbers allowing the calculation of a large number of cross reaction barriers. Among the interesting conclusions was a clear understanding of observations such as why some nucleophiles, such as the halides, were practical leaving groups (having relatively low intrinsic barriers), while other quite (8) Hammond, G. S.J . Am. Chem. SOC.1955, 77, 334. (9) Johnson, C. D. Cfiem. Rev. 1975, 75, 755.
0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 16, 1986 3757
Application of the Marcus Equation to Me Transfers good nucleophiles, such as CN-and OH-, were never significant leaving groups from carbon; their high nucleophilic reactivity was attributed to large thermodynamic driving forces which could overcome the high identity bamers. The treatment was necessarily rough because the data were from different laboratories, the solvents were not always the same (although predominantly aqueous), and the thermodynamic data were not based on direct measurements in solution. Because of irreversible reaction with water, equilibria cannot be established in such solvents. At about the same time measurements of both rates and equilibria in solution in the single solvent sulfolane (tetrahydrothiophene dioxide) appeared;I0 the data of a few years earlier of Jackman and co-workers" on equilibria in some methyl transfers in fortuitously the same solvent proved very valuable. The initial aim of this work was initially to compare rates and equilibria to see if any rate-equilibrium relation analogous to the B r ~ n s t e d relation might exist. In fact, the analogy to the proton transfers was responsible for the name "methyl transfers" instead of nucleophilic substitution. No general rate equilibrium correlation did in fact exist, but the introduction of the idea of the intrinsic barrier applied to the results did allow the estimation of a series of identity rates for several nucleophiles not included in Albery and Kreevoy's aqueous solution tables. The results for the reaction 1 were correlated by the equation 2. X-
+ MeY
$
XMe
+ Y-
This simple equation neglects work terms and quadratic terms of the Marcus equation, and it was not clear at the time how much was being neglected. The quadratic term was deliberately neglected, however, because of earlier ~ o r k ' which ~ J ~ showed no significant reactivity-selectivity relation. As in the Albery and Kreevoy work, the treatment was plausible but not rigorously shown to be correct. It remained to demonstrate the applicability of the Marcus equation by actually measuring the identity rates. This was accomplished by HuI4 in a series of identity rate measurements on substituted benzenesulfonates as nucleophiles, and the cross reaction rates were fitted by the Marcus equation within the limits of experimental error of the rate and equilibrium measurements. The range of equilibrium constants in this series was small; the contribution of the quadratic term using work terms estimated as in the aqueous systems6 was too small to detect. The form of the equation used was AG*yX (AG'xx + A G * y y ) / 2 + A G a y x / 2 ( A G O ~ ~ ) ~ / ~ (AA GG **-~~~ ~~W R (3) )
+
+
which contains implicitly the assumptions that the work term, @, is the same forward and backward and is not sensitive to the nature of X and Y in eq 1. This form has the advantage that it used the overall experimental identity free energy of activation, for example Actxx, and the overall free energy change, AG'yx, rather than those, which are more difficult to measure, after the work term has been overcome. When the nucleophile and the leaving group are very similar, as in the series of arenesulfonates, there is little doubt that the assumptions about the work term are justified. The questions grow as the reactions get more unsymmetrical, and are the least defensible when the charge type changes, as in reaction 4 or its reverse. X
+ MeY = MeX+ + Y-
(4)
The range of applicability of eq 3 has now been greatly extended, with maximum deviations of the calculated rates from the observed of a factor of five over a range of rates of eight powers (10) Lewis, E. S.; Kukes, S.; Slater, C. D. J . Am. Chem. SOC.1980,102, 1619. (11) Wong, C. R.; Jackman, L. H.; Portman, R. G. Tetrahedron Lett. 1974, 921. (12) Lewis, E. S.; Vanderpool, S. J . Am. Chem. SOC.1978, ZOO, 6421. (13) Lewis, E. S.; Kukes, S.; Slate, C. D. J . Am. Chem. SOC.1980, 102, 303. (14) Lewis, E. S.; Hu, D. D. J . Am. Chem. SOC.1984, 106, 3292.
of ten and equilibrium constants also as large as lo8, illustrated recently15 in a graph. A search for systematic deviations that might show the operation of favorable soft-soft and hard-hard interactions vs. unfavorable hard-soft onesI6 showed that such effects would give calculated rates faster than the observed ones for the reactions of a hard MeY (such as a methyl sulfonate) with the soft I-. In all but one case, deviations amounting to no more than a factor of five in this direction were seen. In the one case, methyl trifluoromethanesulfonate with iodide ion the calculated rate was 0.4 times the observed. However, the cumulated error in the equilibrium constant for this reaction is one of the largest; there is at least one further piece of evidence suggesting that the methyl triflate equilibrium power is too low by more than one power of ten. Thus a small deviation in the HSAB direction may exist even in this case. A further possible anomaly in the HSAB direction arises from the observation that dimethyl sulfate reacts more rapidly than methyl iodide with a number of first row element nucleophiles, but methyl iodide is faster with most second in one case by a factor of 400.'* Thus row or later n~cleophiles,'~ we cannot exclude an error in the calculation by eq 3 resulting from an interaction of the attacking and leaving groups in the transition state, but so far such errors are small. Up to now, the Marcus treatment is successful. The deviations seen are not large; it is possible that even these small deviations are currently understood. It is anticipated that some even larger deviations will be found, but unless they are unacceptably large as well as unpredictable, the Marcus treatment will continue to be very useful. The Significance of the Zdentity Rates. Among reactions with a single rate-determining step, identity reactions have transition states of severely limited structure; microscopic reversibility imposes a symmetry which for group transfers makes the attacking group and the leaving group indistinguishable. In methyl transfers in a single solvent at the same temperature and pressure, the only remaining variable is the nature of the nucleophile leaving group Y (in eq 1); yet the effect of this variation has been illuminating. When the structural changes are remote and modest, LFERs are found between the identity rate constants and the equilibrium constants for the reactions of MeY with a reference n~cleophile.'~ For the reaction 1 let us write for the reaction in the forward direction the rate constant kyX,for the reverse direction, k x y , and for the equilibrium constant, K y x . The slope of a plot of log k y x vs. log K y x for constant X, variable Y is generally interpreted as being a measure of productlike character, but this is not useful in these methyl transfers. Instead, it is easily shown that, for the above plot (sufficiently near to K y x = l), the slope, a,is given by d 1%
kYX/d
1% KYX =
Y2
+ (Y2Md 1%
kYY/d 1% KYX)
(5)
Thus slopes near are expected; departures from this value are attributed to variable identity rates. There are some useful equivalent relations when the series of variable Y with a constant X obeys the Hammett equation;I4 two are shown as follows: PYY
= PYX + PXY
-PYY = - - 2PYX pep
1
(6)
(7)
pcq
The second term on the right of eq 5 shows the reason that (Y differs from 1/2. In all the cases we have seen this term is zerozo or positive. Alternatively, the reaction rates are more sensitive (15) Lewis, E. S.; McLaughlin, M. L.; Douglas, T. A. J . Am. Chem. SOC. 1985, 107, 6668.
(16) Pearson, R. G.; Songstad, J. J . Am. Chem. SOC.1967, 89, 1827. Pearson, R. G.; Songstad, J. J . Org. Chem. 1967, 32, 2899. (17) Lewis, E. S.; McLaughlin, M. L. Presented at the American Chemical Society Southwest Regional Meeting, Lubbock, TX, 1984. (18) Whitmire, K. H.; Lee, T. R.; Lewis, E. S. Organometallics, in press. (19) These LFERs are definitely far from general; a logarithmic plot of all the established identity rates against the equilibrium constants is very scattered. (20) Lewis, E. S.; Kukes, S. J . Am. Chem. SOC.1979, 101, 417.
3758 The Journal of Physical Chemistry, Vol. 90, No. 16, 1986 P Ib
c,~. IC
\
A Idtle
la R X-Me-Y
X-Me Y -
X - d e Y-
X. M e - Y
X-Me-Y
ia ib IC Id le Figure 1. Location of transition state for methyl transfers showing progress from the reagent R to the product P, with the limiting cationic and anionic niethyls indicated by the corners C and A, respectively. All identity reaction transition states lie on the dashed diagonal C A , since they show equal contributions of the two structures l a and Ib. Points above the diagonal RP have a net positive charge on the methyl group. Points below RP, so far not detected, have a net negative charge on the methyl group. The circles marked x, y, and z are for the identity reactions with X (=Y)= ArSO,, ArSeMe’, and ArS, respectively. All so far observed transition states for unsymmetrical reactions are quite close to the diagonal CA; there is very little excess contribution of the “reagentlike“structure l a in the spontaneous reactions. All the contributing structures are shown below the diagram.
to a change in the leaving group than to an equivalent change in the nucleophile. The positive sign is interpreted as a measure of the excess positive charge on the methyl group in the symmetrical identity reaction transition state. This positive charge corresponds to a significant contribution of structure 1 to the transition state.
1
Consideration of this structure among others is a part of a major theoretical treatment of alkyl transfers by Shaik.21 This contribution of the unbonded structure may correspond to the “loose” transition state in contrast to the compressed one, both are exposed by studies by SchowenZ2on deuterium and carbon isotope effects. Figure 1 shows a More O’Ferrall-Jencks diagram for methyl transfers showing the diagonal CA on which all identity transition states must be located together with the positions of several identity transition states placed now i n this way. Iodide ion is not part of any series which might be expected to give LFERs; thus, we cannot determine the methyl group charge for this interesting nucleophile with the so far uniquely fast identity reaction. However, evidence is accumulating that the identity rates get faster as we go farther down the periodic table. This area is not yet well explored experimentally. The Neglect of the Quadratic Term. Several times above, the quadratic term has been neglected; it now remains to justify this and to show the consequences of this neglect. In eq 3, the quadratic term will become quite unimportant if -AG0/2 >> ACo2/8[(ACtXx+ A G f Y y )- 2wR], which is equivalent to the expression 1 >> -3Go/8[(hC*xx + A c t y y ) - 2wR]. Now the fastest identity reaction that we have found has a rate constant of about I M-’ SKI,corresponding to a free energy of activation of 18 kcal/mol. The largest equilibrium constant we have dealt with has been about IO8, corresponding to AGO = -1 1 kcal/mol, although it is quite likely that numbers more than twice that large may be realistic. Unless wR is substantial the denominator is clearly several times larger than the numerator and the neglect is justified. Furthermore, in any expected methyl transfer of extremely large equilibrium constant, for example the reaction (21) Shaik, S. Prog. Phi’s. Org. Chem. 1985, 15, 197. (22) An example of this extensive work is Rodgers, J.; Femec, D. A.; Schowen. R. L. J . .4m. Chem. Sor. 1982, 104, 3262.
Lewis of methyl triflate with the thiophenoxide ion, the intrinsic barrier will be much larger than the 18 kcal of the iodide identity reaction (an estimatez3 of the thiophenoxide identity rate at 35 O C in aqueous ethanol is M-’ s-’, a free energy of activation of about 36 kcal/mol). Thus for any reaction with identity barriers no smaller than these methyl transfers, the quadratic term is not likely to be significant. This is clearly the reason why the simple eq 2 worked in the case mentioned, and why the slope of log k vs. log K plots can be interpreted in terms of identity rate correlation with equilibria rather than as manifestations of “early” or “late” transition states. The absence of any reactivityselectivity correlation is likewise a consequence of the absence of perceptible contribution of the quadratic term. The availability of a list of equilibrium constants, K,,, for reaction of MeX with a reference nucleophile, in our case the benzenesulfonate ion, allows a large number of equilibria for reaction 1 to be expressed as Ky,/Kx,, and eq 2 can be rewritten as24 log k y x = M y + N x (8) where M y = (log kYY + log K y , ) / 2 ,Nx = (log kxx - log K x , ) / 2 . Thus there is a term, M y , which is a property of the methylating agent MeY only, entirely separable from the other term, Nx, which is a property of the nucleophile X- only. This equation is reminiscent of the Ritchie equation25in the absence of any term to show the sensitivity of the rate to the nucleophilic property but the nucleophilic character term Nx is not likely to show any parallelism to Ritchie’s N’. There is a closer relation between Nx and the Swain-Scottz6 n numbers, for these are defined as log k/k,,,, for the reaction of CH,Br with various nucleophiles and differ from Nxonly in the solvent and the source, which in our case does not involve the measurement of cross-reaction rates. The form of eq 8 makes the absence of any reactivity-selectivity relation obvious. A number of these Nxvalues have been tabulated. There are difficulties with measuring both identity rates and equilibria with many of nucleophiles such as those on the Swain-Scott list; very large equilibria are hard to measure and are often very slowly attained. Similarly, M y values are tabulated only for the relatively powerful methylating agents like methylsulfonates and a few others. It is in principle possible to establish Nx values for many nucleophiles by measuring their reaction rates with a MeY for which MY has been established by using eq 8, and this is experimentally practical, although the farther one gets from values directly determined from the definitions, the more tenuous is the whole procedure. Nevertheless, this classification of nucleophiles and methylating agents independently is intellectually satisfying as well as being a start toward a broad approach to a practical method of reactivity prediction for an important reaction. The fact that in a related series there may be a correlation of the identity rate with the equilibrium methylating power shows that in eq 8, the two terms MY or Nx are both correlated with K y , or Kxr. This accounts for the success of correlations of log k y x with acidities giving respectively pl, or p,,, which may be taken roughly as equivalent to correlations with the equilibria of reaction 1. We assume for the moment that the acidity of H Y is a good model for the ionization of MeY with respect to substituent effects, although this may be sometimes very wrong. The observed direction of the correlations suggests that generally PI, > ‘/z and p,,, < I / * . In passing it may be noted that the more identity rates change with KYr (or K,,), the farther from is the pi, (or fin”,), and for transfers of other alkyl groups which can tolerate a positive charge better than methyl, we can expect pl, to approach unity, and p,, to approach zero. It is significant that these wide changes pi, or p,,, can occur without having the transition state ever get away from the CA diagonal in Figurel; (23) Lewis, E. S.; Douglas, T. A,; McLaughlin, M. L. Zsr. J . Chem., in press. (24) Lewis, E. S . ; Douglas, T. A,; McLaughlin, M. L., submitted to Ado. Chem. ( 2 5 ) Ritchie, C. D.; Virtanen, P. 0. I. J . Am. Chem. SOC.1972, 94, 4666. (26) Swain, C. G.: Scott, C. B.J . Am. Chem. SOC.1953, 75, 141.
Application of the Marcus Equation to Me Transfers in fact, all the unsymmetrical reaction transition states appear to lie very close to this diagonal. The Analytic Form of the Marcus Equation. The question that must arise is whether there is any reason to use the Marcus equation, since the quadratic term is omitted, or whether the quadratic term is ever experimentally justified. The justification of the work term, the intrinsic barrier term, and the linear thermodynamic term is not open to question; they are well supported experimentally. In a series of constant intrinsic barrier, the question is if a plot of log k vs. log K is indeed concave downward, and if the quadratic term is the correct analytical form for this curvature. Let us first dismiss the fact that the quadratic term produces a maximum at extreme values of AGO as being beyond the range of measurement for group transfers. The BEBO based equation derived for hydrogen atom transfers3 does not have this property; instead the rate approaches a high value asymptotically for exoenergetic reactions. One desirable feature of the Marcus equation that should be preserved in any effort to replace it with another analytical form is its symmetry with respect to forward and reverse reactions. There are empirical equations that do not have this feature; they may be adequate for a series of reactions studied which may be imperceptibly reversible, but they cannot give much confidence in extrapolation or consideration of the reverse reaction. Various alternative equations have been proposed to account for the rate energy connection. Some of these have impossible limits for extremes of energy in either direction; the most conspicuous and popular of these are the various linear free energy relationships (LFERs). LFERs are a major part of the arsenal of the physical-organic chemist as well as others. They are of immense value in predicting rates, in establishing mechanisms, and in organizing and systematizing the ever-increasing body of experimental data. Efforts to detect curvature in the supposedly linear plots have often been carried to very large ranges of free energy change, and in a number of cases no curvature has been detected? except sometimes for the limit on bimolecular reactions in solution by diffusion control. Nevertheless, extrapolation to still greater exothermicities does lead ultimately to reactions faster than molecular vibrations; this absurd result, as well as the equivalent problem for the reverse reaction for very endothermic reactions, shows that LFERs for rates cannot be infinitely extrapolated. In fact, we seldom have enough range in AGO to come to any limitation. Cases which have low intrinsic barriers have a better chance of showing curvature, but the diffusional limitation is reached very soon. Cases with small enough intrinsic barriers to allow the Marcus quadratic possibly to contribute may include proton transfers, hydrogen atom transfers, and perhaps a few halogen atom transfers. The only cases of curvature in Bronsted plots are cases of very low limiting rates caused by very large wR terms. Although the Marcus fit is quite good, there is little convincing reason for large work terms in one case, small ones in another. Reaction rates in H atom transfers are seldom measured with enough precision in solution to correlate rate with exothermicity, which is itself not precisely enough known. However, the more easily measured hydrogen isotope effects are rather accessible, and in proton transfers it has been shown that the Marcus equation can be applied: The same treatment can be applied to the H atom transfers, and the isotope effects can be simply related to the more difficultly measurable rates, or at least the variation of these by the Marcus equation using some rough, but qualitatively correct, values of A H o . Here the rates are quite fast and the value of -AHo is clearly far greater than four times the intrinsic barrier. The Marcus BEBO equation is reasonable in explaining the isotope effect, as was another analytic form (a hyperbolic relation between log k and AH0).27 Clearly these data were not precise enough (27) Lewis, E.S.;Shen, C. C.; More OFerrall, R. A. J . Chem. SOC.1981, 1084.
The Journal of Physical Chemistry, Vol. 90, No. 16, 1986 3759 to determine the exact form of a curved log k vs. AHo plot. It can be concluded that the analytic form of the expression corresponding to a concave downward plot of log k vs. log K plot is not experimentally verifiable now. In most cases there is not even any evidence for curvature at all. Thus, if we had a series of constant intrinsic barrier, the plot of log k vs. K would be linear over a long range, and the Marcus quadratic equation would apply adequately over an even wider range. Unfortunately, the constant intrinsic barrier series is unrealistic; even when the series belongs to a Hammett series or a Bronsted series, the intrinsic barrier may vary linearly with log K , so the slope of the plot does not give a measure of the productlike character of the transition state. Values of this slope have therefore often been misinterpreted. The effect of correlation of identity rates with log K has been illustrated in model calculation^.^^ In the case of methyl transfers it was shown that the deviation of the slope of the log k vs. log K plot from was exactly accounted for by the variation of identity rate with s t r ~ c t u r e . ’Bronsted ~ plot slopes may for the same reason be more indicative of identity rate variations than of transition-state asymmetry, even though the actual identity rates may be diffusion controlled. Since these proton transfers probably have a substantial positive charge on the transferring proton, the arguments applied to methyl transfers should work here also; the and a is Bronsted 6 is expected to be uniformly less than expected to be more than Extensions to Other Group Transfers and Other Reactions. There does not seem to be any reason not to attempt to apply the Marcus treatment to other group transfers. A problem can be expected with steric effects, which may differ in the transition state from the identity reaction average. In the transfer of and P03-,29,30 data on effects of the attacking and leaving group changes have led to conclusions rather analogous to ours on the methyl transfers, and identity rates have been calculated from LFERs, although without using the Marcus equation formally. The Marcus treatment has been used in a complete way to study hydride transfer^;^' it was concluded that the transferring group carries a partial negative charge in the transition state. There is less information on a number of other one-step group transfers. There is a temptation to apply some related theory to reactions which do not have identity reactions but to still have a separation of thermodynamic effects on rates from those of empirically derived “intrinsic barriers”. Although this has been attempted,32 it is not widely accepted33 and may or may not prove useful.
Conclusions The Marcus equation has proven to be a very useful way to look at reactivities in group transfers. The concept of the intrinsic barrier, determined by the mean of identity barriers, is very useful. The use of the intrinsic barrier allows the better understanding of thermodynamic effects on rates. The identity barriers themselves contain information of great interest, which might have remained obscure without the stimulation of the Marcus treatment. It must be stated, however, that all of the information might have been obtained without ever using the equation, but this does not diminish the effect of Marcus in stimulating these studies and providing a simple framework for understanding them. Acknowledgment. This work was supported by grants from the National Science Foundation and from the Welch Foundation. (28) D’Rozano, P.;Smyth, R. L.; Williams, A. J . Am. Chem. SOC.1984, 106, 5027.
(29) Skoog, M.T.; Jencks, W. P. J . Am. Chem. SOC.1984, 106, 7579. (30) Bourne, N.;Williams, A. J . Am. Chem. SOC.1984, 106, 7591. Williams, A. J . Am. Chem. SOC.1985, 107, 6335. (31) Kreevoy, M.M.;Lee, 1 3 . H. J . Am. Chem. SOC.1984, 106, 2550. (32) Albery, W. J. Annu. Reu. Phys. Chem. 1980, 31, 227. (33) Ritchie, C.D.; Kubisty, C.; Ting, G.Y .J. Am. Chem. SOC.1983, 105, 279.
