PHYSICAL ORGANIC CHEMISTRYl

By EDWARD R. THORNTON Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania The author, who considers himself to have interests typical of a physical organic chemist, found about 2300 papers published during the last year that were of special interest to him. He confesses that he could not possibly read them all and hopes that those whose work may have been left out by neces­ sity or oversight will understand the problems involved. Most of this review discusses secondary and solvent isotope effects. Mention is also made of recent developments in quantum chemistry, es­ pecially in the qualitative discussion of orbital symmetry as a determining factor for certain reaction pathways. It cannot be claimed that enough space was available for comprehensive coverage of even these restricted topics.

SECONDARY DEUTERIUM ISOTOPE EFFECTS A great deal of interesting information on secondary isotope effects has become available since the comprehensive review by Halevi (1) in 1963. Advances have been made in both experimental studies and theoretical un­ derstanding. Some of this new work, along with the present author's inter­ pretation of secondary isotope effects, will be discussed. Origin of secondary isotope effects.-A great deal of difficulty occurs in attempting to describe the causes of secondary isotope effects. Nevertheless, as far as the author knows, there is no case where an appropriate statistical treatment of isotope effects [Bigeleisen & Wolfsberg (2), Melander (3), Thornton (4)] does not adequately describe experiment. Even in terms of isotopic effects of the order of a few per cent, this theory and the approxima­ tions it uses are very precise. Qualitatively, the fundamental assumptions are that electronic, vibrational, rotational, and translational energies of a molecule may be treated as separate, so that the total energy of a molecule

by National Taiwan University on 04/09/13. For personal use only. is a sum:

E = E, + E. + Er + E, Because of this separability a molecular partition function may be written Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org as the product of electronic, vibrational, rotational, and translational partition functions:

Q = Q,Q.Q..Q. and, of especial importance, electronic energies of molecules may be calcu­ lated as a function of nuclear positions, the set of electronic energies so calculated serving as a potential-energy surface for nuclear motions (Born­ Oppenheimer approximation). In this (nonrelativistic) approximation, the

1 The survey of literature pertaining to this review was concluded in December 1965. 349 350 THORNTON electronic energy of any particular geometry of the molecule is dependent only on the charged particles (nuclei and electrons) which interact according to Coulomb's law, except for the very tiny (less than 0.1 per cent) effect produced by the fact that the kinetic energies of the electrons are determined not only by their masses but actuaIly by some sort of reduced mass of nuclei and electron for their relative motion with respect to the center of mass of the molecule-which, however, is a manifestation of the nonseparability of electronic and nuclear motions. For the simple case of a hydrogen atom, the m in Schrodinger's equation is replaced by the reduced mass J.L(1/J.L=11m. + I/mH) of electron and proton:

Therefore, the potential energy surfaces of isotopic molecules are essentially identical. Weston (5) gives some exceIlent examples showing no detectable difference. What this means is that isotope effects are determined only by the different energies of nuclear motions, which very directly involve the mass of the isotopic nucleus, and not by electronic energy differences. Nu­ clear motions occur in the vibrations, rotations, and translations of a mole­ cule; but, especially for large molecules with many other nuclei than the one(s) which is isotopicaIly substituted, isotope effectsare determined largely by vibrational energy level differences. This idea that isotopic effects on electronic energies are negligible is widely accepted, but is subject to misinterpretation unless great care is taken, for it is possible to interpret certain phenomena as if they were elec­ tronic in origin, even though it is implicitly understood that their real origin is largely vibrational. For example, the dipole moment of a molecule is usually thought of as an electronic property. Since the dipole moment changes slightly when a molecule vibrates, the dipole moment observed ex­ perimentally will be an average over all the vibrations [i.e., the sum or integral of : (the dipole moment of a given nuclear geometry) times (the probability of the molecule's having that geometry)J. Now, even though the by National Taiwan University on 04/09/13. For personal use only. dipole moment of, say, (CHs)sC- H is exactly the same as that of (CHshC-D if the nuclear geometries are exactly the same, the observed dipole moments

differ by (J.LD-J.LH)= +0.009 Debye unit [Lide (6)J. In the case of this sym­ Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org metrical molecule, the only vibration which can cause such a difference is the C-H or C-D stretching vibration, which could give a difference, (a) because for slightly anharmonic vibrations, the C-H bond is on the average slightly longer than the C-D band, and (b) because for a dipole moment which changed in a nonlinear fashion when the bond length was changed the greater "mean-square" amplitude of vibration of the C-H bond (caused by the greater vibrational energy of C-H than of C-D) would give different average dipole moments even if the vibration were strictly harmonic [See Halevi (1), pp. 114-19, for a lucid discussion, and Muenter (7) for more recent dataJ. PHYSICAL ORGANIC CHEMISTRY 351 It is worth repeating this conclusion : The different dipole moments arise because of different average geometries for (vibrating) isotopic molecules and not because of differences in electronic potential energy surfaces, which are in fact essentially identical for isotopic molecules. The average dipole moment is not a strictly electronic property and can be different for isotopic isomers.2 Aside from detailed theoretical analysis of small molecules, the only case known to the author where an almost strictly electronic property has been investigated is the elegant work of Traficante & Maciel (8), where the p9 NMR chemical shifts of m- and p-fluorotoluene and m- and p-fluorotoluene­ a,a,a-da were precisely measured:

m-F-C6HcCHa VS. m-F-C6HcCD,

p-F-CsHcCHa VS. p-F-CsHcCD. No difference was found between the meta compounds; the shift of the undeuterated para compound was 0.7 cps downfield from that of the deu­ terated para compound. Based on inductive and resonance effect estimates established by comparison with other substituents than methyl, it was ex­ pected that shifts of the order of 4 cps would occur if the observed secondary isotope effects in certain equilibria were purely electronic effects (8). The tiny observed effects indicate that purely electronic differences between the isotopic isomers ani essentially absent; the observed shift in the case of the para compounds is most reasonably ascribed to long-range coupling of the vibrations of the methyl and p-fluoro groups-a vibrational, not an elec­ tronic, effect. This case is about as close as one can hope to get to isolating the purely electronic effects from the average vibrational effects. Since the models of "steric" isotope effects of Bartell (9, 10) and "in­ ductive" isotope effects of Halevi (0), pp. 134-38] are in reality vibrational, not purely electronic, effects, it is desirable to describe these models in such a way as to make this fact clear. Bartell's argument is that, since the mean-square amplitude of vibration of D is less than that of H, D is on the average closer to the equilibrium bond

by National Taiwan University on 04/09/13. For personal use only. length r. than is H. Then, for example, decreasing the steric repulsions of H and D by other groups within the molecule (as in going from tetrahedral to planar bonding) will be favorable both to H and D, but will favor H more

Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org since it is farther from r. on the average and its repulsions by other groups wiII be especially severe when the bond has reached its maximum amplitude. Alternatively, this same effectcan be described by saying that decreasing the steric repulsion of H and D by other groups wiII decrease the curvature of the electronic-energy surface (and presumably increase the bond length slightly), i.e., decrease the vibrational force constant. Since the force con­ stant determines the vibrational-energy levels, the vibrational zero-point

• The term "isotopic isomers" is used to denote "molecules which differ only by isotopic substitution" (and not in spatial configuration, such as geometric, optical, or conformational properties). 352 THORNTON energy difference between H and D bonds will be decreased, which will be a more favorable energy change for H than for D:

Difference in zero·point energy == hC(WR - wD)/2

where w is in em-I. In the harmonic approximation

W = (1/27rc)(k/ f.l) 1/' where k is the force constant (identical for H and D because the electronic potential.energy surfaces are identical) and f.L is the reduced mass for the vibration (f.L would equal 1 for H and 2 for D if the vibrations involved only motion of H and of D, respectively). The zero·point energy difference (dZPE) is then:

LlZPE = hkl/2[(1/f.lH)1/2 - (1/f.lD)1/2]/41r

or, correcting f.L from atomic mass units to grams and k to millidyne A-t, giv· ing dZPE in erg moleculet, LlZPE 8:f 7 X 1013hk1/2/41r 1. and dZPE decreases with decreasing force constant. That these two descriptions are really of the same vibrational effect can be seen by considering the nature of Bartell's argument in quantum me­ chanical terms. Bartell's calculation is basically a perturbation calcula·

tion using the square of the (zero-order) vibrational eigenfunction 'lr2(x) = k exp (-x2/21;2), where x is the displacement of the proton or deuteron from

r., 1,2 is the mean-square amplitude of vibration, k is a constant, and 'lr2(x)

is the probability that the displacement will be x. Since 1,2 is greater for H than for D, there will be a greater probability of large values of x for H than for D. Bartell then considers the change in steric repulsion in going from initial state to finalstate as a potential-energy perturbation, which must be averaged over the probability function 'lr2(x).According to first-order per­ turbation theory, the kinetic energy will not change if the perturbation is

entirely a potential-energy function, so the change in electronic potential energy changes only the vibrational potential energy in this approximation.

by National Taiwan University on 04/09/13. For personal use only. Considered in this way, Bartell's average energy differences between H and D are vibrational, not electronic, changes. The electronic-energy surface of the system changes on going from initial to final state, but the changes are Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org exactly the same for H and Di i.e., the potential-energy surfaces for the initial state are identical for H and D, and the potential-energy surfaces for the finalstate are identical for H and D. Thus, Bartell's qualitative statement that the smaller average size of a C-D bond than of a C-H bond gives rise to an isotopic energy difference is identical to a statement that a force constant change will be "felt" more by H than by D because H vibrates into regions of greater x (since it has greater zero-point energy) . Halevi's model of the effectof bringing a positive point charge close to a C-H or C-D bond, considered as a dipole, is actually a similar type of perturbation treatment, as clearly pointed out by him [(1), p. 138]. His cal- PHYSICAL ORGANIC CHEMISTRY 353 culation, which neglects possible polarization of the C-H and C-D bonds by the point charge, is actually equivalent to using the zero-order electronic wave function for calculating the electronic potential-energy change and then using this perturbed electronic potential energy along with the zero-order vibrational wave function to calculate the vibrational-energy change. Halevi makes the following prediction. Assuming that, because a C-D bond is on the average shorter than a C-H bond, the electronic "density" on C is greater in C-D than in C-H, Le., D is electron-supplying relative to H, the placement of a positive charge near the carbon should stabilize C-D more than C-H. Thus, introduction of a positive charge should favor D more than H in rates or equilibria and give "inverse" secondary isotope effects. However, the Qualitative argument about the effect of the positive charge does not seem complete, because the interaction of a point charge with a dipole is proportional to the dipole moment, i.e., to separation of charge. It seems highly probable that charge separation is less for C-D than for C-H on the average, since C-D is on the average shorter than C-H. This difference in average bond lengths, of course, only occurs for anharmonic vibrations and not in the harmonic approximation, although average charge separation for C-D could be smaller in the harmonic approximation as a result of smaller mean-square amplitude of vibration if the dipole moment changed in a

proper, nonlinear fashion with displacement of H or D from r•. If charge separation, and therefore dipole moment, is less on the average for C-D, then for the following model where C is considered to be more electronegative than H: Ii-li+ Ii-li+ Il-li+ Ii-li+

C-H-> EB C-H VS. C-D-> EB C-D it is expected that the presence of the point positive charge will stabilize both C-H and C-D, but stabilize C-H more, thus favoring C-H and leading to "normal" isotope effectson rates or equilibria. On the other hand, for the following model where H is considered to be more electronegative than C: Ii+ Ii­ Ii+ Ii- 1i+1i­ by National Taiwan University on 04/09/13. For personal use only. C-H-> EB C-H VS. C-D-> E9 C-D it is expected that the presence of the point positive charge wi1\ destabilize

Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org both C-H and C-D, but destabilize C-H more, thus favoring C-D and lead­ ing to "inverse" isotope effects on rates or equilibria. Although there appears to be relatively little concrete evidence, studies of C-D stretching force constants in substituted monodeutero-benzene molecules [Steffa (11)] indicate that the polarization of the C-D bond (and therefore also of the C-H bond in undeuterated molecules) is in the sense:

Ii+ Ii- Ii+ Ii- C-D C-H 2. whereas, based on general electronegativity differences (C, 2.5; H, 2.0), one expects the opposite polarization. It seems possible that the nature of 354 THORNTON the bonding, and particularly of the hybridization, of the carbon may in­ fluence the C-H bond dipole. Thus, the qualitative argument that the smaller average dipole moment of C-D than of C-H gives rise to an isotopic energy difference is identical to a statement that a change in charge distribution in the molecule will give rise to a force constant change which will be "felt" more by H than by D because H vibrates into regions of greater x, i.e., greater bond dipole mo­ ment (since it has greater zero-point energy). The causes of secondary isotope effects can be summzrized in the follow­ ing way. The electronic potential-energy surfaces are essentially identical for isotopic isomers. The motions of the nuclei, and in particular the isotopic nuclei, are determined by this (identical) potential energy surface. C-H can have a longer bond length and a more polar bond than C-D, but this results simply from the fact that the motions of the heavier isotope, D, are more restricted by this potential-energy surface than are the motions of H. In this light, anharmonicity of vibrations can be significant in determining dif­ ferences between H and D, but it is still the same anharmonic surface which determines the motions of both H and D. The smaller "average size" of C-D than of C-H and the different "inductive" effect of C-D than of C-H are not separate effects; they arise just as described above. The solution of the problem of nuclear motion of H and of D on their potential-energy surface leads to predictions of isotope effects, isotopic differences in average bond lengths, and isotopic differences in average charge distribution in a bond, but all of these p.ffects are determined in the final analysis by the potential­ energy surface. It may be possible to use differencesin average bond lengths, for example, to predict isotope effects, but not because the differences in average bond lengths determine the isotope effects. Rather, it may be possi­ ble because both the isotope effect and the average bond lengths are de­ termined by the potential-energy surface and are therefore closely related, not directly, but indirectly through the fundamental determining factor, the potential-energy surface. While the above descriptions of Bartell's and Halevi's models are by National Taiwan University on 04/09/13. For personal use only. obviously oversimplified, the discussion brings out the fact that their models, which seem to be assuming that electronic differences exist between H and D, are really for vibrational effects. Halevi (1) has clearly demonstrated this Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org for his model; the confusing factor is his assumption that deuterium is more electron supplying than protium. It is hoped that the above discussion makes clear the connection between Halevi's idea and the idea of predicting isotope effects on the basis of force constant differences between initial and final states. Isotopic substituent effects.-Recently, an attempt has been made to con­ sider secondary isotope effects as qualitatively similar to ordinary sub­ stituent effects used by physical organic chemists to correlate and attempt to understand reaction mechanisms [Halevi (1); Streitwieser & Klein (12); Streitwieser, Verbit & Andrcades (13); Halevi & Ravid (14)]. While in a very precise sense, the isotope effects are analogous to ordinary substituent PHYSICAL ORGANIC CHEMISTRY 355 effects, there is one peculiarity of isotopic effects: the electronic energy sur­ faces of the substituted and unsubstituted isotopic molecules are essentially identical, whereas the electronic energy surfaces of other substituted mole­

cules (e.g., where, say, -Cl or - NO. is substituted for - H) must be much different, giving different equilibrium molecular geometries as well as force constants. The unique feature of isotopic substitution in the study of reac­ tion mechanisms is that isotopic substituent effects originate entirely from nuclear motions and are therefore much more easily analyzed theoretically. T�is easier theoretical study of isotope effects arises because molecular vibrations can be treated, to a high degree of accuracy, as "normal" vibra­ tions of a set of simple-harmonic or slightly anharmonic oscillators, whereas to study electronic energy effects requires solution of a very complex Schrodinger's equation, which even in the one-electron approximation must implicitly take account of the motions of other electrons and is very dif­ ficult to solve for accurate energies even of diatomic molecules, hopeless at present for polyatomic molecules. Given the fact that secondary isotope ef­ fects are entirely vibrational in origin, it seems unfortunate to discuss them in the same terms used for the effect of replacing ethyl by t-butyl. The latter effects must be discussed in terms of shifts in electronic potential energy, i.e., in the minimum of the potential-energy surface, in addition to shifts in vibrational energy, i.e., in the shape of the potential-energy surface near the minimum, but isotopic isomers have the same minimum and shape, so that shifts in electronic energy always cancel out in considering isotope effects, and only vibrational (force constant) changes need be considered at all. (In this discussion, differences in rotational and translational motions were not mentioned ; these must be considered in the case of isotope effectsas well as in the case of other substituent effectsbut will usually be rather small rela­ tive to vibrational effects of substituents except in unusual cases or in very small molecules.) Others have broken substituent effects up into various components in order to try to understand them more clearly [Hine (15); Leffler & Grun­ wald (16)]. The author will attempt to subdivide these effects differently in by National Taiwan University on 04/09/13. For personal use only. order to show qualitatively the difference between an isotope effect and an ordinary substituent effect. For clarity, a specific reaction will be discussed, but it will be obvious that the same discussion will apply to any reaction. Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org Consider the effect of substitutents on the ionization of benzoic acid : KH H-CeH.-CO.H � H-CeH.-CO.- + H+ Kn D-CeH.-CO.H P D-CeH.-CO. - + H+ KCl CJ-CsH.-CO.H ti CI-CeH.-C02- + H+ It is possible to break up the energies of these molecules into separate "effects" which will be labeled, for the un substituted acid, EH-R (translated as "the effect of H on the ring"), EcOOH-R, ER-H, ER--COOH, EH-coOH, and EcOOH-H; for the deuterated acid, ED-R, EcOOH-R, ER-D, ER-COOH, ED-COOH, 356 THORNTON

and EeOOH-Di for the chlorinated acid, Eel-R, EeOOH-R., ER-ch ERr-COOH, Eel-COOH, and EeOOH-CI. Note that some of these effects, such as EcoOH-R, occur for all three acids and are by definition equal. This subdivision will be exactly correct as long as the "interaction" terms such as Eel-COOH and EeOOH-c1 are included. In considering the equilibria, we have terms for both reactant and product, some of which are equal and cancel:

6.EH = EOOO_R - BeOOH-R + ER-COO - ER-OOOH + EH-COO - EH-OOOH + EeOO-H - EeOOH-H

6.ED = BeOO-R - BeOOH-R + ER-OOO -ER-oOOli + ED-COO -ED-COOH + ECOO-D - ECOOH-D

6.BeI = BeOO-R - BeOOH-R + ER-COO - ER-COOH + Eel-ooo - ECi-COOH + Ecoo-cl - BeOOH-Cl These "effects" may be loosely thought of as free energies or average energies. Now KH/KD will be determined by (an exponential function of) LlEH-LlED and KH/KCl by LlEH-LlEel:

6.EH - 6.ED = EH-COO - Ev-eoo - EH-COOH +ED-COOII + Ecoo-II

- ECOO-D - EcoolI_1I+ BeoolI-D

6.ER - 6.Em= ER-COO - Em_coo - ER-COOH + Eel-cooR + Ecoo_JI - EOOO-Cl - ECOOJI-JI + BeOOJI-Cl Since the isotopic isomers have the same potential-energy surface, EH..;.coo = ED-COO and EH-COOH=ED-cOOH, i.e., the effect of H on CO2- (or C02H) is the same as the effect of D on CO2- (or C02H) because the CO2- (or C02H) group will have the same potential-energy surface whether the substituent is H or D. In contrast, EeOO-H"eEeOO-D and EcOOH-H ;eEcOOH-D because, although the potential surface of each molecule is the same for H and D, their energies will not be the same because of vibrational (largely zero-point energy) differences between H and D. Furthermore, the difference BeOO-H -EeOO-D is not expected to be the same as EeOOH-H-EcoOH-D because the entire potential energy surface (including the part near H and D) will be different for the product anion containing a CO2- group than for the re­ by National Taiwan University on 04/09/13. For personal use only. actant acid containing a C02H group. Therefore, the isotope effectsimplifies to 6.EH - tJ.ED = Beoo-H - BeOO-D - BeOOH-H + EcOOH-D Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org and is determined almost entirely by the relative effects of the groups CO2- and C02H on the vibrational energy difference between H and D. The isotope effect is an effect on the isotopic substituent rather than an effect of the isotopic substituent. No such simplification occurs in the case of the chlorine effectLlEH -.:lEeh and, in fact, this subdivision of "effects" shows clearly a point that is not often considered in discussing substituents effects: the effect "of" a substituent is really composed of effects of the substituent on the reaction site groups COr and C02H and the effects of the reaction site groups on the substituent. It would seem to be the crudest of approxima­ tions to consider effects of a substituent and neglect effects on a substituent PHYSICAL ORGANIC CHEMISTRY 357 as we frequently do implicitly. When we say that Cl is electron-withdrawing relative to H, we mean that it tends to stabilize the production of negative charge more than H does. This effect is presumably reflected in a stabiliza­ tion of CO2- relative to C02H by CI as opposed to H and/or a stabilization (or destabilization) of. Cl relative to H by CO2- as opposed to C02H (e.g., the C-CI force constant may be weakened in going from reactant to product -a destabilization). In other words, it is largely because of net changes in the electronic structure of the whole molecule that the substituent has any effect different from Hj vibrational changes occur simultaneously, but these are usually thought to be small relative to electronic changes and are ignored. These mutual interactions are certainly worthy of further thought. It will be noted that the isotope effect is not quite so simple as set forth above, because, even though H and D have the same effect on the electronic energy surface, it is conceivable that there could be a small effect of H versus D if there were strong coupling between the vibrations of H or D and CO2- or C02H-but even this is a vibrational effect, not an electronic effect. This kind of effect might be expected to show up clearly in secondary isotope effects on bond lengths. The difference in root-square carbon-halogen bond lengths has been measured for CHa-Cl versus CDa-Cl and for CHa-Br versus CDrBr by Schwendeman & Kelly (17), who find the deuterated molecules to have shorter bond lengths: the difference for C-Cl is 0.0008 A±O.OOOl, for C-Br, 0.0011 A±o.oOO1. They believe the most probable cause of this effect is a rotation-vibration interaction and not a failure of the Born­ Oppenheimer approximation. These exceedingly small effects,in a case where the halogen atom is directly bonded to the carbon atom which is substituted with deuterium and where the molecule is a very small one, suggest that, for larger molecules, effects of deuterium such as EU-COOH- ED-coOH will be completely negligible (though it will be recalled that a vibrational effect of deuterium seems like the most reasonable explanation for the p9 NMR shift observed (8) by Traficante & Maciel). Secondary isotope effects on root-mean-square amplitudes of vibration are unlikely to produce shifts in mean distances greater than a few ten-thousandths of an angstrom unit, by National Taiwan University on 04/09/13. For personal use only. according to Bartell (18). Inductive and steric isotope effects.-A few examples of the application of "force constant shift" terminology as opposed to "substituent effect" Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org terminology will illustrate some advantage in the former. The only example of this approach which is completely grounded in experiment is the very significant calculation of the relative acid dissociation constants of HC02H and DC02H, giving reasonable agreement with experiment by Bell & Crooks (19). Using values of the fundamental frequencies observed for HC02H, DC02H, HC02-, and DC02- by other workers, an isotope effect KH/KD of

1.09 was calculated. The experimental results bracket this, 1.06 [Ropp (20)],

1.12 [Bell & Ballund-Jensen (21)], 1.07 [Streitwieser & Klein (12) , and 1.084 [Bell & Miller (22)]; since the latter investigation was most careful and took care of activity coefficients explicitly, the agreement between theory and 358 THORNTON

experiment can be considered excellent. The calculations reveal two impor­ tant points: The calculated isotope effect receives a significant contribution from the rotational and translational partition functions, an expected phe­ nomenon when dealing with small molecules whose moments of inertia and molecular masses may be changed by a large fraction on substitution of D for H. Also, the vibrational contributions come not only from the C-H or C-D stretching and (two) bending vibrations, but also from a variety of others; the only mode not giving any appreciable contribution is the O-H stretching vibration of the acid. The shifts in the other (non-C-H) fre­ quencies upon deuteration are effects of deuterium; certainly a reaction such as this where the isotopic substituent is directly attached to the reaction site is where one would expect such a vibrational coupling effect. It is in some ways distressing that these effects are so large, however. For example, if one calculates approximately the expected isotope effect using only the three C-H and C-D vibration (stretch and two bends) differences in zero­ point energy, the isotope effect turns out to be ca. 1.25, as noted by Halevi [(1), p. 156]. This result arises from the fact that the isotopic frequency ratios for these three vibrations are not all close to the value 1.41 (square root of 2) expected for simple harmonic bond vibrations : for the acids

WH/WD ratios are 1.32, 1.44, and 1.19; for the anions, 1.33, 1.35, and 1.16. The ratios (especially for the out-of-plane C-H bend) are in general con­ siderably less than 1.41, a result caused by the fact that coupling with some of the other vibrations takes place, so that WH/WD ratios for the other vibrations (such as the C-O stretch, etc.) are not equal to ca. 1.0 as expected for simple harmonic bond vibrations of bonds that are not isotopically substituted. In other words, some of the 1.41 ratio expected for the C-H /C-D bond vibrations is "incorporated" into other molecular vibrations through coupling (because, of course, the normal vibrations of the molecule as a whole are not simple bond vibrations and in general involve simultaneous vibration of more than two nuclei). It is very interesting that if one uses the three C-H vibrations of the acid and the three of the anion, but calculates the C-D vibration frequencies assuming WH/WD is 1.414, the calculated by National Taiwan University on 04/09/13. For personal use only. isotope effect (based on zero-point energy differences only) is 1.067 versus the best experimental value of 1.084± .005 and the effect calculated rigor­ ously by Bell & Crooks of 1.09. It is difficult to speculate whether such a Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org simplification is justified or fortuitous; theoretical calculations to be dis­ cussed below indicate that results obtained by neglecting completely all atoms more than two bonds distant from the point of isotopic substitution are essentially identical to those obtained by including all atoms of the molecule in the calculation, provided only that the valence force constants retained in the "cut-off" calculation are identical to those used for the com­ plete molecule [Wolfsberg & Stern (23)]. I t is also of interest to note that the use of experimental infrared or Raman bands (which of course correspond to the energy of excitation from the lowest to the first excited vibrational level of each normal mode) in a PHYSICAL ORGANIC CHEMISTRY 359

calculation like that of Bell & Crooks tends to help correct for anharmonicity when the vibrational partition function ratio is evaluated ; anharmonicity is difficult to include explicitly because an extensive vibrational analysis of observed spectra is necessary to evaluate it even in the simple case of diatomic molecles. On the other hand, when the Redlich-Teller product rule is used for evaluating rotational and translational isotopic partition func­ tions ratios, the use of the experimental frequencies rather than the zero­ order frequencies introduces some error, but this error should probably be considerably smaller than the improvement gained by using the observed frequencies in evaluating the vibrational partition function.

Isotope effects for a series of other acids have been measured by Streit­ wieser & Klein (12): KH/Kn for CHgC02H/CDgC02H is 1.03; for (CHa)aCC02H/(CDa)aCC02H, 1.04; for C6H6C02H/C6D6C02H, 1.02; and

for CeH6C02H/2,6-DrC6HaC02H, 1.01. Qualitatively, if the C-H and C-D bonds were polarized in the sense: 0-0+ C-H it would be expected that ionization of the acid to its anion would tend to increase the stretching force constant and favor deuterium in the anion (Cf. Eq. 1.), leading to KH/KD> 1 in contrast to experiment. The only acid for which complete spectral data are available is formic, discussed above, for which KH/Kn> 1 also ; Weston (5) mentions that the C-H stretching frequencies are lower in the anion of acetic acid than in the acid. Since C-H stretching frequencies decrease on going to the anion in both formic and acetic acids, it may be that in both cases C-H bond is polarized in the op­ posite sense. Because of vibrational coupling effects in formic acid, the iso­ tope effect is, of course, not determined merely by the C-H stretching force constant change. A more detailed analysis of other acids and their anions, to determine whether the C-H force constants increase or decrease on ionization, would be very interesting. Streitwieser & Klein (12) also report on the isotope effects for solvolysis of benzhydryl chloride (C6H5)2CHCl versus a series of ring-deuterated

by National Taiwan University on 04/09/13. For personal use only. benzhydryl chlorides in 80 per cent acetone-20 per cent water (by volume before mixing) at 25° ; the effect is inverse, kD/kH being 1.018 per ortho D, 1.014 per meta D, and 1.010 per para D. These effects seem explainable as Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org inductive effects on the C-H (C-D) force constants giving rise to a net in­ crease in these force constants on going to the transition state. Similar in­ verse effects, of nearly the same magnitude, are found for the equilibrium ionization of ring-deuterated triphenylmethyl chlorides to the triphenyl­ methyl cations [Kresge, Lichtin & Rao (24)]. It should be noted, however, that several vibrational frequencies involving the C-H (C-D) bonds change significantly on ionization [Tsukamoto & Lichtinj Weston (25)], and it is not yet clear what kinds of force constant changes occur, because of exten­ sive coupling of vibrations and the complexity of the spectra. Neverthless, a preliminary analysis (25) indicates that the spectral shifts are in the right 360 THORNTON

direction and of approximately the right magnitude to account for the ob­ served isotope effects. That this ionization equilibrium is indeed very interesting is further shown by the fact that the carbon-13 isotope effect for the central carbon atom is inverse also, even though this carbon is going from a tetravalent to

a trivalent state upon ionization (KI2/KI3 = 0.983) [Kresge et al. (26)]. The inverse effect is well understood; it results from a substantial increase in force constants for the bonds from the phenyl rings to the central carbon upon ionization, more than offsetting the complete loss of (the zero-point energy of) the carbon-chlorine bond. The effect of replacing one CHa group by a CD3 group upon the ioniza­ tion equilibrium of triphenylmethyl chloride

(CsHshC(CI)CsH4CDa - p p (CsHshC+C6H4CDa - P + Cl-

is rather small; KH/Kn is ca. 1.008 (all these equilibria were studied at 0° in 502 solution) [Lichtin et al. (27)]. This effect can be explained by a com­ petition between hyperconjugative and inductive effects giving a net de­ crease in force constants associated with the methyl group upon ionization. It is not clear, however, whether hyperconjugation must be invoked here; it is conceivable that the direction of the inductive effectmay be reversed on going to a carbonium ion (with a full positive charge). Although electron withdrawal near carbon is expected to increase the force constant if the C-H bond is polarized with H more negative than C as in Equation 2, very strong electron withdrawal must eventually reduce the electron probability density in the C-H bond to the point where the bond is weakened and the force constants presumably reduced. The formation of ?r-complexes between toluene and chloranil [Halevi & Nussim (28, 29); Halevi (1), pp. 165-67] and between toluene and HCI [Halevi & Ravid (14)] has been studied. For the chloranil complex, a CDs group in toluene leads to a KH/ Kn of 1.07 for the association equilibrium; for the HCI complex, a KH/Kn of 0.98. Ring-deuteration of toluene or use of C6D6 versus C6H6 leads to inverse effects (KH/Kn <1). It might be ex­ by National Taiwan University on 04/09/13. For personal use only. pected that steric effectsof inhibiting and thus increasing the force constants of bending vibrations on going to the ?r-complex would be the major de­ termining factor leading to inverse isotope effects as observed for the HCI Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org complexes. The steric factors should be even more important in the chloranil complex, since chloranil is larger than HCI, but in fact the isotope effect is in the reverse direction. Recent experimental work indicates, however, that the measured effects in these cases may result entirely from deviations from Beer's law by the ?r-complex [Emslie et al. (30); Emslie & Foster (31)]; in particular, for the complexation of 1,3,5-trinitrobenzene with benzene and benzene-de, no isotope effect was detected by sensitive, nonoptical NMR. measurements [(31); Foster & Fyfe (32)]. A number of examples of steric kinetic isotope effectshave been reported [Mislow et al. (33); Melander & Carter (34) ; Raaen & Collins (35); Horeau, Nouaille & Mislow (36)]. In each case, it is found that increasing steric strain, PHYSICAL ORGANIC CHEMISTRY 361

as, e.g., in the transition state for racemization of biphenyls (33, 34), favors deuterium over protium. These steric isotope effects are reasonably ex­ plained by the hypothesis that increased steric strain should lead to in­ creased force constants, presumably for C-H bending. Theoretical calculation of secondary isotope effects.�While a number of approximate calculations of isotope effects have been made, it has not been possible until recently to make good calculations for even the "simplest" organic molecules. The use of digital computer programs has made it possible to make complete calculations in the transition state approximation for large molecules, using only molecular geometries, atomic masses, force constants, and the temperature(s) as input data [Wolfsberg & Stern (23)]. It has been found that the isotope effect depends largely on force constant changes at the isotopic position(s) on going from reactant to transition state. This finding has led to the "cut-off" procedure (23) discussed above and demonstrates quantitatively that in analyzing secondary isotope effects qualitatively, the effect of changes in the rest of the molecule upon the elec­ tronic potential-energy surface in the vicinity of the isotopic substituent (and thus on force constants in that vicinity) is of prime importance. Further studies [Wolfsberg & Stern (37)] show that, aside from possible effects of changes in mass and moments of inertia on going from reactant to transition state, or more precisely in ptlL/pt2L, the ratio of "frequencies" for the imaginary reaction coordinate vibration, negligible isotope effects (at or above room temperature) result from changes in the coupling of bond and bond-angle vibrations�as long as the force constants involving the isotopic atoms do not change. Since ptlL/pt2L � 1, small isotope effects in the direc­ tion favoring a light over a heavy element (e.g., kH/kD > 1) may in some cases result almost entirely from that imaginary frequency ratio. Almost any observable isotope effect may be explained by suitable force constant changes (37), and even the temperature dependence may be re­ produced. For example, a rather large (and therefore partly of vibrational origin) temperature-independent isotope effect may be obtained "if some force constants which give rise to small frequencies (e.g., those correspond­ by National Taiwan University on 04/09/13. For personal use only. ing to torsions) in the reactant become larger in the transition state while some 'large' force constants which give rise to large frequencies (e.g., those corresponding to stretches) in the reactant become smaller in the transi­ Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org tion state" (37). This sort of explanation seems to be required to explain the lack of temperature dependence of secondary .a-deuterium isotope effects in hydrolysis of isopropyl compounds, although in the case of t-butyl-d9 chloride the isotope effect is very temperature dependent, having no temperature­ independent component at all [Hakka, Queen & Robertson (38)]. The differ­ ent temperature dependence of these isotope effects may indicate that the t-butyl and isopropyl compounds hydrolyze by different mechanisms, possibly SNI and SN2, respectively (38). It is possible to estimate stretching force constants and even their anharmonicities quite accurately based on "Badger's Rule "[Herschbach & Laurie (39)]. This same rule applies to nonbonded interactions [Johnston 362 THORNTON (40)]. Unfortunately, no such rule exists at present for bending vibrations, but hopefully some kind of empirical generalizations will eventually arise. It is sometimes difficult to decide from the magnitude of a deuterium isotope effect whether it is primary, i.e., involves bond-making or -breaking at the isotopic atom, or secondary. Causes of "small" primary hydrogen isotope effects have been discussed by Westheimer (41) and by Bader (42). The exact nature of this problem has been clarified by Willi & Wolfsberg (43) and by Bigeleisen (44), perhaps the most important points being that such effects are expected to be "large" (with kH/kD > 1, of course) for wide changes in the relative amounts of bond-making and bond-breaking at the transition states for proton transfer and that, on the other hand, it is not impossible to have even an inverse primary effect if bending or stretching force constants, or both, are larger than in the reactant and the transition state is reactant-like or product-like. There appears to be only one case in the

literature of an inverse primary isotope effect (kn/kD = 0.85 for decarboxyla­ tion of P-CH3C6H4COCH2C02D, a (j-keto acid) [Swain et al. (45)]. Thus, even the observation kH/kD < 1 does not prove the isotope effectis secondary. Theoretical calculations on the possibility that nonbonded repulsion

changes may determine secondary a and {j deuterium isotope effects have been made by Bartell (9, 10), as discussed above. Effects comparable in magnitude to those observed experimentally in "SN1" solvolyses were pre­ dicted, leading Bartell to speculate that the fJ effects, usually attributed to hyperconjugative interaction between the fJ C-H bonds and the developing p orbital of the incipient carbonium ion, might really be of steric origin. Shiner & Jewett (46) determined that the apparent isotope effect kH/kD for axial (3 deuterium in the solvolysis of cis-4-t-butylcyclohexyl-trans-2-d p­ bromobenzenesulfonate (brosylate) in 50 per cent ethanol-50 per cent water (by volume before mixing) at 35° was 1.436, the largest secondary {j isotope effect known for a single deuterium substituent. For the equatorial (3 deuterium in the corresponding -cis-2-d brosylate, kH/kD was only 1.096. The value 1.436, being ten times greater an isotope effectthan that calculated by Bartell for a single deuterium atom, was believed to eliminate the simple by National Taiwan University on 04/09/13. For personal use only. steric model as the cause of of the isotope effect.The very differenteffects for axial and equatorial deuteration were thought to support the hypercon­ jugation postulate, which predicts orientational effects of this type for Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org orbital overlap. Recent elegant experiments by Shiner & Jewett (47), in which separate and different isotope effects were determined for each of the four (3 deuterium atoms in cis-4-t-butyl-cyclohexyl brosylate, indicate, how­ ever, that neighboring group participation by one axial (3 deuterium atom occurs. Thus the largeness of isotope effect used to rule out Bartell's sterk model is really caused by the neighboring group participation (a primary isotope effect); the simple steric model is not ruled out for the other three (nonparticipating) (3 deuterium atoms. Shiner & Jewett think of participa­ tion of hydrogen as an extreme form of hyperconjugation; they feel that the only reasonable explanation of their data, including lack of rearranged solvolysis products, is formation of an unsymmetrical, bridged, nonclassical PHYSICAL ORGANIC CHEMISTRY 363

carbonium ion. Since the major solvolysis product is olefin, however, it seems difficult to rule out competition between elimination involving con­ certed loss of {3 deuterium (rather than bridging) and another reaction, possibly without bridging, leading to alcohols and ethers. The fact that the olefin fraction is not appreciably lowered on deuteration of all four {3 posi­ tions is difficult to explain with any mechanism, except perhaps the non­ classical bridged-ion hypothesis or initial formation of olefin followed by re­ action of olefin with water or alcohol (unlikely). Using a method developed by Shiner, Murr & Heinemann (48), the isotope effects for each type of {3 deuterium in the transition state model involving bridging could be calcu­ lated (47) (1.07) (2.2) H H H

ja ,/ ' ,/" C C ------\ ----- I I /- I H OBs (0.96) where a represents axial, e, equatorial and the kH/ kD factors are in parentheses adjacent to the respective protons. The solvolysis of t-butyl chloride is, on the other hand, very probably concerted in the sense that all three methyl groups are very nearly equivalent in the transition state (48) . An operational distinction between "hyperconjugation" (cumulative isotope effects from equivalent reactant C-H bonds) and participation (noncumulative) is thus provided by {3 deuterium isotope effects (47). Solvolyses of trans-4-t-butyl­

cyclohexyl brosylate [Shiner & Jewett (49)] and of cyclohexyl tosylate [Saunders & Finley (50)] seem to proceed by way of a non-chair, probably

twist-boat , conformation of the rings in the transition states. The extent to which the hyperconjugative effect may be important in determining {3 deuterium isotope effects or other phenomena frequently ex­

by National Taiwan University on 04/09/13. For personal use only. plained by hyperconjugation is the subject of considerable controversy [see, for example, Dewar (con) (51) ; Ehrenson (pro) (52)]. There is good evi­ dence that {3-deuterium isotope effects are stereospecific, i.e., that their

Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org magnitude depends upon the orientation of the C-H or C-D bond-pre­ sumably with respect to the incipient p orbital of a carbonium-ion-forming transition state [Shiner & Humphrey (53)]. It does not seem completely im­ possible, however, that increase or relief of nonbonded interactions on going from reactant to transition state could account for stereospecificity. That nonbonded interactions are not the only determining effect is made clear by experiments by Shiner & Kriz (54) on deuterium substitution insulated from the carbonium-ion-like center by a carbon-carbon triple bond: (CH.).C(CI)-C=C-CD. (CD.).C(CI)-C=C-CHa

kH/kD = 1.092 kH/kD = 1.655 isotope effects being given relative to undeuterated compound at 25° in 80 364 THORNTON

per cent ethanol-20 per cent water (by volume before mixing). The rela­ tively large 0 isotope effect, though much smaller than the (:3 effect [1.092 vs. (1.655)1/2 ""'1.29], clearly is too large to be of steric origin and must presum­ ably arise from electronic effects. It is difficult to decide whether the effect is hyperconjugative or inductive, though the hyperconjugative explanation is favored by the authors (54). Study of substituted l-phenylethyl chlorides and bromides and of substituted benzhydryl chlorides in acetone-water and

ethanol-water mixtures shows "markedly different sensitivity" of a and (:3 deuterium isotope effects to the above variables [Buddenbaum (55)]. The (:3 deuterium isotope effect in the solvolysis of 1-phenylethyl bromide is very similar to that for the chloride; the fJ deuterium isotope effect is reduced by electron-releasing ring substituents in solvolysis of 1-phenylethyl chlorides (56). Based on presently available facts, the so-called inductive effect of deuterium is very reasonably described as an inductive effectof other groups on the force constants which determine the vibrational frequencies for protium and deuterium.

Other secondary deuterium isotope effects.-Secondary deuterium isotope effects on the association equilibria of deuterated oletins with silver ion are inverse (deuteration increases complex stability) for a number of olefins [Cvetanovic et al. (57)] and can perhaps be best explained by increased force constants for "out-of-plane" bending in the complex. Reactions (SN2) of three trialkylamines (ca. 0.89) and pyridine (0.919), 2-methylpyridine (0.877) and 2,6-dimethylpyridine (0.876) with CHaI versus CDaI gave the weak inverse isotope effects, k-H/kD' shown in parentheses, in benzene at 50° [Leffek & MacLean (58)]. The isotope effect for the reaction with 2-methyl­ pyridine was shown to be essentially temperature-independent with very high precision (58). Increased steric hindrance by the nucleophile in the transition state might be expected to increase C-H bending force constants, leading to the inverse isotope effects. The great difference in steric hindrance between pyridine and 2,6-dimethylpyridine leads to only a modest change in isotope effectfrom 9 per cent to 14 per cent; this can be partly explained by by National Taiwan University on 04/09/13. For personal use only. the hypothesis that increased steric strain causes the transition state to be­ come more product-like, so that as steric interaction with the nudeophile increases, steric interaction with the leaving iodide ion decreases. A con­ Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org tribution from an inductive effect cannot be ruled out, however; in fact, a decrease in C-H stretching-force constants as a result of an inductive effect, coupled with an increase in C-H bending-force constants as a result of steric effects, may explain the temperature-independence of the isotope effect [See Wolfsberg & Stern (37)]. A great deal of other work on secondary deuterium isotope effects has been published recently. This includes studies of exo­ norbornyl bromide [Schaefer & Weinberg (59)]; endo-norbornyl brosylate [Lee & Wong (60)]; 1,1-dimethylallyl-3,3-d2 and 3,3-dimethylallyl-1,1-d2 chlorides [Belanic-Lipovac, Borcic & Sunko (61)]; 2-(Ll3-cylopentenyl)ethyl tosylate [Humski, BorCic & Sunko (62)]; 2-cyclopentylethyl, 2-(A2-cyclo- PHYSICAL ORGANIC CHEMISTRY 365 pentenyi)ethyl, and 2-(A3-cyclopentenyl)ethyl p-nitrobenzenesulfonates [Lee & Wong (63)]; a-phenylethylazomethane [Seltzer & Dunne (64)]; acetyl peroxide and two t-butyl peresters [Koenig & Brewer (65)]; 2,4- dinitrophenyl phenyl ether reacting with piperidine [Pietra (66)]; decomposi­ tion of the Diels-Alder adduct of maleic anhydride and 2-methylfuran [Seltzer (67)]; cyanoethylenes reacting with deuterated anthracenes [Brown & Cookson (68)]; 2-phenylethyltrimethylammonium ion reacting with hydroxide ion [Asperger, Klasinc & Pavlovic (69)]; N-methylaniline-N-d reacting with 3-chloro-l-butene [Dittmer & Marcantonio (70)]; propylene reacting with D2SOcD20 [Ehrenson, Seltzer & Diffenbach (71)]; benzyl and 2- and 3-thienylmethyl chlorides [Ostman (72)]; N -methyl-2,4,6-trinitro­ aniline reacting with N02+ [Halevi, Ron & Speiser (73)]; methyl isocyanide [Rabinovitch, Gilderson & Schneider (74)]; 2-hexyl and 2-octyl free radicals [Pearson, Rabinovitch & Whitten (75)]; and ethyl acetate-da hydrolysis, which show a temperature dependence giving a minimum isotope effect at 35°, possibly implying a change of mechanism [Halevi & Margolin (76)]. SOLVENT ISOTOPE EFFECTS The role of the solvent in solvolysis is a continuing problem. Disagree­ ment still exists over the nature of the initial-state and transition-state solvent shells in hydrolysis and the way solvation effects determine the solvent isotope effectsfor hydrolysis in H20 versus D20 [Laughton & Robert­ son (77)]. Isotope effects upon initial states were determined by measuring the solubilities of methyl halides [Swain & Thornton (78)] and t-butyl chloride [Clarke, Williams & Taft (79)]; in each case there was practically no isotope effect, i.e., KH/ KD for the following equilibria was nearly unity (hypothetical perfect standard states in parentheses) : KH ) RX(gas, 1 atm) E RX(H20 solution, 1 M) Kn ) RX(gas, 1 atm) E RX(D20 solution, 1 M) The "transition state isotope effe�ts" could then be calculated directly from by National Taiwan University on 04/09/13. For personal use only. the solubility isotope effects and the observed kinetic isotope effects for hydrolysis (78). A derivation using different standard states than originally used (78), which is exactly equivalent to that originally used except for the Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org different standard state definitions, makes the meaning of the transition state isotope effects more clear: KHt RX(H20 solution, 1 M) ( ) RXt(H20 solution, 1 M) KDt ) RX(D20 solution, 1 M) E RXt(D20 solution, 1 M) In the above equilibria, RX� is the transition state, and if the mechanism is SN2 the H20 or D20 nudeophile is simply considered to be one of the water molecules solvating the transition state. Thus, no assumption is being made about the reaction mechanism; and the transition state isotope effect, de- 366 THORNTON fined below, will include the isotope effects for interaction, whether covalent or weak solvation, of the transition state with all surrounding solvent molecules. According to the above equations KH; kH --=- KDt kD where kH/kD is the experimental kinetic isotope effect, i.e., the ratio of first-order rate constants (determined at effectively infinite dilution). Then KH kH (RXt)H,O KHTS = KD kD (RXt)D2o KDTS where KHTS RX*(gas, 1 atm) ( ) RX*(H20 solution, 1 M) 3. KDTS RX*(gas, 1 atm) ( ) RX*(D.O solution, 1 M) 4. The transition state isotope effectK HTS/KDTS can be seen to be numerically equal to the transition-state isotope effect calculated by Swain & Thornton (78) and is also, of course, exactly equivalent to the equilibrium constant

D.ORX*(D.O solution, 1 M) + H20(H20 solution, 1 M)

<=' H.ORXt(H.O solution, 1 M) + D.O(D.O solution, 1 M) 5. which was defined by explicitly including a "solvating" nucleophile in the equation but including other solvating molecules implicitly; this equilibrium, of course, assumes the mechanism is SN2. Note that pure H20 has almost exactly the same molar concentration as pure D20, so that the standard­ state convention does not affect the equilibrium constant of Equation S. That the two numerically-equal isotope effects (Eqs. 3 & 4 and Eq. 5) are exactly equivalent can be seen as follows. Both isotope effects measure precisely (only) the difference in solvation energies of the transition state in H20 versus 020, including the "general solvation" as well as any specific nucleophilic isotope effect, relative to unperturbed solvent molecules in pure bulk (or infinitely dilute) H20 or 020.

by National Taiwan University on 04/09/13. For personal use only. Thus, these transition state isotope effects do indeed measure differences between the transition states in H20 and 020, and it can be concluded,from the facts that, e.g., for three methyl halides, KH/KD �1.0, kH/kD�1.3, and

Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org KHTS / KDTS �1.4 (78), that the kinetic isotope effect is almost entirely caused by isotopic solvation differences between the transition states in H20 versus D20. Laughton & Robertson (77) based their argument on the incorrect equations:

RX (gas) + H20 p RX(in H20)

which have inadvertently included H20 and D20 molecules explicitly on the left-hand sides but not on the right-hand sides. The equilibria should be expressed in the following form: RX(gas) + D20(?) p RX(solution in D20) + D20(solvation, in D20) PHYSICAL ORGANIC CHEMISTRY 367 Though the standard state was not specified, it must be liquid water (at 1 M, 55.5 M, or unit mole fraction) if the isotope effect is to be numerically equal to the solubility as defined(78) ; if it were gaseous water, the activity of water would have to be included in the calculation of the solubility constant.

It would seem more appropriate to include ca. 20 water molecules (78) and not just one in the above equation, however. With a consistent definition of the equilibrium, the free energies of solution then become:

I:J.Fn,o = F(solution of RX in D20) + F(D20 solvating RX) - F(RX gas) - F(D20 liquid)

I:J.FH,O = F(solution of RX in H20) + F(H20 solvating RX) - F(RX gas) - F(H20 liquid) After the inclusion of terms for D20 and H20 solvating RX, which will be nearly equal to the terms for H20 and D20 liquids, it becomes clear that F(solution of RX in D20) - F(solution of RX in H20) will be small. The solvation isotope effect has simply been broken up into terms for the "solu­ tion of RX" and for the difference between a "solvating" water molecule and a "liquid" water molecule. Although it is quite true that there is a substantial difference in free energy between the solvation shells of RX in H20 and D20 (relative, say, to the separated H and 0 or D and 0 atoms, respectively), it is not customary to include such factors when speaking of a solvation effect. A solvation free­ energy effect is usually defined as the difference in free energy between the solvated solute plus its solvating molecules and the nondissolved solute plus bulk liquid molecules, in contrast to the implicit definition of Robertson & Laughton (77) . The solvation (using the customary definition) differences between the two transition states (in H20 and in D20) are therefore greater than those be­ tween the initial states. Other differences of interpretation (77, 78) are largely semantic, except one, where Robertson & Laughton have pointed out a flaw in our (78) argument : Although the initial-state isotope effectsare near unity and seem by National Taiwan University on 04/09/13. For personal use only. to indicate no change in water structure upon solution of methyl halides, the partial molal volumes, entropies, and heat capacities for the solution process indicate that the process is not so simple. To explain the small isotope effects Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org along with the other effects, it seems necessary to hypothesize that some force constants (possibly for hindered rotations or translations of solvating water molecules, or both) decrease while others increase. Robertson & Laughton (77) look upon the process of going from initial to transition state in hydrolyses of alkyl halides as akin to "melting" of water molecules "frozen" around the reactant. We (78) look upon this process as akin to "boiling" of water molecules present in "melted" form around the reactant. The net changes are the same; the only question is the status of the reactant solvation shell. The measurements of isotope effectson solubilities (78) seem to establish that at least with regard to isotope effects, the "boiling" hypothesis is more nearly realistic. The isotope effects of 368 THORNTON

Laughton & Robertson (77) on alkyl fluorides are very interesting, being nearly the same as for other alkyl halides. They (kH/kn) would be expected to be lower since fluoride ions (partly formed at the transition state) increase water stucture, while other halide ions decrease water structure. It is difficult to decide what this effectcould be in individual cases, however, because the effective amount of carbon-halogen bond breaking at the transition state may differ for fluoride versus other halides. In addition, the initial state iso­ tope effects shouldbe known; the only fluoride for which data are available is methyl fluoride (78). The fact that the isotope effect kH/kn for hydrolysis of t-butyl chloride decreases from 1.35 in H20 versus D20 to 1.05 in 60 per cent dioxane-40 per cent H20 or D20 (by volume before mixing) [Craig et al. (80)] does not seem necessarily to indicate that the solvation shell is "frozen" around the re­ actant in water [See (4), pp. 225-26], although it may indicate that initial state structure is lost on going to the transition state. It is interesting to note the small, though real, changes in ionization constant isotope effects for acetic acid and water (self-ionization) on going from water to dioxane­ water mixtures [Gold & Lowe (81)]. It seems likely that the observation of isotope effects upon heat ca­ pacities of solution of simple salts different from the effects calculated from the theory of Swain & Bader (82) will require minor modifications in that theory [Davies & Benson (83)] which may aid in the understanding of other solvation isotope effects such as those for methyl halides. The recent discus­ sion of heat capacities of activation for hydrolysis (only in H20) [Leffek, Robertson & Sugamori (84)] is also pertinent to the consideration of water structure. Solubility isotope effects for small hydrocarbon molecules (as well as amino acids) [Kresheck, Schneider & Scheraga (85)] and for argon [Ben-Nairn(86)] in H20 versus D20 have been determined. Propane, butane, and argon are a few per cent more soluble in D20 than in H20, an "inverse" effect. Data for helium would be exceedingly interesting. The effects of ethanol added to water upon the heats of solution of non­ electrolytes and ions [Arnett et al. (87)] were explained in terms of the effect by National Taiwan University on 04/09/13. For personal use only. of ethanol on the structure of water. It seems to the present author as if the effects could be explained by the hypothesis that both nonpolar and ionic species break up the structure; the problem of interpretation is that in com­ Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org paring ethanol-water (more structure) with water (less structure) two effects exist. More structure probably implies a lower electronic energy (more stabil­ ity), but at the same time a higher zero-point "vibrational" energy for the hindered rotations of the solvent molecules (less stability); whether the effect of solute on solvent structure differsfrom water to ethanol-water as a result of electronic or of vibrational changes, or the extent to which both changes may be important, is a very interesting question but is not easy to decide. The problem of how accurate the "rule of the geometric mean" for iso­ topic partition function ratios really is has been reopened. Based on the observation that such an equilibrium constant as for: PHYSICAL ORGANIC CHEMISTRY 369

H20 + D20 +=±2HDO has a value very close to the symmetry number (statistical) value 4, it was concluded that the rule was very good. However, recent data [For discussion, see Weston (88), Pyper & Long (89), and Narten (90)] indicate that con­ stant may even be as low as 3.4, in which case a considerable change in the theory and numerical calculations of isotope effects for reactions in H20 -D20 mixtures [For recent discussion, see (4), and Kresge (91)] will be re­ quired. The answer is rumored to be near at hand. Other recent work involving solvent isotope effectsincludes the hydrogen­ transfer isotope effecttheory of Swain, Kuhn & Schowen (92) and the studies of Gary, Bates & Robinson (93, 94) on standardization of a pD scale. ORBITAL SYMMETRY Although detailed discussion is probably out of place in this chapter, recent studies on molecular orbital theory are of great interest to physical organic chemists. Certain "stereoelectronic selection rules" based on orbital symmetry ex­ plain the course of: "electro cyclic" ring-opening reactions [Woodward & Hoffmann (95) ; Longuet-Higgins & Abrahamson (96); Fukui (97)]; con­ certed cycloaddition reactions [Hoffmann & Woodward (98-99)]; "sigma­ troptic" intramolecular rearrangements [Woodward & Hoffmann (100) ; Hoffmann & Woodward (101)]; interconversion of C,H4 and C6H6 isomers, including the stability of "Dewar" benzene [Hoffmann (102) ; Van Tamelen (103)]. The theory is based on correlation diagrams for the electronic states or reactants and products. On application of a slow perturbation which con­ verts reactants into products, all electronic energy levels of the reactants must be converted adiabatically into those of the products. If, in one mecha­ nism, it turns out that this most favorable (adiabatic) process requires that the energy be increased greatly at geometries intermediate between reactant and product, whereas in another mechanism reactant and product states are correlated directly without any necessary increase in energy, then, other things being equal, the reaction will take the path which does not require in­

by National Taiwan University on 04/09/13. For personal use only. creased energy. These increased energy requirements come about when ground state molecular orbital(s) of the reactant are correlated with excited orbital(s) of the product (96); the rule of noncrossover of correlation lines for Annu. Rev. Phys. Chem. 1966.17:349-372. Downloaded from www.annualreviews.org orbitals of the same symmetry must be obeyed, of course. This type of argument also implies that, for example, a symmetrical SN2 displacement such as X-+ RX -XR + X- is "forbidden" [For discussion and a very interesting extension of orbital symmetry arguments, see Bader (104)]. other SN2 reactions presumably being "partly forbidden," which may have great significance in discussion of nucleophilic displacement processes and indicates straightforwardly why it should be difficult or impossible to find a true SN2 reaction which forms an intermediate of the type XRX. Also, it appears that the interconversion of two forms of 7- norbornadienyl cation (with C-7 close to one or the other double bond) 370 THORNTON

is "forbidden" by orbital symmetry, which may explain why the seemingly stable symmetric structure (with C·7 interacting equally with both double bonds) in fact appears to correspond to an energy maximum [according to calculations of Hoffmann (105)]. The "extended Huckel method" of Hoffmann & Lipscomb (1 06-111) may provide a convenient way of studying orbital symmetry relationships (even

for large molecules, including (J' electrons), although its results cannot be considered precise (112). Mention should also be made of significant advances in SCF·MO calcu­ lations for organic molecules [Chung & Dewar (113); Dewar & Gleicher (114-116); Dewar & Thompson (117»). One very interesting aspect of these calculations is that they could be empirically made self-consistent for geometry by calculating bond-orders, using the calculated bond-orders to estimate (empirically) bond length, and repeating for the new geometry, until further iteration produced no change in geometry. Calculations were also made for cyclobutadiene [Dewar & Gleicher (11 8») which predicted it should be stable, fortunately, since one of the most significantevents of 1965 in physical organic chemistry was the probable synthesis of cyclobutadiene rWatts, Fitzpatrick & Pettit (119)].

LITERATURE CITED

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