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PHYSICAL ORGANIC Chemistryl 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.
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