Page 120 - Mechanism and Theory in Organic Chemistry

Isotope Effects 109

for this mode will be less than 1. Part of the contribution from the reactant zero-
point energy of the reaction coordinate mode will be canceled and the isotope
effect will be lowered. In the limit that the transition state is nearly the same as
reactant, the symmetric stretch (32) will involve nearly as much motion of H or

D as the reactant stretch, and its zero-point difference will largely cancel the
contribution from the reactant stretch zero-point energy. The isotope effect, in
this simple model at least, thus becomes a rough measure of the position of the
transition state along the reaction coordinate. The isotope effect is expected to be
largest for the most symmetrical location of the transition state, and smaller the
closer the transition state is to either reactant or product.

Primary isotope effects in non-linear transition states If the transi-
tion state is nonlinear, the vibration corresponding to the symmetric stretch looks
like 33. Now even for the symmetrical case, the H (D) moves with relatively high

frequency, and this mode cancels most of the zero-point contribution from the
reaction coordinate mode of the reactants. Hence a bent transition state should
show a small isotope effect. This mode is furthermore little affected by dissym-
metry, and so the isotope effect for a nonlinear transition state will not be a
sensitive indicator of position ofthe transition state along the reaction ~oordinate.~~

Secondary Isotope Effects56
A secondary isotope effect is one that results from isotopic substitution at a bond not
being broken in the reaction. As the reaction cordinate, not being affected by the
substitution, does not make any contribution, the secondary effects must arise
solely from changes of zero-point energies of ordinary vibrations. Thus if an
isotopically substituted C-H bond experiences a change of force ,constant on
going from reactant to transition state, the effect is approximately

or, using the approximation that v, = v,/ 1.35,

55 R. A. More O'Ferrall, J. Chem. Soc. B, 785 (1970).
68 For a review of secondary isotope effects, see E. A. Halevi, Prog. Phys. Org. Chem., 1, 109 (1963).