The Theory of the Racemization of Optically Active Derivatives of Diphenyl

Abstract

T. L. Hill has recently shown that it is possible to compute the magnitude of steric strain in certain organic molecules. The present paper summarizes the results of a similar but independent investigation directed towards a computation of the rate of racemization of optically active (i.e., sterically hindered) derivatives of diphenyl. The energy of the planar form of a sterically hindered diphenyl can be approximated by the equation: $$\mathrm{E=}{\displaystyle \sum _i}\frac{1}{2}{a}_i{q}_i^2{\mathrm{+A}}_i\exp {\mathrm{(-d}}_1{\mathrm{/\rho }}_1{\mathrm{)+A}}_2\exp {\mathrm{(-d}}_2{\mathrm{/\rho }}_2\mathrm{),}$$ where the q_i are the normal coordinates of the unstrained molecule in question and the exponential terms are approximations (over the limited range of interest) to the steric repulsions of the non‐bonded groups which repel each other. There are two such exponential terms, for in most sterically hindered diphenyls the repulsion is caused by two pairs of ortho substituents. The equation for E₀, the activation energy for racemization, has been found for the symmetrical case by minimizing E; the constants a_i, A, and ρ, and the dimensions of the diphenyl derivative appear in the expression for E₀. It is also possible to derive equations for the vibration frequencies of the planar form of the sterically hindered molecule (and, therefore, find the entropy of activation); these equations are complicated by the essential degeneracy of the vibrations in question.