A Calculation of the Energy of Activation for the Racemization of 2,2′-Dibromo−4,4′-Dicarboxydiphenyl

Abstract

In a recent article J. E. Mayer and the author presented a method of calculating the energy of activation for the racemization of optically active diphenyl derivatives from known force constants and from the van der Waals repulsion between ortho substituents. In the present paper, the calculation of this activation energy is carried through in detail for the racemization of 2–2′‐dibromo−4,4′‐dicarboxydiphenyl. The value obtained is 18 kcal./mole. The experimental value is not known, but the free energy of activation for the same process is 19.5 kcal./mole. In the discussion of probable errors, it is shown that the calculated energy of activation is unlikely to be in error by as much as 7 kcal./mole, and that the probable error is only about 4 kcal./mole. The racemization involves distorting the various angles and stretching the various bonds in the molecule, as well as forcing the ortho substituents to approach one another so that the distance between them is less than the sum of their van der Waals radii. In the present treatment, all these deflections and stretchings are computed; that is to say, an accurate model for the activated complex is obtained.