Level distributions, partition functions, and rates of chirality changing processes for the torsional mode around O–O bonds

Abstract

In view of the particular attention recently devoted to hindered rotations, we have tested reduced kinetic energy operators to study the torsional mode around the O–O bond for H2O2 and for a series of its derivatives (HOOCl, HOOCN, HOOF, HOONO, HOOMe, HOOEt, MeOOMe, ClOOCl, FOOCl, FOOF, and FOONO), for which we had previously determined potential energy profiles along the dihedral ROOR′ angle [R,R′ = H,F,Cl,CN,NO,Me ( = CH3), Et ( = C2H5)]. We have calculated level distributions as a function of temperature and partition functions for all systems. Specifically, for the H2O2 system we have used two procedures for the reduction in the kinetic energy operator to that of a rigid-rotor-like one and the calculated partition functions are compared with previous work. Quantum partition functions are evaluated both by quantum level state sums and by simple classical approximations. A semiclassical approach, using a linear approximation of the classical path and a quadratic Feynman–Hibbs approximation of Feynman path integral, introduced in previous work and here applied to the torsional mode, is shown to greatly improve the classical approximations. Further improvement is obtained by the explicit introduction of the dependence of the moment of inertia from the torsional angle. These results permit one to discuss the characteristic time for chirality changes for the investigated molecules either by quantum mechanical tunneling (dominating at low temperatures) or by transition state theory (expected to provide an estimate of racemization rates in the high energy limit).