Approximation for sums and densities of state of vibrations coupled with symmetric top K-rotor

Abstract

The energy of a symmetric top rotor depends on quantum numbers J and K. In unimolecular rate theory the energy of the K-rolor, i.e. the K-dependent part of the symmetric top rotor energy, may be considered under some conditions as "active", i.e. mixed with vibrational energy and thus contributing to the sum and density of vibrational states of the molecule, subject to the restriction -J ≤ K ≤ + J. In these cases proper evaluation of the sum/density of vibrational plus active K-rotor states at specified energy and J involves a summation of sums/densities over all the allowed Ks, a computationally intensive exercise. This work proposes simple and accurate approximations that require only trivial machine time. For the prolate symmetric top, the K-dependence of vibrational + rotational sum/density of states is approximated by a truncated Gaussian, and for the oblate top by a hyperbolic cosine. In each case the necessary parameters are obtained by a fit to smoothed "exact" vibrational sums/densities at K = 0 and one, or at most two, other values of K. The approximations are tested on a selection of typical symmetric top molecules at several energies and values of J with satisfactory results. The use of symmetry numbers is briefly invoked. Copyright © 1996 Elsevier Science Ltd.