ON THE EFFECT OF CENTRIFUGAL STRETCHING ON THE ROTATIONAL PARTITION-FUNCTION OF AN ASYMMETRIC-TOP

Abstract

Correction terms (up to third order in temperature) for the effect of centrifugal distortion on the rotational partition function of linear molecules, spherical, symmetric, and asymmetric tops are evaluated by means of the classical partition function. It is shown that for the linear, spherical, and symmetric cases, the expressions thus obtained differ from the exact quantum expressions only in the absence of a very small constant correction term. It is then proposed that the partition function for a nonrigid asymmetric top, for which no exact expression has as yet been derived, be evaluated as the product of Watson's asymptotic expansion for the rigid rotor and the centrifugal correction factor derived in the present work. Numerical comparison with direct numerical summation shows that, even for troublesome cases, this approximation holds very well even at 2000 K. Similar performance is observed for the heat content function, except for pathological cases at high temperatures. In the rigid-rotor case, Watson's asymptotic series holds very well. As an example application, pilot calculations have been performed on the thermodynamic functions of water and formaldehyde. The present method yields functions in excellent agreement with those obtained by direct rovibrational summation, whereas computer-time requirements are reduced by 3 or 4 orders of magnitude.