Hybrid calculation of the partition functions of prolate top molecules:Using HOCl as the test case.

Abstract The partition function of a molecule can be obtained by a direct sum-over-states (SOS) calculation using the molecule’s quantum energy levels. These energies can be those obtained by a model fitted to experimental data. For molecules with “exotic” behaviour (such as large amplitude vibrational motion) physically motivated models can be required. Often, however, such models can be limited in the range of quantum levels that can be reliably calculated, making a converged SOS calculation impractical. Here we present a hybrid approach for prolate top molecules. Our hybrid approach allows the simple extension from a limited SOS calculation to a good approximation for the infinite sum limit. This is achieved by adding easily calculated closed-form corrections to the limited SOS result. We test our approach using the Generalised SemiRigid Bender (GSRB) program as the physically motivated model. HOCl serves as a good test case because for it the GSRB model can extend to high enough levels for convergence of the direct SOS calculation. Then, by limiting the range of GSRB calculated rotational levels included in the SOS, we confirm our hybrid approach. The technique we present here should be particularly applicable to quasilinear molecules, including those exhibiting quantum monodromy. The Appendix presents step-by-step instructions for implementing this hybrid procedure. Also presented there is a brief discussion of how to adapt the hybrid technique to approximately account for rotational or vibrational dissociation in the case that that is necessary.