Monte Carlo Simulation Approach to Internal Partition Functions for van der Waals Molecules

Abstract

The calculation of the internal partition function Qint, and the density of states N, is an important topic which has a vast range of applications. In fact, its accurate determination for a nonseparable potential is a long standing problem which goes back to the foundations of statistical mechanics. The density of states is required for the evaluation of reaction rate constants in transition state theory (conventional or variational), while the calculation of Qint is important, e.g., to study the equilibrium properties of bound systems. In turn, its temperature dependence is necessary to evaluate various thermodynamic quantities, such as the Gibbs enthalpy and the Helmholtz function, which are used as standard input for many models in astrophysics; see ref 1. For example, the solution of the equation of state for cool stellar atmospheres requires very accurate values of Qint. 2,3 However, the calculation of Qint becomes particularly difficult for systems involving weakly bound states such as van der Waals (vdW) molecules. Indeed, the application of approximate methods like the harmonic oscillator and rigid rotor (HO+RR) approximation (which has been widely used to build up the JANAF 4 tables of thermodynamic functions) is expected to give poor results for such floppy (anharmonic) molecules. Recently, we have been interested in the study of thermolecular association reactions of the general type