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

Abstract

Classical Monte Carlo simulation methods have been used to evaluate the internal partition function of diatomic and triatomic van der Waals molecules. All simulation methods are simple to implement and are shown to yield very accurate results for Ar‚‚‚O, Ar‚‚‚O 2 , and Ar‚‚‚CN when compared with the corresponding exact quantum mechanical results. Their efficiencies are also examined. 8303

Vibrational partition functions for atom–diatom and atom–triatom van der Waals systems

“…Thus, we will evaluate the multidimensional phase space integral of eqn. (1) using the Monte Carlo method described elsewhere [5][6][7] which employs a stratified and guided sampling procedure. The basic idea is to choose a sampling domain which resembles as much as possible the integration domain.…”

“…Although first-principle rovibrational calculations have seen a tremendous advance in recent years, [1][2][3][4] the QSM approach still represents a formidable task which prevents its routine application. In recent work, we have shown [5][6][7] that in some situations a viable alternative to QSM is classical statistical mechanics (CSM). In this approach, one evaluates the internal partition function by replacing the sum over states with the following multidimensional phase space integral 8…”

“…When used jointly with a Monte Carlo technique, such an approach yielded good results for the internal partition functions of both diatomic and triatomic van der Waals molecules. 5,6 The theoretical investigation of both classical and quantum molecular properties starts with the formulation of the molecular Hamiltonian, which can be quite cumbersome for medium size and large molecules. However, many chemical processes can be described using simplified Hamiltonians which rely on a subset of the system's degrees of freedom.…”

“…To solve it, we utilize a Monte Carlo technique initially suggested by Barker 11 in the context of transition state theory, and subsequently employed by us for the calculation of molecular internal partition functions. [5][6][7] The paper is organized as follows. Section 2 presents the general Hadder-Frederick method, which is there used to derive the classical Hamiltonians for the atom-(rigid diatom) and atom-(rigid linear triatom) vdW systems.…”

A Direct Evaluation of the Partition Function and Thermodynamic Data for Water at High Temperatures

“…[10][11][12][13] However, the accuracy of the results obtained by using the traditional methods is expected to be poor at high temperatures 8,14 and for floppy (anharmonic) systems. 15 For the above reasons, several procedures have been proposed as routes to the direct sum-over-states approach and fitting of experimental data. These include the hybrid analytic/direct summation method of ab initio calculations, 14 Fourier pathintegral Monte Carlo methods, [16][17][18] and classical statistical mechanics (CSM) methods both with consideration of quantum, 19 semiclassical, 20 and semiempirical 21 corrections and without consideration of such corrections.…”