Sums and Densities of Fully Coupled Anharmonic Vibrational States: A Comparison of Three Practical Methods

Three practical methods for computing Sums and densities of states Of fully coupled anharmonic vibrations are compared. All three methods are based oil the standard perturbation theory expansion for the vibrational energy. The accuracy of the perturbation theory expansion is tested by comparisons with computed eigenvalues and/or experimental vibrational constants taken from the literature for three- and four-atom molecules. For a number of examples, it is shown that the X-ij terms in the perturbation theory expansion account for most of the anhamionicity, and the Y-ijk terms also make a small contribution; Contributions from the Z(ijkl) terms are insignificant. For molecules Containing Lip to similar to 4 atoms, the Sums and densities of states can be Computed by using nested DO-loops, but this method becomes impractical for larger species. Ail efficient Monte Carlo method published previously is both accurate and practical for molecules containing 3-6 atoms but becomes too slow for larger species. The Wang-Landau algorithm is shown to be practical and reasonably accurate for molecules containing similar to 4 or more atoms, where the practical size limit (with a single computer processor) is Currently oil the order of perhaps 50 atoms. It is shown that the errors depend mostly oil the average number of stochastic samples per energy bill. An automated version of the Wang-Landau algorithm is described. Also described ire the effects of Fermi resonances and procedures for deperturbation of the anharmonicity coefficients. Computer codes based oil all three algorithms are available from the authors and can also be downloaded freely from the Internet (http://aoss.engin.umich.edu/multiwell/).