An ab initio study of low-frequency, large-amplitude molecular vibrations

Abstract

The ab initio treatments of molecular vibrational motion often invoke only the harmonic oscillator approximation. For vibrational modes whose amplitudes access anharmonic regions of the potential energy surface, the harmonic oscillator approximation fails. Low-frequency large-amplitude vibrations, in particular, can access anharmonic regions in addition to other minima of the potential energy surface. Ab initio harmonic frequencies are often scaled to lower values by empirical factors which presumably account for anharmonicity effects as well as an incomplete basis set and account of electron correlation. However, the scaling of those ab initio harmonic frequencies corresponding to low-frequency large-amplitude vibrations results in theoretical values that are still typically several times larger than the experimental values. It is demonstrated in this dissertation that transforming the nuclear motion Hamiltonian to internal coordinates facilitates construction of ab initio potential energy curves, or surfaces, pertaining to low-frequency large-amplitude molecular vibrational modes. The use of internal coordinates complicates the expression of the kinetic energy in the Hamiltonian, and makes it difficult to obtain. Six different methods for determining the kinetic energy expression in internal coordinates are presented and reviewed. The computational implementation of these six methods was performed to allow their critique. Several example calculations of the presented methodology are given. The solution for the vibrational expectation values of the modes expressed by the developed Hamiltonian was also computationally implemented. The resultant theoretical transition frequencies of the molecular systems of 2-sulpholene and 2-aminopyrimidine are combined with experimental studies, and demonstrate the practical usefulness of the presented methodology.