Internal coordinate Hamiltonian model for Fermi resonances and local modes in methane

Abstract

A vibrational model which is based on a Hamiltonian expressed in terms of curvilinear internal coordinates is applied to the overtone spectrum of methane, CH4. Symmetrized internal coordinates and their conjugate momenta are used as the bending variables. The stretching part of the Hamiltonian is expressed in an unsymmetrized form. Both the kinetic operator and the potential energy function are expanded as Taylor series around the equilibrium configuration. Symmetrized local mode basis functions for the stretches and symmetrized two- and three-dimensional harmonic oscillator basis functions in the Cartesian representations for bending degrees of freedom are used. Only resonance couplings are taken into account. Apart from some standard diagonal contributions harmonic oscillator matrix elements have been employed. This results in a simple block diagonal Hamiltonian model. The nonlinear least squares method is used to optimize model parameters for 12CH4. Observed vibrational term values up to 6050 cm−1 are included as data. Potential energy parameters obtained from the Hamiltonian parameters agree well with a previously published anharmonic force field calculation. A unitary transformation between internal coordinate and normal coordinate representations is found to provide simple interpretations for the standard normal mode theory based spectroscopic parameters.