Effective rotational Hamiltonian for molecules with two periodic large-amplitude motions

Abstract

Starting from a general Hamiltonian for a molecule with two periodic large-amplitude motions, an effective rotational Hamiltonian is developed for bound states of the internal motions. It contains two types of matrix elements: (i) The internal motion energy, expressed as two-dimensional Fourier series, and transformed to a reference axes system. (ii) Matrix elements of rotational operators in the reference axes system multiplied by two-dimensional Fourier series. The spectroscopic parameters are the coefficients of the Fourier series (integrals of localized functions), the internal motion parameters ρ, and the angles between the vectors ρ and the reference axes. Expressions are given for cases with higher symmetry. The effectiveness of the Hamiltonian is demonstrated by fitting the rotational spectrum of the ground state of dimethylether (356 frequencies involving levels up to J=25) to experimental precision. The data of five vibrational excited states can be fit to almost the same precision.