Calculation of rotational–vibrational energies of methane-shaped molecules directly from an anharmonic potential function

Abstract

A method has been developed for calculating a selected number of the lowest rotational–vibrational energies of non-linear, semi-rigid molecules directly from the anharmonic potential function, without the use of the conventional contact transformation. Instead the matrix of the second-order Hamiltonian is set up in a large basis of anharmonic vibrational wavefunctions multiplied by symmetric-top rotational functions. This matrix is reduced by a van Vleck transformation, and the resulting submatrix diagonalized directly. A principle is given for selecting an optimum vibrational basis in the computer. The method has been realized as a computer program applicable to methaneshaped molecules. A discussion is given of the magnitude of the errors due to the various approximations involved, based on extensive test calculations. The largest errors are due to the use of a limited basis and to the truncation of the potential function rewritten in terms of normal coordinates.