Calculation of rotation-vibrational energies directly from an anharmonic potential function

Abstract

A method has been developed for calculating a selected number of the lowest rotation-vibrational energies of nonlinear semirigid molecules directly from the anharmonic potential function. The use of the conventional contact transformation and the resulting intermediate spectroscopic constants is avoided. Instead the matrix of the untransformed, second-order Hamiltonian is set up in a systematically selected basis of anharmonic vibrational wavefunctions multiplied by symmetric top rotor functions. This matrix is block-diagonalized by a van Vleck transformation, and the relevant diagonal block is diagonalized directly. The method has been tested on the isotopic species CH 4, CH 2D 2, and CD 4, as well as on CF 4. Extensive test calculations indicate that a mean value of the errors at about 0.7 cm −1 for CH 4 and CH 2D 2, 0.1 cm −1 for CD 4, and 0.01 cm −1 for CF 4 may be obtained, computing the rotational states for J up to 20 for all the fundamental vibrational states and states of similar energies. These errors include the effects of the limited basis and of the van Vleck transformation, but not those of the Born-Oppenheimer approximation or of the truncation of the Hamiltonian operator. This method should be useful for checking potential functions computed by ab initio methods against spectroscopic data and eventually for determining the anharmonic potential functions of middle-size molecules directly from experimental data.