Variational calculations of vibrational energy levels for XY4 molecules 1. Stretching states

A variational method for calculating excited stretching states of symmetric tetrahedral pentaatomic molecules is presented based on the use of Radau coordinates and Morse oscillator-like basis functions. Symmetry is used both to reduce the size of the secular matrix to be diag-onalized and to calculate the potential energy matrix elements over a reduced grid of quadrature points. Test results are presented for methane, silane and germane. For CH₄, stretch-bend coupling is found to be significant, whereas it is less important for the more strongly local mode SiH₄ and GeH₄ molecules. Converged results are obtained for stretching states significantly higher than considered in previous calculations. These states will be used to represent stretching motions in a fully coupled stretch-bend calculation.