An exact variational method to calculate vibrational energies of five atom molecules beyond the normal mode approach

Abstract

A full dimensional variational algorithm to calculate vibrational energies of penta-atomic molecules is presented. The quantum mechanical Hamiltonian of the system for J=0 is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame without any dynamical approximation. The vibrational Hamiltonian has been obtained in an explicitly Hermitian form. Variational calculations are performed in a direct product discrete variable representation basis set. The sine functions are used for the radial coordinates, whereas the Legendre polynomials are employed for the polar angles. For the azimuthal angles, the symmetrically adapted Fourier–Chebyshev basis functions are utilized. The eigenvalue problem is solved by a Lanczos iterative diagonalization algorithm. The preliminary application to methane is given. A comparison with previous results is made.