Vibrational Energy Levels via Finite-Basis Calculations Using a Quasi-Analytic Form of the Kinetic Energy.

A variational method for the calculation of low-lying vibrational energy levels of molecules with small amplitude vibrations is presented. The approach is based on the Watson Hamiltonian in rectilinear normal coordinates and characterized by a quasi-analytic integration over the kinetic energy operator (KEO). The KEO beyond the harmonic approximation is represented by a Taylor series in terms of the rectilinear normal coordinates around the equilibrium configuration. This formulation of the KEO enables its extension to arbitrary order until numerical convergence is reached for those states describing small amplitude motions and suitably represented with a rectilinear system of coordinates. A Gauss-Hermite quadrature grid representation of the anharmonic potential is used for all the benchmark examples presented. Results for a set of molecules with linear and nonlinear configurations, i.e., CO2, H2O, and formyl fluoride (HFCO), illustrate the performance of the method and the versatility of our implementation.