An Application of Error Reduction and Harmonic Inversion schemes to the Semiclassical Calculation of Molecular Vibrational Energy Levels

A singular value decomposition based harmonic inversion (HI) signal processing scheme is applied to the semiclassical initial value representation (IVR) calculation of molecular vibrational states. Relative to usual IVR procedure of Fourier analysis of a signal made from the Monte Carlo evaluation of the phase space integral in which many trajectories are needed, the new procedure obtains acceptable results with many fewer trajectories. Calculations are carried out for vibrational energy levels of H2O to illustrate the overall procedure. New results are given for the zero point energy (ZPE) of CH5+.