Extracting accurate bound-state spectra from approximate wave packet propagation using the filter-diagonalization method

We present an extension of the filter-diagonalization (FD) approach which allows the extraction of accurate bound-state spectra from a time-dependent wave function determined by an approximate propagation scheme. To investigate the method, an approximate wave function is generated by a wave packet propagation on a two-dimensional potential energy surface for the LiCN molecule, employing a second-order differencing integrator with large step size. When applied to this inaccurate wave function, our formulation of the FD technique is capable of yielding eigenenergies considerably more precise than those obtained with the original FD method, while the effort is almost the same. The present FD scheme contains some additional refinements that increase the method's efficiency, accuracy, and practicability. We demonstrate that the accuracy of the FD procedure can be improved by using cosinetype filters. The quality of different variational principles employed to determine the eigenenergies is examined. These variational principles can also be utilized to estimate the error of the energies and intensities inexpensively and reliably. (C) 1998 American Institute of Physics. [S0021-9606(98)01334-8].