An evaluation of methods designed to calculate energy levels in a selected range and application to a (one-dimensional) Morse oscillator and (three-dimensional) HCN/HNC

Abstract

In this paper we study three methods designed to calculate energy levels in a range of interest. The methods are applied to a one-dimensional (1-D) Morse oscillator and to HCN/HNC (in three-dimensions). Energy levels in the chosen range are computed using the filter-diagonalization method proposed by Neuhauser [J. Chem. Phys. 93, 2611 (1990)], a spectral transform Lanczos method, and a guided Lanczos method we suggest in this paper. In the guided Lanczos method convergence of the energy levels of interest is favored by choosing the Lanczos starting vector so that it has a substantial overlap only with eigenvectors of the eigenvalues in the chosen range. This biased starting vector is calculated from a solution of the time-dependent Schroedinger equation. Of the three methods the guided Lanczos is the most efficient for both the Morse oscillator and HCN/HNC. None of the methods designed to favor a chosen energy range are, however, (for the two problems we considered) as efficient as a straightforward Lanczos method (without an optimized starting vector).