Computing vibrational energy levels by using mappingsto fully exploit the structure of a pruned product basis

摘要

For the purpose of calculating (ro-)vibrational spectra, rate constants, scattering cross sections, etc.product basis sets are very popular. They, however, have the important disadvantage that they areunusably large for systems with more than four atoms. In this paper we demonstrate that it ispossible to efficiently use a basis set obtained by removing, from a product basis set, functionsassociated with the largest diagonal Hamiltonian matrix elements. This is done by exploiting the factthat for every factor of every term in the Hamiltonian, there is a basis-set order in which the matrixrepresentation of the factor is block diagonal. Due to this block diagonality the Lanczos algorithmcan be implemented efficiently. Tests with model Hamiltonians with as many as 32 coordinatesillustrate the merit of the ideas.