Assessing the utility of phase-space-localized basis functions: Exploiting direct product structure and a new basis function selection procedure

James Brown; Tucker Carrington Jr

doi:10.1063/1.4954721

Assessing the utility of phase-space-localized basis functions: Exploiting direct product structure and a new basis function selection procedure

J Chem Phys. 2016 Jun 28;144(24):244115. doi: 10.1063/1.4954721.

Authors

James Brown¹, Tucker Carrington Jr¹

Affiliation

¹ Chemistry Department, Queen's University, Kingston, Ontario K7L 3N6, Canada.

PMID: 27369505
DOI: 10.1063/1.4954721

Abstract

In this paper we show that it is possible to use an iterative eigensolver in conjunction with Halverson and Poirier's symmetrized Gaussian (SG) basis [T. Halverson and B. Poirier, J. Chem. Phys. 137, 224101 (2012)] to compute accurate vibrational energy levels of molecules with as many as five atoms. This is done, without storing and manipulating large matrices, by solving a regular eigenvalue problem that makes it possible to exploit direct-product structure. These ideas are combined with a new procedure for selecting which basis functions to use. The SG basis we work with is orders of magnitude smaller than the basis made by using a classical energy criterion. We find significant convergence errors in previous calculations with SG bases. For sum-of-product Hamiltonians, SG bases large enough to compute accurate levels are orders of magnitude larger than even simple pruned bases composed of products of harmonic oscillator functions.