Calculating vibrational spectra with sum of product basis functions without storing full-dimensional vectors or matrices

• Published in: The Journal of chemical physics 2014-05, Vol.140 (17), p.174111-174111
• Main Authors: Leclerc, Arnaud, Carrington, Tucker
• Format: Article
• Language: English
• Subjects: Basis functions; Chemical Sciences; Computer memory; Computing costs; Iterative methods; Mathematical analysis; Matrix algebra; Matrix methods; Physics; Vibrational spectra; Wave functions
• ISSN: 0021-9606; 1089-7690
• DOI: 10.1063/1.4871981

We propose an iterative method for computing vibrational spectra that significantly reduces the memory cost of calculations. It uses a direct product primitive basis, but does not require storing vectors with as many components as there are product basis functions. Wavefunctions are represented in a basis each of whose functions is a sum of products (SOP) and the factorizable structure of the Hamiltonian is exploited. If the factors of the SOP basis functions are properly chosen, wavefunctions are linear combinations of a small number of SOP basis functions. The SOP basis functions are generated using a shifted block power method. The factors are refined with a rank reduction algorithm to cap the number of terms in a SOP basis function. The ideas are tested on a 20-D model Hamiltonian and a realistic CH3CN (12 dimensional) potential. For the 20-D problem, to use a standard direct product iterative approach one would need to store vectors with about 10(20) components and would hence require about 8 × 10(11) GB. With the approach of this paper only 1 GB of memory is necessary. Results for CH3CN agree well with those of a previous calculation on the same potential.