Using symmetry-adapted optimized sum-of-products basis functions to calculate vibrational spectra

TL;DR

This paper introduces a symmetry-adapted sum-of-products basis function approach with a power method and alternating least squares to compute vibrational spectra efficiently, enabling symmetry-based state separation and improved accuracy.

Contribution

The paper presents a novel symmetry-constrained SOP basis function method combined with a power method and ALS optimization for vibrational spectra calculation.

Findings

Successfully applied to acetonitrile molecule

Enhanced state assignment accuracy

Improved computational efficiency

Abstract

Vibrational spectra can be computed without storing full-dimensional vectors by using low-rank sum-of-products (SOP) basis functions. We introduce symmetry constraints in the SOP basis functions to make it possible to separately calculate states in different symmetry subgroups. This is done using a power method to compute eigenvalues and an alternating least squares method to optimize basis functions. Owing to the fact that the power method favours the convergence of the lowest states, one must be careful not to exclude basis functions of some symmetries. Exploiting symmetry facilitates making assignments and improves the accuracy. The method is applied to the acetonitrile molecule.