Calculating vibrational spectra of molecules using tensor train decomposition

TL;DR

This paper introduces a tensor train decomposition-based algorithm for efficiently computing vibrational spectra of molecules, enabling accurate results with minimal memory and computational resources.

Contribution

It presents a novel tensor train approach combined with iterative methods for low-rank eigenfunction approximation in vibrational spectra calculations.

Findings

Computed 84 vibrational states of acetonitrile on a laptop in one hour.

Used only 100 MB of memory for all eigenfunctions.

Achieved accurate vibrational spectra with low computational cost.

Abstract

We propose a new algorithm for calculation of vibrational spectra of molecules using tensor train decomposition. Under the assumption that eigenfunctions lie on a low-parametric manifold of low-rank tensors we suggest using well-known iterative methods that utilize matrix inversion (LOBPCG, inverse iteration) and solve corresponding linear systems inexactly along this manifold. As an application, we accurately compute vibrational spectra (84 states) of acetonitrile molecule CH$_3$CN on a laptop in one hour using only $100$ MB of memory to represent all computed eigenfunctions.