Calculating vibrational spectra of molecules using tensor train decomposition
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 lowparametric manifold of lowrank tensors we suggest using wellknown iterative methods that utilize matrix inversion (locally optimal block preconditioned conjugate gradient method, 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.
 Publication:

Journal of Chemical Physics
 Pub Date:
 September 2016
 DOI:
 10.1063/1.4962420
 arXiv:
 arXiv:1605.08422
 Bibcode:
 2016JChPh.145l4101R
 Keywords:

 Mathematics  Numerical Analysis;
 65Z05;
 15A69;
 65F15
 EPrint:
 11 pages, 4 figures, 2 tables