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 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.

11 pages, 4 figures, 2 tables

References in corpus (3)

• The density-matrix renormalization group in the age of matrix product states
• Calculating vibrational spectra with sum of product basis functions without storing full-dimensional vectors or matrices
• Grid-based electronic structure calculations: the tensor decomposition approach

Cited by in corpus (22)

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• Excited-state DMRG made simple with FEAST
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• 2500 vibronic eigenstates of the NO${}_3$ radical
• Benchmarking vibrational spectra: 5000 accurate eigenstates of acetonitrile using tree tensor network states
• QCMaquis 4.0: Multi-Purpose Electronic, Vibrational, and Vibronic Structure and Dynamics Calculations with the Density Matrix Renormalization Group
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• Trotter simulation of vibrational Hamiltonians on a quantum computer
• A Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics