Comparison of different eigensolvers for calculating vibrational spectra using low-rank, sum-of-product basis functions

TL;DR

This paper compares various low-rank eigensolvers for calculating vibrational spectra of molecules using sum-of-product basis functions, highlighting their efficiency and computational advantages.

Contribution

It adapts and compares different reduced-rank iterative eigensolvers for vibrational spectra calculations using low-rank SOP basis functions.

Findings

Chebyshev iteration shows competitive performance.

More sophisticated methods offer CPU time advantages.

Low-rank SOP basis functions effectively reduce memory usage.

Abstract

Vibrational spectra and wavefunctions of polyatomic molecules can be calculated at low memory cost using low-rank sum-of-product (SOP) decompositions to represent basis functions generated using an iterative eigensolver. Using a SOP tensor format does not determine the iterative eigensolver. The choice of the interative eigensolver is limited by the need to restrict the rank of the SOP basis functions at every stage of the calculation. We have adapted, implemented and compared different reduced-rank algorithms based on standard iterative methods (block-Davidson algorithm, Chebyshev iteration) to calculate vibrational energy levels and wavefunctions of the 12-dimensional acetonitrile molecule. The effect of using low-rank SOP basis functions on the different methods is analyzed and the numerical results are compared with those obtained with the reduced rank block power method introduced in J. Chem. Phys. 140, 174111 (2014). Relative merits of the different algorithms are presented, showing that the advantage of using a more sophisticated method, although mitigated by the use of reduced-rank sum-of-product functions, is noticeable in terms of CPU time.