A Critical Analysis of Least-Squares Tensor Hypercontraction Applied to MP3

TL;DR

This paper critically evaluates LS-THC-MP3, a method to reduce computational scaling in wavefunction calculations, analyzing its accuracy, efficiency, and practical applicability for systems up to 40 atoms.

Contribution

It identifies four variants of LS-THC-MP3, analyzes their performance and errors, and discusses practical considerations like grid pruning and crossover points.

Findings

Errors are small compared to density fitting.

Pruning grids improves efficiency.

Crossover point around 240 electrons.

Abstract

The least-squares tensor hypercontraction (LS-THC) approach is a promising method of reducing the high polynomial scaling of wavefunction methods, for example those based on many-body perturbation theory or coupled cluster. Here, we focus on LS-THC-MP3, and identify four variants with differing error and efficiency characteristics. The performance of LS-THC-MP3 is analyzed for regular test systems with up to 40 first-row atoms. We also analyze the size-extensivity/size-consistency and grid- and basis set-dependence of LS-THC-MP3. Overall, the errors observed are favorably small in comparison with standard density fitting, and a more streamlined method of generating grids via pruning is suggested. Practical crossover (the point at which LS-THC-MP3 is cheaper than the canonical method) is achieved around 240 correlated electrons. Despite several drawbacks of LS-THC that have been identified: a small but non-zero size-consistency error, poor description of angular correlation, and potentially large increase of error with basis set size, the results show that LS-THC has significant potential for practical application to MP3 and other wavefunction methods.