  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.
