Spatial Signatures of Electron Correlation in Least-Squares Tensor Hypercontraction

Least-squares tensor hypercontraction
(LS-THC) has received
some
attention in recent years as an approach to reduce the significant
computational costs of wave function-based methods in quantum chemistry.
However, previous work has demonstrated that LS-THC factorization
performs disproportionately worse in the description of wave function
components (e.g., cluster amplitudes T̂2) than Hamiltonian components (e.g., electron repulsion integrals
(pq|rs)). This work develops novel
theoretical methods to study the source of these errors in the context
of the real-space T̂2 kernel, and
reports, for the first time, the existence of a “correlation
feature” in the errors of the LS-THC representation of the
“exchange-like” correlation energy EX and T̂2 that is remarkably consistent across ten molecular species, three
correlated wave functions, and four basis sets. This correlation feature
portends the existence of a “pair point kernel” missing
in the usual LS-THC representation of the wave function, which critically
depends upon pairs of grid points situated close to atoms and with
interpair distances between one and two Bohr radii. These findings
point the way for future LS-THC developments to address these shortcomings.