The steep polynomial scaling of wavefunction-based electronic structure methods is a central challenge in systematically addressing the correlation energy of large molecules. Common methods scale between O(n<sup>5</sup>) [MP2] and O(n<sup>7</sup>) [CCSD(T)], which sharply limits the size of molecules that can be addressed. Thus, scaling reduction is of the utmost importance. Besides methods based on orbital localization and/or fragmentation, tensor factorization methods have recently become of interest in combating this problem. In particular, the least-squares tensor hypercontraction (LS-THC) approach offers an effective, physics-based factorization of the two-electron integral tensor. However, we have recently shown that the effectiveness of LS-THC for the integrals is not reproduced when it is applied to wavefunction components (double excitation amplitudes). In this talk, we discuss two approaches to ameliorate this deficiency. First, we compare LS-THC to full, non-linear tensor hypercontraction and related decompositions, and analyze the resulting decompositions for MP2 and cluster amplitudes in terms of the pair orbital subspaces spanned in each case. We also relate these subspaces to the grid-based representation of LS-THC and possible extensions. Second, we examine the potential for reduction in the error of LS-THC decompositions of amplitudes via internal error cancellation. These strategies are benchmarked on typical systematic structures (e.g. one-dimensional chains and three-dimensonal clusters), as well as representative systems including binding energies, reaction potential energy surfaces, and conformational rearrangements.

Improvements in least-squares tensor hypercontraction of MP2 and coupled cluster amplitudes

ACS Fall 2021

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