Communication: Tensor hypercontraction. III. Least-squares tensor hypercontraction for the determination of correlated wavefunctions

Abstract

ARTICLES YOU MAY BE INTERESTED INThe manipulation of the rank-four tensor of double excitation amplitudes represents a challenge to the efficient implementation of many electronic structure methods. We present a proof of concept for the approximation of doubles amplitudes in the tensor hypercontraction (THC) representation. In particular, we show how THC can be used to both reduce the scaling with respect to molecular size of coupled cluster singles and doubles (CCSD) (and related methods) by two orders [from O(N 6 ) to O(N 4 )] and remove the memory bottleneck associated with storage of the doubles amplitudes. The accuracy of correlated methods as integral and amplitude approximations are introduced is examined. For a set of 20 small molecules, single and double-excitation configuration interaction (CISD), quadratic CISD (QCISD), and CCSD correlation energies could be reproduced with millihartree accuracy after the introduction of these approximations. Our approach exploits otherwise hidden factorizable tensor structure in both the electron repulsion integrals and the wavefunction coefficients and should be applicable with suitable modifications to many methods in electronic structure theory.

An efficient basis set representation for calculating electrons in molecules

“…The set of two-electron matrix elements is a fourth-rank tensor, such that transformations of the set require O(N 4 ) multiplication operations; sophisticated methods such as coupled cluster must cope with even poorer scaling, O(N 6 ). There has been much work to circumvent this basic problem [1][2][3][4][5], especially by Martinez and coworkers.…”

Communication: Acceleration of coupled cluster singles and doubles via orbital-weighted least-squares tensor hypercontraction

“…Some authors have proposed factorizations of the amplitude tensors which might achieve scalings as low as O(N 5 ), 16,17 and we have recently shown that THC factorization of the ERIs and amplitudes can produce an accurate CCSD implementation scaling as O(N 4 ). 18 However, there are significant prefactors affiliated with such proposals. Another quite impressive area is the family of local correlation methods, 19,20 which have recently managed to produce CCSD(T)-quality results on systems as large as proteins.…”

Density-fitted singles and doubles coupled cluster on graphics processing units

“…DF and CD techniques are of great use in efficient CPU implementations of coupled cluster theory [49,[57][58][59][60][61][62][63], and we demonstrate herein their utility in a GPU-accelerated CCSD implementation. Other approximate tensor factorisations including singular-value decomposition [64] and the tensor hypercontraction DF [65][66][67] will undoubtedly become important in future CPU and GPU implementations of coupled cluster methods.…”