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arXiv:2306.04880 · Journal of Chemical Theory and Computation

Low-Scaling Algorithm for the Random Phase Approximation Using Tensor Hypercontraction with k-point Sampling

Chia-Nan Yeh, Miguel A. Morales

Published Aug 25, 2023• 27 citations
arXivHTMLPDF

Abstract

We present a low-scaling algorithm for the random phase approximation (RPA) with k -point sampling in the framework of tensor hypercontraction (THC) for electron repulsion integrals (ERIs). The THC factorization is obtained via a revised interpolative separable density fitting (ISDF) procedure with a momentum-dependent auxiliary basis for generic single-particle Bloch orbitals. Our formulation does not require preoptimized interpolating points or auxiliary bases, and the accuracy is systematically controlled by the number of interpolating points. The resulting RPA algorithm scales linearly with the number of k -points and cubically with the system size without any assumption on sparsity or locality of orbitals. The errors of ERIs and RPA energy show rapid convergence with respect to the size of the THC auxiliary basis, suggesting a promising and robust direction to construct efficient algorithms of higher order many-body perturbation theories for large-scale systems.

DOI
10.1021/acs.jctc.3c00615

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