The tensor hypercontracted parametric reduced density matrix algorithm: coupled-cluster accuracy with O(r^4) scaling

Abstract

Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral (ERI) tensor and the two-particle excitation amplitudes used in the parametric reduced density matrix (pRDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r4), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the traditional pRDM algorithm, somewhere between that of CCSD and CCSD(T).

11 pages, 1 figure

Cited by in corpus (11)

• Low rank representations for quantum simulation of electronic structure
• Low rank factorization of the Coulomb integrals for periodic coupled cluster theory
• Tensor-Structured Coupled Cluster Theory
• Efficient ab initio auxiliary-field quantum Monte Carlo calculations in Gaussian bases via low-rank tensor decomposition
• Improved Grid Optimization and Fitting in Least Squares Tensor Hypercontraction
• Robust approximation of tensor networks: application to grid-free tensor factorization of the Coulomb interaction
• A Critical Analysis of Least-Squares Tensor Hypercontraction Applied to MP3
• Robust Tensor Hypercontraction of the Particle-Particle Ladder Term in Equation-of-Motion Coupled Cluster Theory
• Fast algorithm for periodic density fitting for Bloch waves
• Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost
• Near-exact CCSDT energetics from rank-reduced formalism supplemented by non-iterative corrections