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MiS Preprint

Møller-Plesset (MP2) Energy Correction Using Tensor Factorizations of the Grid-based Two-electron Integrals

Venera Khoromskaia and Boris N. Khoromskij


We present a tensor-structured method to calculate the M{\o}ller-Plesset (MP2) correction to the Hartree-Fock energy with reduced computational consumptions. The approach originates from the $3D$ grid-based low-rank factorization of the two-electron integrals performed by the purely algebraic optimization. The computational scheme benefits from fast multilinear algebra implemented on the separable representations of the molecular orbital transformed two-electron integrals, the doubles amplitude tensors and other fours order data-arrays involved.

The separation rank estimates are discussed. The so-called quantized approximation of the long skeleton vectors comprising the tensor factorizations of the main entities allows to reduce the storage costs. The detailed description of tensor algorithms for evaluation of the MP2 energy correction is presented. The efficiency of these algorithms is illustrated in the framework of Hartree-Fock calculations for compact molecules, including alanine and glycine amino acids.

MSC Codes:
65F30, 65F50, 65N35, 65F10
Hartree-Fock equation, Two-electron integrals, tensor decompositions, quantized approximation, truncated Cholesky factorization, Møller-Plesset perturbation theory

Related publications

2014 Repository Open Access
Venera Khoromskaia and Boris N. Khoromskij

Møller-Plesset (MP2) energy correction using tensor factorization of the grid-based two-electron integrals

In: Computer physics communications, 185 (2014) 1, pp. 2-10