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

We present a tensor-structured method for calculating the Møller–Plesset (MP2) correction to the Hartree–Fock energy with reduced computational cost. The approach originates from the 3D grid-based low-rank factorization of the two-electron integrals tensor performed by the purely algebraic optimization. The computational scheme benefits from fast multilinear algebra implemented on separable representations of transformed two-electron integrals, doubles amplitude tensors, and other fourth order data arrays. The separation rank estimates are discussed. The so-called quantized approximation of the long skeleton vectors comprising tensor factorizations of the main entities allows a reduction in storage costs. A detailed description of tensor algorithms for evaluating the MP2 energy correction is presented. The efficiency of these algorithms is illustrated in the framework of Hartree–Fock calculations for compact molecules, including the amino acids alanine and glycine.