MiS Preprint Repository

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.