Application of Structured Matrices for Solving Hartree-Fock Equations

TL;DR

This paper introduces a novel method for solving Hartree-Fock equations using structured matrices like Toeplitz and tensor matrices, demonstrating its effectiveness through modern computational experiments.

Contribution

The work presents a new approach employing structured matrices and finite element bases for Hartree-Fock calculations, with implementation and validation on contemporary datasets.

Findings

Results align well with theoretical predictions

Reduced computational complexity demonstrated

Effective use of structured matrices in quantum chemistry

Abstract

This work was originally published by the author in 1999 in a book [1] and later became part of the author's doctoral thesis in 1999 [2]. Since the original language of these works is not English, the author provides a translation of the key ideas of these publications in this work. In addition, the chapter related to numerical experiments was recalculated on modern computers and using contemporary benchmark datasets. This article presents a novel approach to solving Hartree-Fock equations using Toeplitz and tensor matrices and bases based on regular finite elements. The issues discussed include the choice of basis, the dependence of data volume and number of arithmetic operations on the number of basis functions, as well as the arithmetic complexity and accuracy of computing two- and four-center integrals. The approach has been implemented in a software package, and results have been obtained that are in good agreement with theory.