Grid-based electronic structure calculations: the tensor decomposition approach

TL;DR

This paper introduces a grid-based method for electronic structure calculations using low-rank tensor decompositions, enabling efficient and accurate solutions for large-scale quantum chemistry problems.

Contribution

It develops a low-rank tensor decomposition approach for grid-based electronic structure calculations, achieving linear complexity with respect to grid size.

Findings

Efficient handling of large grids up to 8192^3 points.

Systematic convergence with desired accuracy across tested systems.

Applicable to atoms, molecules, and hydrogen clusters.

Abstract

We present a fully grid-based approach for solving Hartree-Fock and all-electron Kohn-Sham equations based on low-rank approximation of three-dimensional electron orbitals. Due to the low-rank structure the total complexity of the algorithm depends linearly with respect to the one-dimensional grid size. Linear complexity allows for the usage of fine grids, e.g. $8192^3$ and, thus, cheap extrapolation procedure. We test the proposed approach on closed-shell atoms up to the argon, several molecules and clusters of hydrogen atoms. All tests show systematical convergence with the required accuracy.