Avoiding the 4-index transformation in one-body reduced density matrix functional calculations for separable functionals

TL;DR

This paper introduces an efficient cubic-cost algorithm for evaluating separable 1RDM functionals, avoiding the computationally expensive 4-index transformation, thus enabling larger-scale electronic structure calculations.

Contribution

The paper demonstrates that separable 1RDM functionals can be computed without 4-index transformations, significantly reducing computational cost in 1RDM functional theory.

Findings

Separable functionals can be evaluated at cubic cost

Most approximate 1RDM functionals are separable

New algorithm enables large-scale 1RDM calculations

Abstract

One of the major computational bottlenecks in one-body reduced density matrix (1RDM) functional theory is the evaluation of approximate 1RDM functionals and their derivatives. The reason is that more advanced approximate functionals are almost exclusively defined in the natural orbital basis, so a 4-index transformation of the two-electron integrals appears to be unavoidable. I will show that this is not the case and that so-called separable functionals can be evaluated much more efficiently, i.e. only at cubic cost in the basis size. Since most approximate functionals are actually separable, this new algorithm is an important development to make 1RDM functional theory calculations feasible for large electronic systems.