Variational minimization scheme for the one-particle reduced density matrix functional theory in the ensemble N-representability domain

TL;DR

This paper introduces a variational minimization scheme for 1-RDM functional theory within the ensemble N-representability domain, enabling more flexible functional development beyond natural orbital restrictions, and demonstrates its effectiveness on model systems.

Contribution

It proposes a novel variational scheme that splits the 1-RDM minimization, facilitating the development of orbital occupation functionals and extending the applicability of 1-RDM theory.

Findings

Successful application to the Hubbard model with known functionals

Effective testing on the dihydrogen molecule

Potential for improved functional development in quantum chemistry

Abstract

The one-particle reduced density-matrix (1-RDM) functional theory is a promising alternative to density-functional theory (DFT) that uses the 1-RDM rather than the electronic density as a basic variable. However, long-standing challenges such as the lack of Kohn--Sham scheme and the complexity of the pure $N$-representability conditions are still impeding its wild utilization. Fortunately, ensemble $N$-representability conditions derived in the natural orbital basis are known and trivial, such that almost every functionals of the 1-RDM are actually natural orbital functionals which do not perform well for all the correlation regimes. In this work, we propose a variational minimization scheme in the ensemble $N$-representable domain that is not restricted to the natural orbital representation of the 1-RDM. We show that splitting the minimization into the diagonal and off-diagonal part of the 1-RDM can open the way toward the development of functionals of the orbital occupations, which remains a challenge for the generalization of site-occupation functional theory in chemistry. Our approach is tested on the uniform Hubbard model using the M\"uller and the T\"ows--Pastor functionals, as well as on the dihydrogen molecule using the M\"uller functional.