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

• URL: http://arxiv.org/abs/2405.10593v2
• Date: Mon, 19 Aug 2024 12:15:42 GMT
• Title: Variational minimization scheme for the one-particle reduced density matrix functional theory in the ensemble N-representability domain
• Authors: Matthieu Vladaj, Quentin Marécat, Bruno Senjean, Matthieu Saubanère,
• Abstract summary: The one-particle reduced density-matrix (1-RDM) functional theory is a promising alternative to density-functional theory (DFT) 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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