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

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 Müller and the Töws--Pastor functionals, as well as on the dihydrogen molecule using the Müller functional.

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Cited by in corpus (4)

• A toolbox of spin-adapted generalized Pauli constraints
• Capturing electron correlation at mean-field cost: Assessment of i-DMFT and the underlying correlation conjecture
• Refining ensemble $N$-representability of one-body density matrices from partial information
• Spin adaptation of the cumulant expansions of reduced density matrices