Local reduced-density-matrix-functional theory: Incorporating static correlation effects in Kohn-Sham equations

Abstract

We propose a novel scheme to bring reduced density matrix functional theory (RDMFT) into the realm of density functional theory (DFT) that preserves the accurate density functional description at equilibrium, while incorporating accurately static and left-right correlation effects in molecules and keeping the good computational performance of DFT-based schemes. The key ingredient is to relax the requirement that the local potential is the functional derivative of the energy with respect to the density. Instead, we propose to restrict the search for the approximate natural orbitals within a domain where these orbitals are eigenfunctions of a single-particle hamiltonian with a local effective potential. In this way, fractional natural occupation numbers are accommodated into Kohn-Sham equations allowing for the description of molecular dissociation without breaking spin symmetry. Additionally, our scheme provides a natural way to connect an energy eigenvalue spectrum to the approximate natural orbitals and this spectrum is found to represent accurately the ionization potentials of atoms and small molecules.

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• On derivatives of the energy with respect to total electron number and orbital occupation numbers. A critique of Janak's theorem
• Towards a Resolution of the Static Correlation Problem in Density Functional Theory from Semidefinite Programming
• Quasi-particle energy spectra in local reduced density matrix functional theory
• Orbitals from local RDMFT: Are they Kohn-Sham or Natural Orbitals?
• Spectroscopy of the Hubbard dimer: the spectral potential
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• Many Electrons and the Photon Field -- The many-body structure of nonrelativistic quantum electrodynamics
• Effective local potentials for density and density-matrix functional approximations with non-negative screening density
• Strong correlation and charge localisation in Kohn-Sham theories with fractional orbital occupations