A local-orbital density functional formalism for a many-body atomic Hamiltonian: Hubbard–Hund’s coupling and DFT + U functional

Abstract

In the conventional DFT + U approach, the mean field solution of the Hubbard Hamiltonian associated with the d or f (iσ) electrons of a transition metal atom is used to define the DFT + U potential acting on the iσ-electrons. In this work, we go beyond that mean field solution by analyzing the correlation energy and potential for a multi-level atom described by a Kanamori Hamiltonian connected to different channels representing the environment. As a first step, we analyze the many-body solution of our model, using a local-orbital density functional formalism that takes as independent variables the orbital occupancies, n iσ , of the atomic orbitals; accordingly, we present the corresponding density functional solution describing the correlation energy and potential as a function of n iσ . Then, we use this analysis to introduce a DFT + U potential extending previous proposals to materials with arbitrarily high correlation. In particular, we find that this potential mainly screens the conventional mean field potential contribution, and also yields new terms associated with the number of atomic electrons. Our results show that the atomic correlation effects enhance the role played by the intra-atomic exchange interaction and favor the formation of magnetic solutions.