Ensemble interpretation ofL(S)DA+U

Abstract

We propose an ensemble interpretation of the $\text{L}(\text{S})\text{DA}+U$ functional aiming at the construction of a well-defined rigorous scheme as a reference point for further investigations of the functional. An explicit ensemble state, which realizes the conventional $\text{L}(\text{S})\text{DA}+U$ interaction term proportional to the product of the orbital-occupation numbers, is presented. It cannot, however, represent the correct interaction in the general case as it produces spurious self-interaction. We propose to consider the interaction term as resulting from a variational problem and present a method for its solution. As a functional of orbital occupations the interaction term results in piecewise constant corrections to the orbital potentials. The double-counting term is treated as the value of the interaction term for a spherically symmetric atomic configuration. The resulting expression is related to the so-called atomic limit for the double-counting term. It completely cancels the isotropic part (corresponding to the parameter $U$ of the Hubbard model) of the interaction term, so that only the anisotropic part responsible for the so-called orbital polarization correction remains.