Jensen-Feynman approach to the statistics of interacting electrons

TL;DR

This paper extends and numerically applies the Jensen-Feynman variational approach to better account for two-electron interactions in the statistical modeling of interacting electrons, improving free energy calculations.

Contribution

It introduces an extended Jensen-Feynman method with a new reference energy including intra-orbital interactions and demonstrates its effectiveness through numerical applications.

Findings

Linear reference energies are often sufficient for accuracy.

The recursion relation improves partition function calculations.

Applying Jensen's inequality to convex functions enhances the approach.

Abstract

Faussurier et al. [Phys. Rev. E 65, 016403 (2001)] proposed to use a variational principle relying on Jensen-Feynman (or Gibbs-Bogoliubov) inequality in order to optimize the accounting for two-particle interactions in the calculation of canonical partition functions. It consists in a decomposition into a reference electron system and a first-order correction. The procedure appears to be very efficient in order to evaluate the free energy and the orbital populations. In this work, we present numerical applications of the method and propose to extend it using a reference energy which includes the interaction between two electrons inside a given orbital. This is possible thanks to our efficient recursion relation for the calculation of partition functions. We also show that a linear reference energy, however, is usually sufficient to achieve a good precision and that the most promising way to improve the approach of Faussurier et al. is to apply Jensen's inequality to a more convenient convex function.