Modifying the HF procedure to include screening effects

TL;DR

This paper introduces a generalized Hartree-Fock scheme incorporating screening effects through a self-consistent, diagrammatic approach, applied to the homogeneous electron gas, resulting in modified self-energy spectra and screening properties.

Contribution

It develops a novel self-consistent formulation of the Hartree-Fock method that includes screening effects via a diagrammatic energy functional and applies it to the electron gas.

Findings

Self-energy dispersion does not vanish at the Fermi level.

Screened potentials lead to higher energies than traditional HF.

Static screening modifies electron spectrum and screening properties.

Abstract

A self-consistent formulation is proposed to generalize the HF scheme with the incorporation of screening effects. For this purpose in a first step, an energy functional is defined by the mean value for the full Hamiltonian, not in a Slater determinant state, but in the result of the adiabatic connection of Coulomb plus the nuclear (jellium charge) in the Slater determinant. Afterwards, the energy functional defining the screening approximation is defined in a diagrammatic way, by imposing a special "screening" restriction on the contractions retained in the Wick expansion. The generalized self-consisting set of equations for the one particle orbitals are written by imposing the extremum conditions. The scheme is applied to the homogeneous electron gas. After simplifying the discussion by assuming the screening as static and that the mean distance between electrons is close to the Bohr radius, the equations for the electron spectrum and the static screening properties are solved by iterations. The self-consistent results for the self-energies dispersion does not show the vanishing density of states at the Fermi level predicted by the HF self-energy spectrum. In this extreme non retarded approximation, both, the direct and the exchange potentials are strongly screened, and the energy is higher that the one given by the usual HF scheme. However, the inclusion of the retardation in the exact solution and the sum rules associated to the dielectric response of the problem, can lead to energy lowering. These effects will be considered in the extension of the work.