Probabilistic method to determine electron correlation energy

TL;DR

This paper introduces a probabilistic approach to calculating electron correlation energy by representing the Coulomb interaction with mean and standard deviation, providing a new, general method beyond mean-field approximations.

Contribution

It presents a novel probabilistic method that models electron interactions using mean and standard deviation, improving correlation energy estimation without higher unoccupied states.

Findings

Provides a new representation of orbital energies as Ei ± delta(Ei)

Determines correlation energy within the independent electron approximation

Offers a universal technique applicable to any interacting particle system

Abstract

A new method to determine electron correlation energy is described. This method is based on a better representation of the potential due to interacting electrons that is obtained by specifying both the average and standard deviation. The standard deviation is determined from a probabilistic interpretation of the Coulomb interaction between electrons. This leads to a better representation of orbital energies as Ei (plus-minus) delta(Ei), where Ei is the Hartree-Fock orbital energy and delta(Ei), the spread, is an indicator of the magnitude of correlation energy. This new representation of the potential when combined with an empirical constant leads naturally to a new method to determine electron correlation energy. Correlation energy is determined within the independent electron approximation without any contribution from higher energy unoccupied states. A consistent physical interpretation that an electron occupies a given position when other electrons are farther than on average can be made. It is a general technique that can be used to determine correlation energy in any system of particles with inter-particle interaction V(r1, r2) and can be considered to be universal first step beyond mean-field theory.