Exact-Exchange Density Functional Theory applied to a strongly inhomogeneous electron gas

TL;DR

This paper applies a new quasi-two-dimensional exact-exchange density functional theory to a strongly inhomogeneous electron gas and finds excellent agreement with computationally intensive quantum Monte Carlo simulations, especially as the system becomes more quasi-two-dimensional.

Contribution

It introduces a novel quasi-two-dimensional exact-exchange formalism within Density Functional Theory and validates it against high-accuracy Variational Quantum Monte Carlo results.

Findings

Remarkable agreement between DFT and VMC in exchange-hole densities

Quantitative match in exchange-energy densities and total exchange energies

Improved agreement as the external potential strength increases

Abstract

A recently developed quasi two-dimensional exact-exchange formalism within the framework of Density Functional Theory has been applied to a strongly inhomogeneous interacting electron gas, and the results were compared with state-of-the-art Variational Quantum Monte Carlo (VMC) numerical simulations for a three-dimensional electron gas under a strong external potential. The VMC results, extremely demanding from the computational point of view, could be considered as a benchmark for the present theory. We observe a remarkable qualitative and quantitative agreement between both methods from the comparison of the exchange-hole densities, exchange-energy densities, and total exchange-energies per particle. This agreement is increasingly improved with the strength of the external potential when the electron gas becomes quasi-two-dimensional.