Monte Carlo tests of Orbital-Free Density Functional Theory

TL;DR

This paper uses Monte Carlo simulations to analyze the relationship between quantum kinetic energy density and semiclassical approximations in Density Functional Theory, proposing empirical corrections to improve orbital-free methods.

Contribution

It introduces an empirical correction to the semiclassical kinetic energy functional based on Monte Carlo analysis, enhancing orbital-free DFT accuracy.

Findings

Semiclassical form matches the statistical expectation of quantum kinetic energy.

Proposed empirical correction improves orbital-free DFT results.

Monte Carlo simulations validate the relationship between quantum and semiclassical energies.

Abstract

The relationship between the exact kinetic energy density in a quantum system in the frame of Density Functional Theory and the semiclassical functional expression for the same quantity is investigated. The analysis is performed with Monte Carlo simulations of the Kohn-Sham potentials. We find that the semiclassical form represents the statistical expectation value of the quantum nature. Based on the numerical results, we propose an empirical correction to the existing functional and an associated method to improve the Orbital-Free results.