Beyond the local approximation to exchange and correlation: the role of the Laplacian of the density in the energy density of Si

TL;DR

This paper demonstrates that the Laplacian of the electron density effectively predicts and corrects the discrepancies in exchange-correlation energy densities between local density approximation and variational Monte Carlo calculations for silicon.

Contribution

It introduces a Laplacian-based correction to the LDA energy density, improving accuracy across different silicon systems without extensive additional modeling.

Findings

Laplacian of density predicts XC energy density discrepancies effectively.

A simple Laplacian-based correction improves LDA accuracy.

The correction works for both Si atom and crystal.

Abstract

We model the exchange-correlation (XC) energy density of the Si crystal and atom as calculated by variational Monte Carlo (VMC) methods with a gradient analysis beyond the local density approximation (LDA). We find the Laplacian of the density to be an excellent predictor of the discrepancy between VMC and LDA energy densities in each system. A simple Laplacian-based correction to the LDA energy density is developed by means of a least square fit to the VMC XC energy density for the crystal, which fits the homogeneous electron gas and Si atom without further effort.