The scaling properties of exchange and correlation holes of the valence shell of second row atoms

TL;DR

This paper investigates the scaling behavior of exchange and correlation holes in the valence shells of second row atoms using advanced quantum Monte Carlo methods, providing insights into density functional theory models.

Contribution

It offers a detailed analysis of exchange and correlation hole scaling in second row atoms, testing the accuracy of the PBE functional against high-precision calculations.

Findings

Exchange hole exhibits competition between two scaling forms.

Correlation hole scaling is influenced by atomic size relative to the hole radius.

PBE model captures the main trends of exchange-correlation behavior.

Abstract

We study the exchange and correlation hole of the valence shell of second row atoms using variational Monte Carlo techniques, especially correlated estimates, and norm-conserving pseudopotentials. The well-known scaling of the valence shell provides a tool to probe the behavior of exchange and correlation as a functional of the density and thus test models of density functional theory. The exchange hole shows an interesting competition between two scaling forms -- one caused by self-interaction and another that is approximately invariant under particle number, related to the known invariance of exchange under uniform scaling to high density and constant particle number. The correlation hole shows a scaling trend that is marked by the finite size of the atom relative to the radius of the hole. Both trends are well captured in the main by the Perdew-Burke-Ernzerhof generalized-gradient approximation model for the exchange-correlation hole and energy.