Local and global interpolations along the adiabatic connection of DFT: A study at different correlation regimes

TL;DR

This paper explores local and global interpolation methods along the adiabatic connection in density functional theory, analyzing their effectiveness across different correlation regimes using the solvable Hooke's atom series.

Contribution

It compares global and local interpolation approaches in DFT and investigates various energy density features and correlation regimes with analytical models.

Findings

Global and local interpolations show distinct behaviors across correlation regimes.

Energy densities and correlation kinetic energy densities reveal key features of electron correlation.

The study provides insights into constructing more accurate DFT approximations.

Abstract

Interpolating the exchange-correlation energy along the density-fixed adiabatic connection of density functional theory is a promising way to build approximations that are not biased towards the weakly correlated regime. These interpolations can be done at the global (integrated over all spaces) or at the local level, using energy densities. Many features of the relevant energy densities as well as several different ways to construct these interpolations, including comparisons between global and local variants, are investigated here for the analytically solvable Hooke's atom series, which allows for an exploration of different correlation regimes. We also analyze different ways to define the correlation kinetic energy density, focusing on the peak in the kinetic correlation potential.