Properties of short-range and long-range correlation energy density functionals from electron-electron coalescence

TL;DR

This paper investigates the properties of short-range and long-range correlation energy functionals in density functional theory by analyzing electron-electron coalescence, deriving relations for on-top pair densities, and providing parameterizations for uniform electron gas.

Contribution

It derives new properties of correlation functionals for separated electron-electron interactions and offers a parameterization for the uniform electron gas case.

Findings

Derived a general relation for on-top pair density.

Provided a parameterization for the uniform electron gas.

Supported results with extended Overhauser model calculations.

Abstract

The combination of density functional theory with other approaches to the many-electron problem through the separation of the electron-electron interaction into a short-range and a long-range contribution is a promising method, which is raising more and more interest in recent years. In this work some properties of the corresponding correlation energy functionals are derived by studying the electron-electron coalescence condition for a modified (long-range-only) interaction. A general relation for the on-top (zero electron-electron distance) pair density is derived, and its usefulness is discussed with some examples. For the special case of the uniform electron gas, a simple parameterization of the on-top pair density for a long-range only interaction is presented and supported by calculations within the ``extended Overhauser model''. The results of this work can be used to build self-interaction corrected short-range correlation energy functionals.