Degeneracy and size consistency in electronic density functional theory

TL;DR

This paper examines fundamental issues in electronic density functional theory, focusing on size consistency and degeneracy, and analyzes how exact functionals behave with fractional electron numbers in specific atomic systems.

Contribution

It provides a conceptual analysis of size consistency problems related to degeneracy and fractional electron numbers in density functional theory.

Findings

Identifies size consistency issues linked to degeneracy in DFT.

Analyzes behavior of exact functionals for fractional electrons in atomic systems.

Highlights conceptual challenges in achieving high accuracy in DFT.

Abstract

The electronic structure calculations based upon energy density functionals are highly successful and widely used both in solid state physics and quantum chemistry. Moreover, the Hohenberg-Kohn theorems and the Kohn-Sham method provide them with a firm basis. However, several basic issues are not solved, and hamper the progress to achieve high accuracy. In this paper we focus on the conceptual problem of size consistency, basing our analysis on the non-intensive character of the (spin) electronic density in the presence of degeneracy. We also briefly discuss some of the issues concerning fractional electron numbers from the same point of view, analyzing the behavior of the exact functionals for the He and the Hooke's atom series when the number of electrons fluctuates between one and two.