On connecting density functional approximations to theory

TL;DR

This paper explores the theoretical foundations of density functional approximations, proposing alternative perspectives such as pair density models and extrapolation methods to better understand their connection to density functional theory.

Contribution

It introduces new conceptual frameworks linking density functional approximations to underlying physical models and pair densities, addressing the lack of systematic connection.

Findings

Proposes viewing density functional models as pair density models

Suggests using density functional approximations for extrapolating physical results

Challenges traditional interpretations of density functional models

Abstract

Usually, density functional models are considered approximations to density functional theory, However, there is no systematic connection between the two, and this can make us doubt about a linkage. This attitude can be further enforced by the vagueness of the argumentation for using spin densities. Questioning the foundations of density functional models leads to a search for alternative explanations. Seeing them as using models for pair densities is one of them. Another is considering density functional approximations as a way to extrapolate results obtained in a model system to those of a corresponding physical one.