# Fermionic correlations as metric distances: a useful tool for materials science

## TL;DR

This paper introduces a new metric for measuring distances between exchange-only correlations in many-electron systems, enabling better analysis of density functional approximations and applications in materials design.

## Contribution

The authors present a rigorous, size-independent metric for exchange correlations that captures fundamental physical features and aids in evaluating density functional methods.

## Key findings

- The metric reflects atomic periodicity.
- It effectively assesses density functional approximations.
- Potential applications in high-throughput materials screening.

## Abstract

We introduce a rigorous, physically appealing, and practical way to measure distances between exchange-only correlations of interacting many-electron systems, which works regardless of their size and inhomogeneity. We show that this distance captures fundamental physical features such as the periodicity of atomic elements, and that it can be used to effectively and efficiently analyze the performance of density functional approximations. We suggest that this metric can find useful applications in high-throughput materials design.