# Towards a formal definition of static and dynamic electronic correlations

## TL;DR

This paper proposes a new way to quantify static electron correlation in molecules, addressing failures of traditional methods by focusing on the occupancy of natural spin-orbitals, and demonstrates its effectiveness through molecular studies.

## Contribution

It introduces a novel measure for static electron correlation based on the N-representability of the one-body density matrix, improving understanding of electron correlation.

## Key findings

- The proposed measure correlates well with intuitive notions of static and dynamic correlation.
- Occupancy of the highest occupied natural spin-orbital is crucial for quantification.
- Results highlight the importance of the N-representability problem in electronic structure theory.

## Abstract

Some of the most spectacular failures of density-functional and Hartree-Fock theories are related to an incorrect description of the so-called static electron correlation. Motivated by recent progress on the N-representability problem of the one-body density matrix for pure states, we propose a way to quantify the static contribution to the electronic correlation. By studying several molecular systems we show that our proposal correlates well with our intuition of static and dynamic electron correlation. Our results bring out the paramount importance of the occupancy of the highest occupied natural spin-orbital in such quantification.