# Bonds, lone pairs, and shells probed by means of on-top dynamical correlations

## TL;DR

This paper enhances the Electron Localization Function (ELF) by incorporating antiparallel-spin electron pair correlations using density functional approximations, providing improved spatial descriptions of bonds in molecules like H2.

## Contribution

It introduces a novel method that complements ELF with antiparallel-spin pair information, requiring minimal additional computational effort.

## Key findings

- Provides a spatial description of H2 bond not available with ELF
- Captures trends in other systems where ELF is less effective
- Requires only a modest increase in computational resources

## Abstract

The Electron Localization Function (ELF) by Becke and Edgecombe [J. Chem. Phys. {\bf 92}, 5397 (1990)] is routinely adopted as a descriptor of atomic shells and covalent bonds. Since the ELF and its related quantities find useful exploitation also in the construction of modern density functionals, the interest in complementing the ELF is linked to both the quests of improving electronic structure descriptors and density functional approximations. The ELF uses information which is available by considering parallel-spin electron pairs in single-reference many-body states. In this work, we complement this construction with information obtained by considering antiparallel-spin pairs whose short-range correlations are modeled by a density functional approximation. As a result, the approach requires only a contained computational effort. Applications to a variety of systems show that, in this way, we gain a spatial description of the bond in H$_2$ (which is not available with the ELF) together with some trends not optimally captured by the ELF in other prototypical situations.