# Functional Derivative of the Zero Point Energy Functional from the Strong Interaction Limit of Density Functional Theory

## TL;DR

This paper derives an explicit functional derivative for the zero point energy term in a simplified strong interaction limit of density functional theory, providing insights into strongly correlated electron systems.

## Contribution

It presents a new explicit expression for the ZPE functional derivative in a specific two-electron, one-dimensional case, advancing the understanding of strong correlation in DFT.

## Key findings

- Derived explicit ZPE functional derivative for two-electron systems
- Confirmed the expression numerically and verified sum-rule compliance
- Showed ZPE potential can produce a bond mid-point peak in dissociation

## Abstract

We derive an explicit expression for the functional derivative of the subleading term in the strong interaction limit expansion of the generalized Levy--Lieb functional for the special case of two electrons in one dimension. The expression is derived from the zero point energy (ZPE) functional, which is valid if the quantum state reduces to strongly correlated electrons in the strong coupling limit. The explicit expression is confirmed numerically and respects the relevant sum-rule. We also show that the ZPE potential is able to generate a bond mid-point peak for homo-nuclear dissociation and is properly of purely kinetic origin. Unfortunately, the ZPE diverges for Coulomb systems, whereas the exact peaks should be finite.