# Density Functional Theory for the Electron Gas and for Jellium

## TL;DR

This paper investigates the relationship between the exact density functionals for the electron gas and jellium, showing their exchange-correlation functionals are identical, which supports using jellium simulations to develop electron gas functionals.

## Contribution

It demonstrates that the exchange-correlation functionals for inhomogeneous electron gas and jellium are the same, justifying the use of jellium in functional development.

## Key findings

- Exchange-correlation functionals are identical for both systems.
- Supports using jellium simulations to inform electron gas functionals.
- Addresses issues related to the thermodynamic limit.

## Abstract

Density Functional Theory relies on universal functionals characteristic of a given system. Those functionals in general are different for the electron gas and for jellium (electron gas with uniform background). However, jellium is frequently used to construct approximate functionals for the electron gas (e.g., local density approximation, gradient expansions). The precise relationship of the exact functionals for the two systems is addressed here. In particular, it is shown that the exchange - correlation functionals for the inhomogeneous electron gas and inhomogeneous jellium are the same. This justifies theoretical and quantum Monte Carlo simulation studies of jellium to guide the construction of functionals for the electron gas. Related issues of the thermodynamic limit are noted as well.