# Force Balance Approach for Advanced Approximations in Density Functional Theories

## TL;DR

This paper introduces a new systematic method for determining exchange-correlation potentials in density functional theories using force balance equations, applicable to both ground-state and time-dependent cases, simplifying previous approaches.

## Contribution

It presents a novel approach based on equations of motion that avoids reliance on energy functionals and the optimized-effective-potential method, enabling straightforward approximations.

## Key findings

- Provides a feasible method for vector potentials in DFT.
- Reduces to known exchange approximations in specific limits.
- Applicable to both ground-state and time-dependent scenarios.

## Abstract

We propose a systematic and constructive way to determine the exchange-correlation potentials of density-functional theories including vector potentials. The approach does not rely on energy or action functionals. Instead it is based on equations of motion of current quantities (force balance equations) and is feasible both in the ground-state and the time-dependent setting. This avoids, besides differentiability and causality issues, the optimized-effective-potential procedure of orbital-dependent functionals. We provide straightforward exchange-type approximations for different density functional theories that for a homogeneous system and no external vector potential reduce to the exchange-only local-density and Slater X$\alpha$ approximations.