# The Computation of Local Stress in ab initio Molecular Simulations

## TL;DR

This paper develops formulas for calculating local stress in ab initio molecular dynamics models, specifically for Born-Oppenheimer and Ehrenfest dynamics, and compares these with full quantum simulations.

## Contribution

It introduces new formulas for local stress computation in ab initio models, applicable to tight-binding and real-space methods, enhancing analysis accuracy.

## Key findings

- Formulas for local stress are derived for different ab initio models.
- Comparisons show the formulas closely match full ab initio simulations.
- The work improves understanding of stress distribution in quantum-based molecular dynamics.

## Abstract

Motivated by the increasingly more important role of ab initio molecular dynamics models in material simulations, this work focuses on the definition of local stress, when the forces are determined from quantum-mechanical descriptions. Two types of ab initio models, including the Born-Oppenheimer and Ehrenfest dynamics, are considered. In addition, formulas are derived for both tight-binding and real-space methods for the approximations of the quantum-mechanical models. The formulas are examined via comparisons with full ab initio molecular simulations.