# Inertial Extended-Lagrangian Scheme for Solving Charge Equilibration Models

## TL;DR

This paper introduces an inertial extended-Lagrangian scheme for charge equilibration in molecular dynamics, significantly reducing the number of self-consistent field cycles needed for accurate charge calculation.

## Contribution

The paper presents a novel inertial extended-Lagrangian method that accelerates charge equilibration in reactive force field simulations, improving computational efficiency.

## Key findings

- Reduces SCF cycles by 50-80% across various systems
- Applicable to diverse molecular systems including water and energetic materials
- Enhances efficiency of charge calculation in reactive MD simulations

## Abstract

The inertial extended Lagrangian/self-consistent field scheme (iEL-SCF) has been adopted for solving charge equilibration in LAMMPS as part of the reactive force field ReaxFF, which due to the charge conservation constraint requires solving two sets of linear system of equations for the new charges at each molecular dynamics time-step. Therefore, the extended Lagrangian for charge equilibration is comprised of two auxiliary variables for the intermediate charges which serve as an initial guess for the real charges. We show that the iEL-SCF is able to reduce the number of SCF cycles by 50-80% of the original conjugate gradient self-consistent field solver as tested across diverse systems including water, ferric hydroxide, nitramine RDX, and hexanitrostilbene.

---
Source: https://tomesphere.com/paper/1905.10872