**Inertial extended-Lagrangian scheme for solving charge equilibration
models**

I Leven and T Head-Gordon, PHYSICAL CHEMISTRY CHEMICAL PHYSICS, 21, 18652-18659 (2019).

DOI: 10.1039/c9cp02979f

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.

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