Shadow Molecular Dynamics for General Nonlinear Flexible-Charge Models
Abstract
Machine-learned interatomic potentials have greatly expanded the reach of molecular dynamics simulations, but complex chemical environments often require explicit treatment of long-range electronic response, including charge transfer and polarization. Physics-based flexible-charge models capture these effects but require global nonlinear charge equilibration at every time step to obtain Born-Oppenheimer energies and forces. This process is computationally expensive and can lead to instabilities unless tightly converged. Here, we introduce a shadow molecular dynamics framework for flexible-charge models with arbitrary local nonlinearities and long-range multipolar electrostatics. We replace the exact Born-Oppenheimer potential with a nearby shadow potential obtained by exactly equilibrating a partially linearized electronic energy functional. This provides conservative forces and reduces the global nonlinear equilibration to a quasi-diagonal linear problem that can be solved directly at low cost. Auxiliary dynamical electronic degrees of freedom, propagated through an extended-Lagrangian dynamics, capture the long-range electronic response and define the reference state for the linearization of the energy functional. GPU-accelerated simulations with over 100,000 atoms demonstrate that the shadow potential closely follows the tightly converged Born-Oppenheimer surface, while maintaining long-term stability at a computational cost approaching that of a fixed-charge model. These advances establish an efficient and broadly applicable framework for machine-learned interatomic potentials that explicitly incorporate long-range electrostatic interactions and environment-dependent electronic response.
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BibTeX
@misc{thomas2026shadow,
title = {{Shadow Molecular Dynamics for General Nonlinear Flexible-Charge Models}},
author = {Jos Thomas and Anthony P. Baldo and Rae A. Corrigan Grove and Mehmet Cagri Kaymak and Joshua Finkelstein and James Goff and Maksim Kulichenko and Sergei Tretiak and Nicholas Lubbers and Vishikh Athavale and Christian F. A. Negre and Michael Wall and Anders M. N. Niklasson},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03499},
eprint = {2611.03499},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03499},
}
RIS
TY - UNPB
TI - Shadow Molecular Dynamics for General Nonlinear Flexible-Charge Models
AU - Jos Thomas
AU - Anthony P. Baldo
AU - Rae A. Corrigan Grove
AU - Mehmet Cagri Kaymak
AU - Joshua Finkelstein
AU - James Goff
AU - Maksim Kulichenko
AU - Sergei Tretiak
AU - Nicholas Lubbers
AU - Vishikh Athavale
AU - Christian F. A. Negre
AU - Michael Wall
AU - Anders M. N. Niklasson
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03499
UR - https://arxiv.org/abs/2611.03499
AB - Machine-learned interatomic potentials have greatly expanded the reach of molecular dynamics simulations, but complex chemical environments often require explicit treatment of long-range electronic response, including charge transfer and polarization. Physics-based flexible-charge models capture these effects but require global nonlinear charge equilibration at every time step to obtain Born-Oppenheimer energies and forces. This process is computationally expensive and can lead to instabilities unless tightly converged. Here, we introduce a shadow molecular dynamics framework for flexible-charge models with arbitrary local nonlinearities and long-range multipolar electrostatics. We replace the exact Born-Oppenheimer potential with a nearby shadow potential obtained by exactly equilibrating a partially linearized electronic energy functional. This provides conservative forces and reduces the global nonlinear equilibration to a quasi-diagonal linear problem that can be solved directly at low cost. Auxiliary dynamical electronic degrees of freedom, propagated through an extended-Lagrangian dynamics, capture the long-range electronic response and define the reference state for the linearization of the energy functional. GPU-accelerated simulations with over 100,000 atoms demonstrate that the shadow potential closely follows the tightly converged Born-Oppenheimer surface, while maintaining long-term stability at a computational cost approaching that of a fixed-charge model. These advances establish an efficient and broadly applicable framework for machine-learned interatomic potentials that explicitly incorporate long-range electrostatic interactions and environment-dependent electronic response.
ER -