Shadow Molecular Dynamics with a Machine Learned Flexible Charge Potential

We present an extended Lagrangian shadow molecular dynamics scheme with an interatomic Born-Oppenheimer potential determined by the relaxed atomic charges of a second-order charge equilibration model. To parameterize the charge equilibration model, we use machine learning with neural networks to determine the environment-dependent electronegativities and chemical hardness parameters for each atom, in addition to the charge-independent energy and force terms. The approximate shadow molecular dynamics potential in combination with the extended Lagrangian formulation improves the numerical stability and reduces the number of Coulomb potential calculations required to evaluate accurate conservative forces. We demonstrate efficient and accurate simulations with excellent long-term stability of the molecular dynamics trajectories. The significance of the choosing fixed or environment-dependent electronegativities and chemical hardness parameters is evaluated. Finally, we compute the infrared spectrum of molecules via the dipole auto-correlation function and compare to experiments to highlight the accuracy of the shadow molecular dynamics scheme with a machine learned flexible charge potential.