Improving Operator Splitting and Effective Reaction Probability for A Reactive-Step Based Molecular Dynamics Workflow

Classical molecular dynamics (MD) simulation is the most computationally efficient way to model large molecular systems atomistically for extended periods; however, due to fixed forcefield parameters, incorporating on-the-fly quantum reactions is not straightforward. Reactive Step-Based Molecular Dynamics (RSMD) is a simple approach that incorporates quantum reactions by periodically halting the MD simulation and allowing the possibility for reactions at each halt, based on a Poisson-type reaction probability. However, this simple approach cannot capture the simultaneous involvement of diffusion and reaction processes, and because the reaction probability does not include the influence of the diffusion step, errors can be introduced, especially when the diffusion process is not significantly slower than the reaction process. In this work, the efficiency of the RSMD model is increased by reducing these errors and by addressing the influence of the diffusion process on the reaction probability. To improve these errors, we modify the RSMD mathematical framework by replacing the Trotter splitting employed in previous works with the Strang splitting scheme. To implement these Strang schemes in MD simulations and to scrutinize their validity, we introduce mathematical models involving three and four states, which correspond to two common reaction scenarios---association-dissociation reactions and homogeneous charge transfer reactions, respectively---in the presence of diffusion processes. Using these mathematical models, effective reaction probability functions are derived for various diffusion limits, for example, when diffusion processes are extremely fast or extremely slow compared to the reaction processes. All the derived reaction probability functions, in combination with appropriate Strang schemes, are validated for various diffusion regimes with respect to the reaction timescale.