(376bj) Computational Corrections for Long Range Interactions in Periodic Simulations

While molecular simulations continue to provide useful insight into the behavior of chemical compounds and materials, they often neglect important energy and pressure components. Most simulations are carried out in a periodic cell as a computational expedient to avoid boundary effects. However, this approach requires a partitioning of the short-range and long-range energy and pressure components. Typically, binary interaction potentials are truncated to avoid double counting the pair images of interacting atoms. Then, the long-range energy component due to the interactions beyond the truncated potentials is calculated separately. The basic assumption behind this long-range correction is that the atomic pair distribution function has a value of unity beyond the truncation limit. With the exception of supercritical and near critical fluids, this assumption is reasonable as these long-range corrections typically constitute the significant portion of both energy and pressure components for these simulations. Given the complexity of this long-range correction, it is often neglected. Neglecting these corrections is reasonable in drug design because the bulk properties of the system are less important than the local ligand-receptor interactions. However, the bulk system is important in the prediction of fluid equilibrium and the design of materials typically pursued by chemical engineers. Some commercial force fields compensate for these long-range corrections, but the correction is dependent on the size of the simulation. These long-range interactions are analytically calculated for dispersion interactions, but the integrals for these corrections with electrostatic charges are not convergent and require reformulation of the charge distribution with a multipole expansion. Alternatively, inverse space summations may be employed such as Ewald summations, but these are conditionally convergent. To simplify the inclusion of these important long-range corrections, we have developed a simple empirical approach to estimate these energy and pressure corrections via the extrapolation of results from simulations of various sizes. We discuss the range of simulations for which this approach is accurate and provide examples to illustrate how it improves the results of bulk simulations.