A local reaction field method for fast evaluation of long-range electrostatic interactions in molecular simulations

One of the major problems in molecular-dynamics simulations of polar fluids or macromolecular systems is the evaluation of electrostatic interactions. A system of N atoms demands an amount of work proportional to N2 for such calculations. Truncation procedures that neglect a significant part of the long-range effects are often necessary for computational feasibility, though such procedures may introduce serious errors in the simulations. This work introduces a simple and very effective approach for treating the long-range electrostatic forces. The present method, which is referred to as the local reaction field method, follows some of the ideas of the previously developed generalized Ewald method but then develops into a much simpler method. This is done by dividing the system into M groups of atoms and evaluating separately the short- and long-range contributions to the potential of each group. The short-range potential is evaluated explicitly as in any standard truncation method, while the long-range potential is approximated by the first four terms in a multipole expansion. In addition, the long-range potential is updated only once in every L time steps leading to a method of the order of N×M×q/L+N×P where q is related to the number of expansion terms and P is the average number of atoms inside the cutoff range. The speed, accuracy, and precision of the present method is assessed by evaluating the self-energy of a sodium ion in water and the self-energies of the acidic residues of bovine pancreatic trypsin inhibitor using an adiabatic charging free-energy perturbation approach. It is found that the present method reproduces accurately the corresponding results obtained without any cutoff but an order of magnitude faster. Furthermore, at the limit of very large systems, the speed of this method can be 2 orders of magnitude faster than that of the no-cutoff method even when each group contains only a small number of atoms. It is also found that the method gives much better results for electrostatic energies in proteins than those obtained by truncation methods. The stability and speed of the local reaction field method provides a powerful tool for the microscopic evaluation of electrostatic energies in macromolecules.