Screened Electrostatic Interactions in Molecular Mechanics

In a typical application of molecular mechanics (MM), the electrostatic interactions are calculated from parametrized partial atomic charges treated as point charges interacting by radial Coulomb potentials. This does not usually yield accurate electrostatic interactions at van der Waals distances, but this is compensated by additional parametrized terms, for example Lennard-Jones potentials. In the present work, we present a scheme involving radial screened Coulomb potentials that reproduces the accurate electrostatics much more accurately. The screening accounts for charge penetration of one subsystem's charge cloud into that of another subsystem, and it is incorporated into the interaction potential in a way similar to what we proposed in a previous article (J. Chem. Theory Comput. 2010, 6, 3330) for combined quantum mechanical and molecular mechanical (QM/MM) simulations, but the screening parameters are reoptimized for MM. The optimization is carried out with electrostatic-potential-fitted partial atomic charges, but the optimized parameters should be useful with any realistic charge model. In the model we employ, the charge density of an atom is approximated as the sum of a point charge representing the nucleus and inner electrons and a smeared charge representing the outermost electrons; in particular, for all atoms except hydrogens, the smeared charge represents the two outermost electrons in the present model. We find that the charge penetration effect can cause very significant deviations from the popular point-charge model, and by comparison to electrostatic interactions calculated by symmetry-adapted perturbation theory, we find that the present results are considerably more accurate than point-charge electrostatic interactions. The mean unsigned error in electrostatics for a large and diverse data set (192 interaction energies) decreases from 9.2 to 3.3 kcal/mol, and the error in the electrostatics for 10 water dimers decreases from 1.7 to 0.5 kcal/mol. We could have decreased the average errors further, but at the cost of sometimes significantly overestimating the screening; instead we chose a more conservative (safer) parametrization that systematically underestimates the screening (which by definition means it improves over point charges) and only occasionally overestimates it. Despite this conservative choice, we find that the screened MM method is even more accurate for the electrostatics than unscreened QM/MM calculations. This new method is easy to implement in any MM program, and it can be used to develop more physical force fields for molecular simulations.