CALCULATION OF ELECTROSTATIC FREE-ENERGY DIFFERENCES WITH A TIME-SAVING APPROXIMATE METHOD

A method for obtaining approximate electrostatic free energy differences with molecular dynamics or Monte Carlo computer simulations is developed, which yields results that fall within 1 or 2 kcal/mol of those obtained from the corresponding thermodynamic integration calculations, while consuming less than half of the computer time. The method is based on the fact that, in most systems whose reactant and product states differ only in the charges assigned to the atoms, a linear response is observed as one state is transformed into the other. In other words, the transformation from reactant state to product state (or vice versa) may be thought of as the gradual application of a perturbation that the system responds to linearly. For these systems, the integrand in the thermodynamic integration equation can be reliably approximated by a linear function of the coupling parameter used to carry out the transformation from one state to the other. The two coefficients that define this function (and thus also define the approximate free energy difference) can be determined from a single, relatively short simulation on a hybrid potential surface composed of a 50%/50% combination of reactant and product potentials. The approximation may be applied to systems in which dielectric saturation does not occur and in which the conformations of reactant- and product-state molecules are not too different. Criteria for assessing the conditions under which the approximation may be used are discussed.