Efficient Computation of the Electrostatic Component of Solvation Free Energy via a Two-Point Padé Approximation

We develop an efficient method to compute the electrostatic component of the solvation free energy via the two-point Padé approximation. The Padé approximant uses four parameters to describe the electrostatic free energy change of the solvation process, which could be readily determined from four thermodynamic properties obtained in two simulations, namely, the first- and second-order free energy gradients of any two states. Therefore, instead of sampling at multiple intermediate states, only two states, e.g., electrostatically fully solvated and desolvated, are needed to determine the Padé approximant and compute the corresponding free energy contribution. Applications to several model systems, including both neutral and charged species, show that the method can accurately produce electrostatic solvation free energy. The method would be very useful to save computational cost in applications in which accurate but expensive energy functions like quantum mechanics are used.