Fast calculations of electrostatic solvation free energy from reconstructed solvent density using proximal radial distribution functions

Although detailed atomic models may be applied for a full description of solvation, simpler phenomenological models are particularly useful to interpret the results for scanning many large, complex systems, where a full atomic model is too computationally expensive to use. Among the most costly are solvation free-energy evaluations by simulation. Here we develop a fast way to calculate electrostatic solvation free energy while retaining much of the accuracy of explicit solvent free-energy simulation. The basis of our method is to treat the solvent not as a structureless dielectric continuum but as a structured medium by making use of universal proximal radial distribution functions. Using a deca-alanine peptide as a test case, we compare the use of our theory with free-energy simulations and traditional continuum estimates of the electrostatic solvation free energy.