An Overview of Electrostatic Free Energy Computations for Solutions and Proteins

Free energy simulations for electrostatic and charging processes in complex molecular systems encounter specific difficulties owing to the long-range, 1/r Coulomb interaction. To calculate the solvation free energy of a simple ion, it is essential to take into account the polarization of nearby solvent but also the electrostatic potential drop across the liquid-gas boundary, however distant. The latter does not exist in a simulation model based on periodic boundary conditions because there is no physical boundary to the system. An important consequence is that the reference value of the electrostatic potential is not an ion in a vacuum. Also, in an infinite system, the electrostatic potential felt by a perturbing charge is conditionally convergent and dependent on the choice of computational conventions. Furthermore, with Ewald lattice summation and tinfoil conducting boundary conditions, the charges experience a spurious shift in the potential that depends on the details of the simulation system such as the volume fraction occupied by the solvent. All these issues can be handled with established computational protocols, as reviewed here and illustrated for several small ions and three solvated proteins.