A Critical Analysis of Methods of Calculation of a Potential in Simulated Polar Liquids:  Strong Arguments in Favor of “Molecule-Based” Summation and of Vacuum Boundary Conditions in Ewald Summation

The calculation of the electrostatic potential inside a polar liquid in an infinitely large system simulated with periodic boundary conditions allows several alternative choices for carrying out the summation over all particles. For a summation of contributions from charge centers limited to the contents of a sphere surrounding the point where the potential is calculated, the cutoff can be based on the location of individual charge centers (so-called q-based summation) or on the location of molecular centers (M-based summation); these two methods have been found to provide consistently different values of the potential. On the other hand, for a summation based on the Ewald method, the choice of the latter's boundary conditions (“vacuum” versus “tinfoil”) affects the value of the calculated potential. A recent discussion (see, Aqvist et al. J. Phys. Chem. 1998, B 102, 3837−3840, and references therein) did not lead to a conclusion as to which is the right choice. Here, we provide a new analysis of M- and q-based cutoff methods and show the following. (i) The M-based method is the correct method to calculate the Coulombic average potential exerted by a polar molecular liquid in the center of a Lennard-Jones (LJ) solute. (ii) Each solute−solvent force field is characterized by a unique M-center for which the potential is zero in the high-temperature limit. This unique M-center is the center of the solvent−solute hard-core interaction for which the solvent molecule's orientational phase space is uncoupled from its positional phase space in the rotational high-temperature limit. (iii) The best value of the average Coulomb potential of water solvent inside a “methane” LJ solute in SPC water at T = 300 K and P = 1 bar is negative, of the order of −7 to − 8 kcal/(mol·e); this includes a uniform potential of the order of +2 to +3 kcal/(mol·e) produced by the polarized surface of the outer liquid−vapor interface of a macroscopic droplet. (iv) The q-based method of calculation of the potential violates the self-consistency of statistical sampling of the configurations of charged sites of the solvent molecules. (v) The effective M- or q-based potentials calculated with Ewald “vacuum” potential are equal to the respective Coulombic potentials. (vi) Use of “tinfoil” boundary conditions for the Ewald potential overestimates the interaction of the central cell with its surroundings and enhances periodicity, and is therefore less appropriate for simulations of liquid syste