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 particl es. For a summation of contributions from charge centers limited to the con tents of a sphere surrounding the point where the potential is calculated, the cutoff can be based on the location of individual charge centers (so-ca lled q-based summation) or on the location of molecular centers (M-based su mmation); these two methods have been found to provide consistently differe nt 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" ver sus "tinfoil") affects the value of the calculated potential. A recent disc ussion 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 fol lowing. (i) The M-based method is the correct method to calculate the Coulo mbic average potential exerted by a polar molecular liquid in the center of a Lennard-Jones (LJ) solute. (ii) Each solute-solvent force field is chara cterized by a unique M-center for which the potential is zero in the high-t emperature 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-t emperature 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 p olarized surface of the outer liquid--vapor interface of a macroscopic drop let. (iv) The q-based method of calculation of the potential violates the s elf-consistency of statistical sampling of the configurations of charged si tes of the solvent molecules. (v) The effective M- or q-based potentials ca lculated with Ewald "vacuum" potential are equal to the respective Coulombi c potentials. (vi) Use of "tinfoil" boundary conditions for the Ewald poten tial overestimates the interaction of the central cell with its surrounding s and enhances periodicity, and is therefore less appropriate for simulatio ns of liquid systems.