Charging free energies for charges placed in a quasi-spherical solute of radius 4 Å. Symbols represent FEP results for charges placed at different lattice points (x, 0, 0), where x spans the distance from 0 to 3.5 Åfrom the center of the sphere; results for x = 0.5 and x = 1 are omitted in the main figure for clarity, but included in the inset. Curves represent affine-response models derived from quadratic fitting over the interval −0.2e ⩽ q ⩽ +0.2e. Inset shows that the slopes of the charging free energies are practically identical for all charge positions at q = 0, indicating a nearly uniform static potential (mean value of 43.5 kJ/mol/e (thick line) with a standard deviation 1.3 kJ/mol/e) throughout the solute.
Charging free energies for sodium and chloride. Affine-response model captures a portion of the FEP results but not over the entire range of q; piecewise response is needed to fit over the whole range. Inset: The single-coefficient response model (small symbols) reproduces the FEP results less accurately; the model parameters were determined separately over the intervals q > 0 and q < 0 but constrained to have the same static potential.
Piecewise affine response model for charging free energies for buried as well as surface charges in the 4-Å-radius lattice solute. A static potential of 43.5 kJ/mol/e was used for all fits and then the curvatures were fit separately for positive and negative values of q. (Inset) The curvatures reveal symmetric response for deeply buried charges (the center of the sphere is 0), but an increasingly asymmetric response for charges approaching the surface.
Schematic representation of the two contributions to the asymmetric solvent response with respect to the solute charge. (a) Average water orientation at the surface of an uncharged solute gives rise to a non-zero static potential. It can be interpreted as a continuum density of oriented solvent dipoles at the surface. (b) Steric asymmetry in water hydrogen (smaller) and oxygen (larger) drives asymmetric response with water molecules being able to approach a negative charge more closely than a positive charge. This applies even to situations in which the charge is not directly solvent exposed.
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