On the Validity of Electrostatic Linear Response in Polar Solvents

Abstract

The standard approximation in continuum electrostatic theory, that polar liquids respond linearly to changes in electric fields, is examined on a microscopic level by molecular dynamics and thermodynamic perturbation simulations. Electrostatic free energies associated with the process of “charging” a solute in a solvent are evaluated and compared to the predictions from linear response, for a number of compounds. It is found that the linear response approximation generally holds well for monovalent ionic solutes, while it is less accurate for dipolar ones. Deviations observed for dipolar compounds are reflected by unequal curvatures of the free energy functions (potentials of mean force) near their respective minima for the “polar” and “nonpolar states”. The short-range nature of dipolar fields gives relatively larger weight to the innermost solvation shells in determining the electrostatic part of the solvation energy, compared to the case of ionic solutes. These inner shells can exhibit nonlinear response due to saturation and/or disruption of the H-bond network (in protic solvents) near the solute. This nonlinearity appears to reach a maximum when the strengths of solute−solvent and solvent−solvent interactions are matched. We also find that the average potential produced by solvent water is negative for an uncharged van der Waals cavity. While this has no bearing on the validity of linear response, it affects the magnitude of the hydration energy for certain ions. Relationships between solvation energies and average interaction energies, derived in this work, can be useful for simplified free energy calculations and their applications to drug design.

The electrostatic response of water to neutral polar solutes: Implications for continuum solvent modeling

“…These results contrast with prior observations of a linear electrostatic response of water to the charging of small ions of up to about ± 1e, 25,60,77,78 which have lent support to the validity of the linear response approximation in continuum solvation models. The distinctly supralinear pattern of the present macrocyclic hosts cannot be attributed to their ability to sequester water molecules in their binding cavities, because we observe similar nonlinearity for the small molecules formaldehyde and methanol, which bear the main polar functional groups of the CBs and CDs, respectively.…”

“…As observed here and previously, [24][25][26] hydroxyl groups generate a particularly nonlinear solvation response. It has been argued that this results from a special interaction of hydroxyls with the solvent's hydrogen bonding network.…”

“…It has been argued that this results from a special interaction of hydroxyls with the solvent's hydrogen bonding network. 25 In order to test this idea, we systematically modified the hydrogen-bonding network of water around a methanol dimer by varying the intermonomer distance from 2 to 8 Å (Figure 2(a)). The dip in the polar solvation free energy at a distance of 4 Å (Figure 2(a), inset), indicates cooperative localization (bridging) of water molecules, [65][66][67] and con- firms a marked alteration of the hydrogen-bonding network.…”

“…If the actual response were nonlinear, this could lead to errors in computed solvation free energies. Although some degree of sublinearity may be expected for ionic solutes, due to dielectric saturation, simulations with explicit water models have also yielded evidence of a less expected supralinear electrostatic response to neutral polar solutes, [24][25][26] and we recently noticed the same phenomenon when analyzing the hydration of macrocyclic host molecules in the cucurbituril (CB) and cyclodextrin (CD) classes.…”

Predictions of Binding of a Diverse Set of Ligands to Gelatinase-A by a Combination of Molecular Dynamics and Continuum Solvent Models

“…[15][16][17][18][19][20][21][22] In the LIE approach proposed by Åqvist, ∆G b can be computed from ligand interaction energies in the bound and free states. On the basis of the linear response consideration, only averages of the interaction energies between the ligand and its surroundings need to be evaluated.…”