Multipole electrostatics in hydration free energy calculations

Abstract

Hydration free energy (HFE) is generally used for evaluating molecular solubility, which is an important property for pharmaceutical and chemical engineering processes. Accurately predicting HFE is also recognized as one fundamental capability of molecular mechanics force field. Here, we present a systematic investigation on HFE calculations with AMOEBA polarizable force field at various parameterization and simulation conditions. The HFEs of seven small organic molecules have been obtained alchemically using the Bennett Acceptance Ratio method. We have compared two approaches to derive the atomic multipoles from quantum mechanical calculations: one directly from the new distributed multipole analysis and the other involving fitting to the electrostatic potential around the molecules. Wave functions solved at the MP2 level with four basis sets (6-311G*, 6-311++G(2d,2p), cc-pVTZ, and aug-cc-pVTZ) are used to derive the atomic multipoles. HFEs from all four basis sets show a reasonable agreement with experimental data (root mean square error 0.63 kcal/mol for aug-cc-pVTZ). We conclude that aug-cc-pVTZ gives the best performance when used with AMOEBA, and 6-311++G(2d,2p) is comparable but more efficient for larger systems. The results suggest that the inclusion of diffuse basis functions is important for capturing intermolecular interactions. The effect of long-range correction to van der Waals interaction on the hydration free energies is about 0.1 kcal/mol when the cutoff is 12Å, and increases linearly with the number of atoms in the solute/ligand. In addition, we also discussed the results from a hybrid approach that combines polarizable solute with fixed-charge water in the HFE calculation.

Figure 1

Thermodynamic cycle of HFE calculation in explicit water MD simulations. Potential energy of the solute backbone includes valence interactions and vdW interactions within the solute itself.

Figure 2

Convergence of HFE of ethylbenzene at different simulation time with three vdW decoupling protocols. Hydration free energies with 18 vdW steps (a) are in solid line with diamond, 11 vdW steps (b) in dashed line with square, and 9 vdW steps (c) in dotted line triangle. The bars are the statistical errors computed using Bennett's formula

Figure 3

O··O radial distribution function for TIP3P liquid water and TIP3P–like liquid water at 298 K.