Accurate MP2-based force fields predict hydration free energies for simple alkanes and alcohols in good agreement with experiments

Abstract

Force fields for four small molecules, methane, ethane, methanol, and ethanol, were created by force matching MP2 gradients computed with triple-zeta-quality basis sets using the Adaptive Force Matching method. Without fitting to any experimental properties, the force fields created were able to predict hydration free energies, enthalpies of hydration, and diffusion constants in excellent agreements with experiments. The root mean square error for the predicted hydration free energies is within 1 kJ/mol of experimental measurements of Ben-Naim et al. [J. Chem. Phys. 81(4), 2016-2027 (1984)]. The good prediction of hydration free energies is particularly noteworthy, as it is an important fundamental property. Similar hydration free energies of ethane relative to methane and of ethanol relative to methanol are attributed to a near cancellation of cavitation penalty and favorable contributions from dispersion and Coulombic interactions as a result of the additional methyl group.

FIG. 1.

Distribution of hydrogens of methane (left) and of water molecules (right) for dimers extracted from a liquid simulation. Water has been translated to the same C–O distance without changing its relative orientation. Hydrogen atoms are depicted as gray, carbon is depicted as teal, and oxygen is depicted as red. (a) Methane appears isotropic, while water exhibits preferential hydrogen locations. (b) Rotated view showing the region of lowest hydrogen density around water oxygen, which is nearest to methane. (c) Methane hydrogen distribution depicted as purely isotropic, while distribution of water hydrogen represented by the transparent isosurface. Four proposed water orientations, ω1–ω4, are shown.

FIG. 2.

Potential energy scans along the C–O axis of representative methane–water dimer configurations. Scans are performed for two methane orientations for each water orientation, ω1, ω2, and ω3, as described in the text. Percentages of liquid population represented by each orientation of water are given by the bar below the plots.

FIG. 3.

Atom types used for methane, ethane, methanol, and ethanol models. The same atom types in different molecules carry different parameters in our force fields.

FIG. 4.

Scatter plot comparing fitted and SAPE E₂ dispersion energies with and without the C₈/r⁸ term. Inclusion of the C₈/r⁸ term was not found to reduce the RMSE of the fit sufficiently to justify the inclusion in the FF’s dispersion model.

FIG. 5.

Radial distribution functions of water hydrogen (dashed lines and right ordinate axis) and water oxygen (solid lines and left ordinate axis) around the aliphatic carbons of AFM methane, ethane, methanol, and ethanol.

FIG. 6.

Radial distribution functions of water hydrogen (dashed lines and right ordinate axis) and water oxygen (solid lines and left ordinate axis) around the hydroxyl oxygen of AFM methanol (purple curves) and ethanol (green curves).

FIG. 7.

Comparison of experimental (black) and computed (blue) methane–water RDFs. Both RDFs are measured at 145 bars and 291 K.

FIG. 8.

Comparison of experimental (black) and computed (blue) methanol–water RDFs. Both RDFs are measured near 1 bar at 293 K.

FIG. 9.

Vibrational spectra of all aqueous solutes. Frequency scaling corrections for MP2/aug-cc-pVTZ were applied to all AFM spectra according to the literature. Experimental Raman spectra are shown in black for methane, methanol, ethane, and ethanol. Peak intensities have been scaled arbitrarily to aid viewing.