Ion-Hydroxyl Interactions: From High-Level Quantum Benchmarks to Transferable Polarizable Force Fields

Abstract

Ion descriptors in molecular mechanics models are calibrated against reference data on ion-water interactions. It is then typically assumed that these descriptors will also satisfactorily describe interactions of ions with other functional groups, such as those present in biomolecules. However, several studies now demonstrate that this transferability assumption produces, in many different cases, large errors. Here we address this issue in a representative polarizable model and focus on transferability of cationic interactions from water to a series of alcohols. Both water and alcohols use hydroxyls for ion-coordination, and, therefore, this set of molecules constitutes the simplest possible case of transferability. We obtain gas phase reference data systematically from "gold-standard" quantum Monte Carlo and CCSD(T) methods, followed by benchmarked vdW-corrected DFT. We learn that the original polarizable model yields large gas phase water → alcohol transferability errors - the RMS and maximum errors are 2.3 and 5.1 kcal/mol, respectively. These errors are, nevertheless, systematic in that ion-alcohol interactions are overstabilized, and systematic errors typically imply that some essential physics is either missing or misrepresented. A comprehensive analysis shows that when both low- and high-field responses of ligand dipole polarization are described accurately, then transferability improves significantly - the RMS and maximum errors in the gas phase reduce, respectively, to 0.9 and 2.5 kcal/mol. Additionally, predictions of condensed phase transfer free energies also improve. Nevertheless, within the limits of the extrathermodynamic assumptions necessary to separate experimental estimates of salt dissolution into constituent cationic and anionic contributions, we note that the error in the condensed phase is systematic, which we attribute, at least, partially to the parametrization in long-range electrostatics. Overall, this work demonstrates a rational approach to boosting transferability of ionic interactions that will be applicable broadly to improving other polarizable and nonpolarizable models.

Figure 1:

Comparison of substitution energies ΔE obtained from PBE0+TS and the original (MM) and recalibrated (MM-vdW*) molecular mechanics model. The ΔE values are estimated for the substitution reactions given by Equation 2, and they are computed using geometries relaxed separately at the respective levels of theory. The letters W, M, E and P refer, respectively, to water, methanol, ethanol and propanol.

Figure 2:

Comparison of induced dipoles obtained from the MM model against those obtained from MP2. ${\mu }_r^{ind}$ is the component of the induced dipole parallel to the vector connecting the unit point charge to the oxygen atoms of the molecules. Induced dipoles obtained using the original MM model with damping factor a = 0.39 are shown in red and those obtained using modified damping factors are shown in blue. The solid blue lines show induced dipoles obtained using damping factors fitted against MP2 values in the distance range 2.2–3.1 Å, and the dashed blue lines show induced dipoles obtained using damping factors fitted against MP2 values in the distance range 2.6–3.6 Å for water and 2.6–3.65 Å for alcohols. The two distance ranges essentially correspond to the first coordination shells of Na⁺ and K⁺ ions determined from radial distribution functions. The geometries used for these calculations are essentially derived from the geometries of the molecules optimized in the presence of a Na⁺ ion, but after replacing the coordinates of the ion with a point charge and translating the molecule along the vector connecting the point charge and the oxygen atom of the molecule. We note that re-optimization of geometries following translation and with constraints on non-hydrogen atoms has a negligible effect on the reported result. MP2 electron densities are estimated using the aug-cc-pVDZ basis set, and we note that the effect of using a larger basis set (aug-cc-pVTZ) is negligible on the electron density.

Figure 3:

Comparison of substitution energies ΔE obtained from PBE0+TS and the recalibrated MM models, vdW-Pol^† and vdW-Pol*. The ΔE values are estimated for the substitution reactions given by Equation 2, and they are computed using geometries relaxed separately at the respective levels of theory. The letters W, M, E and P refer, respectively, to water, methanol, ethanol and propanol.

Figure 4:

Predicted values of condensed phase transfer free energies (kcal/mol) from the Orig, vdW* and vdw-Pol* models compared against experiment. (a) ΔE_{water→alcohol} is the transfer free energy of an ion from water→alcohol, and (b) $\Delta F_{water\to alcohol}^{K\to Na}$ is the difference between the transfer free energies of K⁺ and Na⁺ ions. While estimation of ΔF_{water→alcohol} from experiments involves extra-thermodynamic assumptions, the estimation of $\Delta F_{water\to alcohol}^{K\to Na}$ does not. Expt-TATB and Expt-CPA refer to two different experimental estimates based on two different extra-thermodynamic assumptions (see text for details). The errors bars on the experimental estimates indiate the upper-limits of uncertainties reported in the respective studies.^,

Figure 5:

(a) Comparison of distance-dependent Na⁺-ligand pair interaction energies obtained from the vdW-Pol* model against reference values from PBE0+TS. (b) Effect of altering Na⁺ vdW parameters on Na⁺-water interaction energies.