Interaction potential of Al3+ in water from first principles calculations

We present a parametrization of the interaction potential for ${\mathrm{Al}}^{\mathrm{3+}}$ in water from first principles calculations. We have performed a critical study of the ${\mathrm{Al}}^{\mathrm{3+}}\mathrm{–water}$ interaction using sequences of correlation consistent basis sets that approach the complete basis set limit and include core-valence correlation effects. We suggest as minimum theoretical requirements treatment of the electron correlation at the MP2 level of theory using a triple zeta quality basis set that accounts for the effect of core-valence correlation. The latter amounts for an increase of ∼5 kcal/mol (3%) to the stabilization energy, a shortening of 0.015 Å in the Al–O distance, and an increase of $\text{22\hspace{0.17em}}{\mathrm{cm}}^{\mathrm{-1}}$ in the harmonic frequency of the Al–O vibration. This is the first time that core-valence effects were investigated for this system. The stabilization energy of the ${\mathrm{Al}}^{\mathrm{3+}}{\mathrm{(H}}_{\mathrm{2}}\mathrm{O)}$ cluster is 201 kcal/mol and the corresponding Al–O bond length is 1.719 Å at the MP2 level of theory with the cc-pwCVQZ basis set. This minimum is metastable with respect to the ${\mathrm{Al}}^{\mathrm{2+}}{\mathrm{+H}}_{\mathrm{2}}{\mathrm{O}}^{\mathrm{+}}$ asymptote since even the second ionization potential (IP) of Al is larger than the first IP of water. The hexa-aqua cluster ${\mathrm{Al}}^{\mathrm{3+}}{\mathrm{(H}}_{\mathrm{2}}{\mathrm{O)}}_{\mathrm{6}}$ is, however, stable upon dissociation to ${\mathrm{Al}}^{\mathrm{3+}}{\mathrm{(H}}_{\mathrm{2}}{\mathrm{O)}}_{\mathrm{5}}{\mathrm{+H}}_{\mathrm{2}}\mathrm{O}$ by 64.8 kcal/mol, demonstrating the capacity of “effective” solvation in stabilizing the charge on the cation. The optimal structures of the $\text{n=5}$ and 6 clusters (having $C_{\text{2v}}$ and $T_h$ symmetries, respectively) and their harmonic vibrational frequencies are the first ones reported at the MP2 level with basis sets of this size. Core-valence correlation effects for the $\text{n=6}$ cluster are found to be of similar magnitude with those observed for the $\text{n=1}$ cluster. The stabilization energy of the $\text{n=6}$ cluster with respect to its fragments is 723.7 kcal/mol and the corresponding Al–O distance is 1.911 Å. These results were used in order to parametrize a pairwise-additive interaction potential for aluminum–water interaction that was grafted onto the Toukan–Rahman interaction potential for water. The potential model reproduces the ab initio results for ${\mathrm{Al}}^{\mathrm{3+}}{\mathrm{(H}}_{\mathrm{2}}{\mathrm{O)}}_{\mathrm{6}}$ within 2.0 kcal/mol for the stabilization energy and 0.003 Å for $R$ (Al–O) distance. Using this potential we estimated the enthalpy of solvation of ${\mathrm{Al}}^{\mathrm{3+}}$ to be −1106±6 kcal/mol, therefore favoring the lower value of the experimentally obtained data (−1115 and −1140 kcal/mol, respectively). In addition, we calculate the first peak of the Al–O radial distribution function at 1.885 Å, in excellent agreement with x-ray diffraction studies that suggest a peak at 1.882±0.004 Å. We compute the first peak of the Al–H radial distribution function at 2.473 Å and the average angle between the plane of a water molecule and the Al–O vector at −28.27°.