A b i n i t i o studies of the hydrated H3O+ ion. II. The energetics of proton motion in higher hydrates (n=3–5)

Abstract

Ab initio molecular orbital calculations on the higher hydrates of H₃O⁺, using a split valence level basis set (4–31G), have led to the following results. (1) Energies for successive hydration are in good accord with gas‐phase thermochemical data. (2) Hydrogen‐bonded OH and O⋅⋅⋅O distances in H₉O₄⁺ are in excellent agreement with condensed phase diffraction data. (3) Large variations in OH (≲0.08 Å) and O⋅⋅⋅O (∼0.25 Å) distances caused by strong hydrogen bonding are monotonically correlated with OH stretching force constants and frequencies, which cover a range of 1500 cm⁻¹. (4) Excellent quantitative correlation is obtained between calculated and observed infrared gas‐phase frequencies for six intense OH stretching bands, as represented by the least‐squares fit, ν_exp=−704+1440 (F_SG_S)^1/2±15 cm⁻¹. This least squares relationship is used to assign some of the other experimental absorption bands from the gas phase. The only major uncertainty is in the case of the symmetric H₃O⁺ mode in H₃O⁺(H₂O)₃. (5) The relative magnitudes of frequencies for symmetric (ν₁) and antisymmetric (ν₃) stretching modes are found to switch upon passing from H₃O⁺ (ν₁<ν₃) to H₃O⁺(H₂O)₃ (ν₁≳ν₃). (6) The isoelectronic species H₃O⁺(H₂O)₃ and OH⁻(H₂O)₃ are predicted have very similar frequencies for symmetric stretching of hydrogen‐bonded OH groups, in accord with Raman data for aqueous acid. (7) Addition of a fourth water molecule to the first solvation shell of H₃O⁺ does not lead to any significant stabilization, a result consistent with x‐ray and neutron diffraction results from aqueous HCl. (8) The most stable isomer of H₁₃O₆⁺ is found to be an H₉O₄⁺ moiety, somewhat perturbed from three‐fold symmetry by two second shell water molecules. (9) The tetrahydrate of the diaquahydrogen ion yields an H₁₃O₆⁺ structure 2.2 kcal/mole higher in energy and provides a possible model for the symmetric intermediate in aqueous proton transfer (observed activation energy, 2.4 kcal/mole). This model emphasizes the importance of concerted reorganization of OH and O⋅⋅⋅O bond lengths in the vicinity of the excess proton, with proton tunneling not expected to be a major factor, since the postulated intermediate offers a symmetric single‐well potential for the excess proton.