DFT Analysis of Fe(H ₂O) ₆ ³⁺ and Fe(H ₂O) ₆ ²⁺ Structure and Vibrations; Implications for Isotope Fractionation

Density functional theory (DFT) calculations of structure and vibrational modes are reported for the ferrous and ferric hexaaquo ions, using B3LYP gradient-corrected hybrid density functionals, standard 6-31G* basis sets on the O and H atoms, and Ahlrichs' valence triple-ζ (VTZ) basis set on the Fe atom. The effect of hydrogen bonding in solvents or in crystals has been approximated with the polarizable continuum model (PCM). The optimized structures predict a regular FeO ₆ octahedron for Fe(H ₂O) ₆ ³⁺, as expected, but inequivalent Fe-O distances (C _i symmetry) for Fe(H ₂O) ₆ ²⁺, reflecting Jahn-Teller distortion. PCM shortens the Fe-O distances and produces excellent agreement with crystallographic data. In vacuo, DFT produces a stable T _h structure for Fe(H ₂O) ₆ ³⁺, with the H ₂O molecules lying in FeO ₄ planes, but PCM induces tilting and rotation of the H ₂O molecules. This effect is shown to be an artifact of the PCM methodology, but it does not significantly affect the computed Fe-O stretching and bending frequencies, which are the main determinants of the equilibrium isotope fractionation. The DFT-computed vibrational modes are consistent with reported Raman and infrared spectra of the complexes in crystals, except that assigned O-Fe-O bending frequencies are higher than predicted, probably owing to strong hydrogen bonding in the ionic lattices. The computation produces a significant revision of the ^54/56Fe isotope sensitivity of the Fe(H ₂O) ₆ ³⁺ and Fe(H ₂O) ₆ ²⁺ vibrational partition functions, relative to a previous estimate from an empirical FeO ₆ force field. The difference arises in part from lowered bending mode frequencies and in part from including modes of the bound H ₂O (rocking, wagging, and twisting), which have nonnegligible ^54/56Fe isotope shifts. Excellent agreement is found with the recently determined isotope fractionation factor for the Fe(H ₂O) ₆ ^3+/2+ exchange equilibrium. DFT vibrational analysis of metal complexes can contribute significantly to the evaluation of geochemical and biogeochemical isotope fractionation data.