DFT Analysis of Fe(H2O)63+ and Fe(H2O)62+ Structure and Vibrations; Implications for Isotope Fractionation

Abstract

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 FeO6 octahedron for Fe(H2O)63+, as expected, but inequivalent Fe−O distances (Ci symmetry) for Fe(H2O)62+, reflecting Jahn−Teller distortion. PCM shortens the Fe−O distances and produces excellent agreement with crystallographic data. In vacuo, DFT produces a stable Th structure for Fe(H2O)63+, with the H2O molecules lying in FeO4 planes, but PCM induces tilting and rotation of the H2O 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(H2O)63+ and Fe(H2O)62+ vibrational partition functions, relative to a previous estimate from an empirical FeO6 force field. The difference arises in part from lowered bending mode frequencies and in part from including modes of the bound H2O (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(H2O)63+/2+ exchange equilibrium. DFT vibrational analysis of metal complexes can contribute significantly to the evaluation of geochemical and biogeochemical isotope fractionation data.