Raman Spectroscopic Measurements and ab Initio Molecular Orbital Studies of Cadmium(II) Hydration in Aqueous Solution

The weak, polarized Raman band assigned to the ν 1 CdO 6 mode of the hexaaquo Cd (II) ion ( O h symmetry for the CdO 6 unit, T h with H-atoms) has been studied over the temperature range from 25 to 152 °C. The isotropic scattering geometry in R format was employed in order to measure the true vibrational contribution of the band and account for the Boltzmann temperature factor B and frequency factor. The band profile as a function of temperature has been examined analytically to extract the parameters: position of band maximum, full width at half-height (fwhh), integral intensity of the band, and relative molar scattering coefficient, S h, over the temperature range measured. The dependence on concentration has also been measured. The 358 cm -1 stretching mode of the hexaaquo Cd(II) shifts only 3 cm -1 to lower frequencies but broadens about 32 cm -1 for a 127 °C temperature increase. Two depolarized modes at 235 and 185 cm -1 could be assigned to ν 2 (e g ) and ν 5 (f 2g ), respectively. The Raman spectroscopic data suggest that the hexaaquo Cd(II) ion is thermodynamically stable in perchlorate solution over the temperature and concentration range measured. These findings are in contrast to CdSO 4 solutions, recently measured by one of us, where sulfate replaces a water molecule of the first hydration sphere. Ab initio geometry optimizations of [Cd(OH 2 ) 6 2+ ] were carried out at the Hartree−Fock and second-order Møller−Plesset levels of theory, using various basis sets up to 6-31+G*. The global minimum structure of the Cd(II) hexaaquo ion corresponds with symmetry T h . The vibrational frequencies of the [Cd(OH) 6 2+ ]cation were also calculated. The unscaled frequencies of the CdO 6 unit are lower than the experimental frequencies (ca. 16%), but scaling the calculated Hartree−Fock/MP2 vibrational frequencies (HF/6-31G*, HF/6-31+G*, and MP2/6-31G* levels) reproduces the measured frequencies. The theoretical binding energy for the hexaaquo Cd(II) ion was calculated and accounts for ca. 66% of the experimental hydration enthalpy of Cd(II). Frequency calculations are also reported for a Cd(OH 2 ) 18 2+ cluster with 6 water molecules in the inner sphere and 12 water molecules in the outer sphere. The global minimum of this cluster corresponds with symmetry T . The ν 1 CdO 6 mode (unscaled) occurs at 335 cm -1, quite close to the experimental value. The water molecules of the first sphere form strong H-bonds with the water molecules in the second hydration shell because of the polarizing effect of the cadmium ion. The importance of the second hydration sphere is discussed.