Ab initio SCF molecular orbital calculations have been performed on the free Cu(OH₂)₆²⁺ complex in D_2h symmetry. Two extrema in the adiabatic electron energy potential surface were obtained corresponding to a tetragonal distortion from the regular T_h symmetry of the octahedral complex, as expected from the Jahn-Teller theorem in a case with strong E-e type vibronic coupling. The tetragonally elongated octahedral structure with Cu-20_ax at 2.25 AA and Cu-40_eq at 2.06 AA gave a slightly lower energy (72 cm^-1) than the compressed geometry with Cu-20_ax at 2.02 AA and Cu-40_eq at 2.17 AA. The calculated Jahn-Teller energy is 650 cm^-1 from that of the regular T_h symmetry with Cu-60 at 2.115 AA. EXAFS measurements were performed on aqueous Cu²⁺ solutions and showed a greater distortion with Cu-40_eq at 1.99 AA and Cu-20_ax at about 2.29 AA. Infrared absorption spectroscopic measurements were made on the O-D stretching vibrations of HDO molecules in aqueous Cu²⁺ and Ni²⁺ solutions with added D₂O in order to study the hydrogen bonds from the hydrated ions. A distorted Cu(OH₂)₆²⁺ ion is expected to form hydrogen bonds of unequal strength because of the stronger polarisation of the more strongly bonded equatorial water molecules. Two bands ascribed to the hydration of the Cu²⁺ ion were obtained, the more intense corresponding to the strongest hydrogen bonds at approximately=2400 cm^-1, and the weaker at approximately=2530 cm^-1, whereas for Ni²⁺ only one band at approximately=2420 cm^-1 was found. With the use of a correlation between R_O...O versus nu _OD from crystal structure data the mean hydrogen-bonded O...O distances to the second hydration shell are estimated to about 2.74 AA from the equatorial water molecules and 2.88 AA from the axial. The IR data show that the distortions induced by the Jahn-Teller effect on the second hydration sphere are visible on a vibrational timescale, despite the fast intramolecular inversion of the distortion axis between the three principal octahedral directions. The splitting of the nu _OD bands in the Tutton salts Cs₂(M(OH₂)₆)(SO₄)₂, M=Cu or Ni, with some added D₂O has also been measured and compared to crystal structure data of the hydrogen bonded distances. The separation of about 107 cm^-1 between the two groups of O-D stretching vibrations found in the Cu salt can be ascribed to a static Jahn-Teller effect.