Abstract
The molecular and solvation structures of the hydrated Cu²⁺ ions and their excitation spectra were investigated using the Kohn–Sham density functional theory (DFT) and the three-dimensional reference interaction site model (3D-RISM) self-consistent field method. Five stable geometrical structures were found to exist in aqueous solution: the distorted octahedral [Cu(H₂O)₆]²⁺ in C_i and D_2h symmetries, the square pyramidal and trigonal bipyramidal [Cu(H₂O)₅]²⁺, and the square planar [Cu(H₂O)₄]²⁺. The distorted octahedral structure in the C_i symmetry is preferred in [Cu(H₂O)₆]²⁺, and the square pyramidal and trigonal bipyramidal [Cu(H₂O)₅]²⁺ show almost the same stability. Among these geometries, the six-coordinate complex [Cu(H₂O)₆]²⁺ in the C_i symmetry had the lowest Helmholtz energy. [Cu(H₂O)₆]²⁺ had a distorted octahedral structure, that is, two long axial bonds and four short equatorial bonds. The spatial and radial distribution function analyses for [Cu(H₂O)₅]²⁺ and [Cu(H₂O)₄]²⁺ showed that [Cu(H₂O)₅]²⁺ and [Cu(H₂O)₄]²⁺ had one and two solvent water molecules that constituted a distorted octahedron with ligand water distribution. The coordination numbers (CNs) derived from the distribution functions were 5.2–5.4 for [Cu(H₂O)₅]²⁺ and 5.3 for [Cu(H₂O)₄]²⁺. These results indicated that the Cu²⁺ ion in an aqueous solution had 5–6 coordination water molecules in the first hydration shell and some structures with different CNs may interchange in the solution. The excitation energies and electronic configurations of low-lying d–d excited states were calculated using the time-dependent DFT with the electric field generated by 3D-RISM. The orbital energies and electronic configurations were in a similar picture to those of the classical crystal field theory because of the highly symmetrical features of all structures. In [Cu(H₂O)₆]²⁺, the degeneracies of orbitals were resolved, whereas in [Cu(H₂O)₅]²⁺ and [Cu(H₂O)₄]²⁺, weak and strong quasi-degeneracies remained. As a result, only the four-coordinate complex generated third and fourth excited states, whereas in other complexes, there were no obvious characters of degeneracies. The resulting excitation energies were in good agreement with the absorption spectra.