Density functional study of the vibrational frequencies of Lindqvist polyanions

Abstract

The structures and vibrational spectra of the Lindqvist polyanions [Mo 6O 19] 2−, [W 6O 19] 2−, [Mo 6O 19] 3−, [VMo 5O 19] 3− and [VMo 5O 19] 4− have been calculated using density functional theory. The agreement between the previously reported vibrational spectra and the calculated values is extremely good. For [Mo 6O 19] 2−, a detailed comparison between the performance of commonly used functionals and basis sets and between Hartree–Fock and density functional methods has been performed. Whilst all density functional methods perform adequately, the Hartree–Fock method overestimates the strength of the metal–oxygen bonding and this is reflected in poor reproduction of the stretching frequencies. The results suggest that the local density approximation with Slater type orbitals and relativistic corrections is best able to model both the structure and vibrational spectra of these polyanions when treated as pseudo-gas phase species. The calculations are extremely computationally demanding requiring precise energies and geometries and cannot presently be considered a standard task for the study of these large, heavy element cluster anions. The vibrational analyses confirm the high symmetry for these anions suggested by previous geometry calculations.