Vibrational versus electronic isotropic polarizability and first hyperpolarizability of a series of cis – Ru (II) – bipyridine complexes: A non-empirical investigation

Abstract

Dipole moments, vibrational and electronic polarizabilities and first hyperpolarizabilities of a set of nine ruthenium (II) complexes, cis-RuL₂L′₂ where L = 2,2’-bipyridine and L′ = SCN⁻ (1), SeCN⁻ (2) or TeCN⁻ (3); L = (4,4’-dicarboxyH ${}_2$ )-2,2’-bipyridine and L′ = SCN⁻ (4), SeCN⁻ (5) or TeCN⁻ (6); L = [(4,4’-dicarboxy)-2,2’-bipyridine]⁻⁴ and L′ = SCN⁻ (7), SeCN⁻ (8) or TeCN⁻ (9) have been evaluated at the non-empirical PBE1PBE/LanL2DZ level. Complete optimizations of their geometrical structures have been made followed by frequency calculations. The order of magnitude and the qualitative variation of μ, $\mathrm{\Delta }{\mathit{\alpha }}^{\mathit{e}}$ , $\mathrm{\Delta }{\mathit{\alpha }}^{\mathit{v}}$ , $\mathrm{\Delta }{\mathit{\alpha }}^{\mathit{t}\mathit{o}\mathit{t}}$ , ${\mathit{\beta }}_{\mathit{v}\mathit{e}\mathit{c}}^{\mathit{e}}$ , ${\mathit{\beta }}_{\mathit{v}\mathit{e}\mathit{c}}^{\mathit{v}}$ and ${\mathit{\eta }}_{\mathit{v}\mathit{e}\mathit{c}}^{\mathit{t}\mathit{o}\mathit{t}}$ in function of the ligands L and L′ have also been made. The complexation effects on the vector first hyperpolarizabilities have been studied. The obtained results show that both contributions to ${\mathit{\beta }}_{\mathit{v}\mathit{e}\mathit{c}}$ are substantially affected by this complexation. The highest effect of complexation is recorded in the case of the complex 8. It has been found that the complexation factor ${\mathrm{\Gamma }}^{\mathit{e}}$ is less than 0.13 and for all the considered complexes is less than ${\mathrm{\Gamma }}^{\mathit{v}}$ . The individual normal modes contributions to the vibrational first hyperpolarizability show that only a bit of fundamental normal modes, with frequencies are smaller than 50 cm⁻¹, contribute to more than 10% to ${\mathit{\beta }}_{\mathit{v}\mathit{e}\mathit{c}}^{\mathit{v}}$ .