Electronic structures and nonlinear optical properties of trinuclear transition metal clusters M-(μ-S)-M′ (M = Mo, W; M′ = Cu, Ag, Au)

A series of trinuclear metal clusters MS4(M′PPh3)2(M′PPh3) (M = Mo,W; M′ = Cu, Ag, Au) have been studied using the density functional theory (DFT) method. The static polarizabilities and hyperpolarizabilities of the model clusters have been calculated using the finite-field (F-F) method. The model clusters, divided into two groups, are alike in the structure of two fragments of rhombic units M- (μ-S)2-M′ (M = Mo, W; M′ = Cu, Ag, Au), perpendicular to each other, which are joined by sharing the bridge metal M. It is the charge transfer from one of these moieties to the other in these characteristic sulfido-transitional metal cores that is responsible for the polarizabilities and hyperpolarizabilities. This kind of electronic delocalization, different from that of the planar π-system, is interesting and warrants further investigation. The structural effects on properties are important. In these models, considerable third-order nonlinearities are exhibited. The element substitution effect of Mo and W is weak, while that of Cu and Ag is relatively substantial. An overall order is γxxxx(Mo-Ag) > γxxxx(W-Ag) > γxxxx(Mo-Au) > γxxxx(W-Au) > γxxxx (Mo-Cu) > γxxxx(W-Cu) and γav(Mo-Ag) ∼ γav(W-Ag) > γav(Mo-Au) ∼ γav(W-Au) ∼ γav(Mo-Cu) ∼ γav(W-CU).