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).