Theoretical Assessment of the Second-Order Nonlinear Optical Responses of Lindqvist-Type Organoimido Polyoxometalates.

The second-order nonlinear optical properties of Lindqvist-type organoimido polyoxometalates bearing donor and acceptor substituents are evaluated by employing density functional theory and time-dependent density functional theory using the ωB97X-D range-separated hybrid exchange-correlation functional to describe accurately the field-induced effects. The hyper-Rayleigh scattering responses, β (-2ω; ω, ω), and the depolarization ratio are the targeted quantities. They are analyzed by resorting to the two-state model, which reduces the full summation-over-state expression to a single diagonal term and relates the response to a few spectroscopic quantities.