Large off-diagonal contribution to the second-order optical nonlinearities of Λ-shaped molecules

The diagonal and off-diagonal tensor components of the first hyperpolarizability of a series of Λ-shaped molecules are compared by means of ab initio and semiempirical molecular orbital calculations. The calculated results are rationalized using expressions derived from a simple valence-bond charge-transfer model in which one ground and two excited state are described as a combination of one valence-bond (VB) and two charge-transfer (CT) states. In addition to the CT character, the angle (2θ) between the two donor (D)/acceptor (A) branches is a key parameter to determine the relative magnitudes between the β_xxz and β_zzz components. In the VB-2CT model, β_xxz presents a maximum value for 2θ = 109.47°, whereas β_xxz and μ_z have the same sign. On the other hand, β_zzz decreases monotonically with θ, and its variations with the CT character follow a curve with two extrema like for one-dimensional D/A chromophores. The ab initio and semiempirical calculations as well as the VB-2CT model show that Λ-shaped molecules with large first hyperpolarizability and specific η = β_xxz/β_zzz can be designed in order to build phase-matchable second-harmonic generation crystals.