Intermolecular interaction effects on second hyperpolarizabilities of clusters including charged species

We investigate the intermolecular-interaction effects on the longitudinal second hyperpolarizabilities (γ) for two types of π-π stacking clusters: C₅H₇⁺ dimer and π-conjugated main chains (C_nH_n+2, 6 ≤ n ≤ 16) interacting in both end regions with two allyl cations (C₃H₅⁺). The γ values are calculated by the finite-field approach using several ab initio molecular orbital and density functional methods. It is found that in the first model the π-π interaction between the upper and lower π-orbitals significantly reduces the magnitude of effective γ per monomer, while the second model exhibits a remarkable enhancement of γ values as compared to those of isolated main chains. The analysis using the hyperpolarizability density and orbital interaction elucidates that the reduction of longitudinal γ value in the first model originates in the reduction of longitudinal π-conjugated electron distributions due to the perpendicular π-π orbital interactions, whereas the enhancement of longitudinal γ in the second model is caused by the intermolecular charge transfer between both end perturbing molecules via the main chain. On the basis of these results, we discuss a novel guideline of controlling third-order nonlinear optical properties of clusters.