Open-Shell Character Dependences of the Second Hyperpolarizability in Two-Dimensional Tetraradicaloids

The open-shell character dependences of the second hyperpolarizability, γ, are investigated for rectangular-shaped tetraradicaloid models, such as diradical dimers, using numerically exact solutions of the extended Hubbard model. The newly defined local diradical characters for intra- and intermolecular interactions (referred to as y_intra and y_inter, respectively) are compared to conventional global ones ( y₀ and y₁) and provide a comprehensive understanding of the electronic structure of the system. The system shows two kinds of enhancements of the γ components, γ_intra and γ_inter (caused, respectively, by intra- and intermolecular diradical interactions): (i) a system with a large y_intra ( y_inter) (>∼0.4) exhibits the enhancement of a single component of γ, γ_inter (γ_intra), at the intermediate y_inter ( y_intra) region (∼0.3-0.4), and (ii) in contrast to conventional diradical systems, the system exhibits a further enhancement of both components of γ (γ_intra and γ_inter) at the region where y_intra ∼ y_inter with small values (≤∼0.3). The obtained relationships are verified by using ab initio quantum chemical calculations of the realistic tertraradical models of a 4,4'-bis(1,2,3,5-dithiazdiazolyl) (BDTDA) dimer and a disilene dimer. The present results are expected to pioneer an alternative class of two-dimensional multiradical NLO systems, which potentially cause further enhancement of γ as compared with conventional intermediate diradical NLO systems.