Second Hyperpolarizabilities of Singlet Polycyclic Diphenalenyl Radicals:  Effects of the Nature of the Central Heterocyclic Ring and Substitution to Diphenalenyl Rings

Adopting density functional theory and a hybrid exchange-correlation functional, the relationship between the second hyperpolarizability (γ) and the diradical character has been investigated for diphenalenyl-based compounds containing different heterocyclic five-membered central rings (C4H4X, where X = NH, PH, O, S, CH2, SiH2, BH, GaH, CO, CS, and CSe) or substituted by donor (NH2)/acceptor(NO2) groups. It turns out that these structural modifications can tune the diradical character from 0.0 to 0.968 and lead to variations of γ over more than 1 order of magnitude, demonstrating the controllability of γ in this family of compounds. In particular, when the central ring is strongly aromatic, the diradical character is larger than 0.7, which is associated with pretty large γ values except for almost the pure diradical case (y ≈ 1). On the other hand, when the aromaticity decreasesor the antiaromaticity increasesthe diradical character and the second hyperpolarizability get smaller. These relationships are correlated to structural (bond length alternation) and charge distribution (charge transfer between the phenalenyl rings and the central ring) properties, which account for the relative importance of the resonance diradical, zwitterionic, and quinoid forms. Therefore, the diradical character and the second hyperpolarizability can be controlled by the aromaticity of the ring while the paradigm of the enhancement of γ for intermediate diradical character is globally verified. Then, upon introducing donor groups, the zwitterionic character increases, leading to closed-shell species and small second hyperpolarizabilities. In the case of substitution by acceptor groups, the charge transfer is reduced but the diradical character and the second hyperpolarizability hardly changes.