Third-Order Nonlinear Optical Properties of Open-Shell Supermolecular Systems Composed of Acetylene Linked Phenalenyl Radicals

The third-order nonlinear optical (NLO) properties, at the molecular level, the static second hyperpolarizabilities, gamma, of supermolecular systems composed of phenalenyl and pyrene rings linked by acetylene units are investigated by employing the long-range corrected spin-unrestricted density functional theory, LC-UBLYP, method. The phenalenyl based superethylene, superallyl, and superbutadiene in their lowest spin states have intermediate diradical characters and exhibit larger gamma values than the closed-shell pyrene based superpolyene systems. The introduction of a positive charge into the phenalenyl based superallyl radical changes the sign of gamma and enhances its amplitude by a factor of 35. Although such sign inversion is also observed in the allyl radical and cation systems in their ground state equilibrium geometries, the relative amplitude of gamma is much different, that is, |gamma (regular allyl cation)/gamma (regular allyl radical)| = 0.61 versus |gamma(phenalenyl based superallyl cation)/gamma(phenalenyl based superallyl radical)| = 35. In contrast, the model ethylene, allylradical/cation, and butadiene systems with stretched carbon-carbon bond lengths (2.0 angstrom), having intermediate diradical characters, exhibit similar gamma features to those of the phenalenyl based superpolyene systems. This exemplifies that the size dependence of gamma as well as its sign change by introducing a positive charge on the phenalenyl based superpolyene systems originate from their intermediate diradical characters. In addition, the change from the lowest to the highest pi-electron spin states significantly reduces the gamma amplitudes of the neutral phenalenyl based superpolyene systems. For phenalenyl based superallyl cation, the sign inversion of gamma (from negative to positive) is observed upon switching between the singlet and triplet states, which is predicted to be associated with a modification of the balance between the positive and negative contributions to gamma. The present study paves the way toward designing a variety of open-shell NLO supermolecular systems composed of phenalenyl radical building blocks.