Enhancement of the third-order nonlinear optical properties in open-shell singlet transition-metal dinuclear systems: effects of the group, of the period, and of the charge of the metal atom.

Metal-metal multiply bonded complexes in their singlet state have been predicted to form a novel class of "σ-dominant" third-order nonlinear optical compounds based on the results of dichromium(II) and dimolybdenum(II) systems (H. Fukui et al. J. Phys. Chem. Lett.2011, 2, 2063) whose second hyperpolarizabilities (γ) are enhanced by the contribution of the dσ electrons with an intermediate diradical character. In this study, using the spin-unrestricted coupled-cluster method with singles and doubles as well as with perturbative triples, we investigate the dependences of γ on the group and on the period of the transition metals as well as on their atomic charges in several open-shell singlet dimetallic systems. A significant enhancement of γ is observed in those dimetallic systems composed of (i) transition metals with a small group number, (ii) transition metals with a large periodic number, and (iii) transition metals with a small positive charge. From the decomposition of the γ values into the contributions of dσ, dπ, and dδ electrons, the γ enhancements are shown to originate from the dσ contribution, because it corresponds to the intermediate diradical character region. Furthermore, the amplitude of dσ contribution turns out to be related to the size of the d(z(2)) atomic orbital of the transition metal, which accounts for the dependence of γ on the group, on the period, and on the charge of the metal atoms. These dependences provide a guideline for an effective molecular design of highly efficient third-order nonlinear optical (NLO) systems based on the metal-metal bonded systems.

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, γ, 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 γ 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 γ 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 γ is much different, that is, |γ(regular allyl cation)/γ(regular allyl radical)| = 0.61 versus |γ(phenalenyl based superallyl cation)/γ(phenalenyl based superallyl radical)| = 35. In contrast, the model ethylene, allyl radical/cation, and butadiene systems with stretched carbon-carbon bond lengths (2.0 Å), having intermediate diradical characters, exhibit similar γ features to those of the phenalenyl based superpolyene systems. This exemplifies that the size dependence of γ 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 π-electron spin states significantly reduces the γ amplitudes of the neutral phenalenyl based superpolyene systems. For phenalenyl based superallyl cation, the sign inversion of γ (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 γ. The present study paves the way toward designing a variety of open-shell NLO supermolecular systems composed of phenalenyl radical building blocks.