The long-range corrected spin-unrestricted density functional theory, LC-UBLYP, method has been employed to unravel the relationship between the hole (referred to as “antidot”) structure of hexagonal graphene nanoflakes (HGNFs) and their properties, including their multiradical characters y i [the occupation number of the lowest unoccupied natural orbital (LUNO)+i (i = 0, 1, ...)], aromaticity, and the second hyperpolarizabilities (γ), which is the third-order nonlinear optical (NLO) response at the molecular level. These systems exhibit a wide range of open-shell/multiradical character, which shows an oscillatory behavior as a function of increasing the size of the antidot. This structural dependence is shown to originate from the oscillatory variations in the HOMO–LUMO energy gap, which result from the fact that the bonding and antibonding interactions between the central antidot-shape HGNFs and the surroundings alternate in both the HOMO and the LUMO as going from the center of the molecule to the peripheral region. Moreover, the multiradical character of these structures is strongly correlated with the variations of magnetic criteria of aromaticity, the nucleus-independent chemical shift (NICS) and the out-of-plane diagonal component of the magnetic shielding tensor (−σ zz ), as well as with the γ. So, systems with larger multiradical characters tend to exhibit larger NICS and −σ zz values, i.e., less aromaticity. Although the number of π electrons of the antidot HGNFs is smaller than that of the corresponding perfect C150H30 HGNF, their γ value can be larger as evidenced by the antidot C126H42 HGNF, which has intermediate multiradical characters (y 0 = y 1 = 0.658) and displays a γ value 1.7 times larger than that of the perfect HGNF. These strong impacts of the antidot structure on the third-order NLO properties indicate that the antidot HGNFs are promising building blocks for a new class of multiradical NLO materials, the properties of which can be controlled by adjusting the antidot size.

UV absorption maxima of trimethylsilyl-, trimethylgermyl-, and trimethylstannyl-substituted pyrenes shifted to longer wavelength than that of unsubstituted pyrene. Absorption maxima of mono-, bis-, tris-, and tetrakis(trimethylsilyl)pyrenes shifted to longer wavelength consecutively at intervals of 10 nm. Fluorescence intensities and lifetimes decreased in the order of Me3SiAr > Me3GeAr > Me3SnAr. Fluorescence intensity of 1,3,6,8-tetrakis(trimethylsilyl)pyrene was the largest among those of a series of pyrenes.

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.

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.

Effects of trimethylsilyl, trimethylgermyl, and trimethylstannyl substituents attached to fused aromatic hydrocarbons such as pyrene, anthracene, phenanthrene, and naphthalene were studied in terms of UV absorption and fluorescence properties in aerated cyclohexane solutions. Absorption maxima of trimethylsilyl-, trimethylgermyl-, and trimethylstannyl-substituted aromatic hydrocarbons shifted to longer wavelengths than those of unsubstituted ones. Absorption maxima of mono-, bis-, tris-, and tetrakis(trimethylsilyl)pyrenes shifted to longer wavelength consecutively at intervals of 10 nm. Fluorescence intensities and fluorescence lifetimes of trimethylsilyl-substituted aromatic hydrocarbons were larger and longer than those of unsubstituted ones, and they decreased in the order of Me 3 SiAr [ Me 3 GeAr [ Me 3 SnAr. Fluorescence intensity of 1,3,6,8-tetrakis(trimethylsilyl)pyrene was largest among those of a series of mono-, bis-, tris-, and tetrakis(trimethylsilyl)pyrenes under aerated conditions.