Focusing on the original and extended indenofluorene frameworks, we theoretically investigate the interplay between the open-shell character, the aromaticity, and the second hyperpolarizabilities γ. Interestingly, the odd-electron density distribution, which illustrates the spatial contribution of the open-shell character, is found to well correlate with the magnetic shielding tensor distribution, which indicates the magnetic criteria of the aromaticity. This can be explained with the partial destruction of the π-delocalization due to the emergence of odd (unpaired) electrons. Further investigation on the γ values, which are third-order nonlinear optical (NLO) properties at the molecular scale, reveals the correlation of strong enhancement of γ and its density distribution to the intermediate open-shell character and its odd-electron density distribution. These results will contribute not only to the detailed understanding of the structure-NLO property relationships in the indenofluorene frameworks but also to building new design guidelines for highly efficient NLO molecules based on the open-shell character-aromaticity correlation.

The aromaticity of dicyclopenta-fused acenes (DPAs) and polyacenes (PAs) of increasing size has been studied by evaluation with the GIMIC method at the DFT level of the magnetically-induced currents (MICs), and by analyzing their spatial distributions. For these open-shell singlet molecules, spin-restricted and -unrestricted treatments provide very different MICs, the latter ones providing the most reliable solution. These MICs and the differences between spin-restricted and -unrestricted treatments are interpreted in terms of the bond current strengths and the current gradients, which indicate the bond aromaticity and enable the spatial distributions of the diatropic and paratropic currents to be analyzed, respectively. In particular, they allow the rationalization of the MICs in correlation with the odd-electron density distributions and their diradical characters. These calculations demonstrate that 1) in increasingly large PAs the bond current strengths get smaller and smaller than in benzene and get almost similar in the central and terminal rings, 2) for DPAs the MICs increase from dominant paratropic currents and antiaromaticity in the small compounds to diatropic currents and aromaticity in the larger ones, and 3) in the largest DPAs, the central rings are characterized by large diatropic currents and the terminal five-membered rings, for which the odd-electron densities are localized by weak ones.

From the analysis based on the broken-symmetry density functional theory (DFT) calculations, we in this study propose a strategy to enhance the open-shell characters and third-order nonlinear optical (NLO) properties of π-stacked dimers composed of antiaromatic molecules with weak open-shell characters. For this purpose, we here constructed cofacial π-stacked dimer models composed of aromatic and antiaromatic Ni porphyrins in order to examine the π-π stacking distance (R) dependence of the diradical characters (y) and static second hyperpolarizabilities (γ). The antiaromatic porphyrin dimers are found to have intermediate y around R∼3.3 Å, the result of which originates in the unique intermolecular interactions between the antiaromatic monomers. Static γ along the stacking direction of such antiaromatic porphyrin dimers with intermediate diradical characters are shown to be enhanced significantly as compared to those of the isolated monomers and the aromatic porphyrin dimers.

Open‐shell singlet nature, aromaticity, and second hyperpolarizabilities of two kinds of curved π‐conjugated fragments of C60 fullerene, called C60 flakes, together with their corresponding planar analogues are theoretically investigated. It is found that one curved system, A-1, exhibits intermediate open‐shell singlet nature, while the other structure, B-1, and the two corresponding planar systems possess a closed‐shell ground state. The variation of the open‐shell singlet nature is explained by the number of Clar's sextets in the resonance structures, which is associated with the local aromaticity, as quantified by the NICS0 values. The calculated orientationally averaged second hyperpolarizabilities show that the intermediate open‐shell singlet system A‐1 exhibits the best performance, and that the other curved system B‐1 is the worst among the four C60 flakes, whereas all systems exhibit better performance than the original spherical C60 system. This tendency suggests that a lower dimensionality in the π‐conjugated structure is beneficial to the construction of efficient nonlinear optical molecules. The present results not only show that the open‐shell singlet system A‐1 is a performant nonlinear optical molecule, but they also contribute to a deeper understanding of the electronic structure of curved π‐conjugated molecules. Copyright © 2016 John Wiley & Sons, Ltd.

Using the spin-unrestricted density functional theory method, we investigate the interplay between the diradical character y and second hyperpolarizabilities γ (the third-order nonlinear optical (NLO) properties at the molecular scale) of corannulene derivatives with two phenoxyl radicals. This molecule in the singlet state exhibits intermediate y and thus displays a significantly larger γ value than the triplet state and the closed-shell bis-phenol analogue. We also examine the planar molecules involving a coronene moiety in place of the curved corannulene. The intermediate y and large γ values of the corannulene systems are found to originate not from their curved skeleton but from the equilibrium between benzenoid/quinoid resonance forms due to delocalization of the radical electrons of the terminal phenoxyl rings. The longitudinal γ value of the singlet state is found to be comparable to that of s-indaceno[1,2,3-cd;5,6,7-c'd']diphenalene, which is known to be one of the organic molecules with the largest two-photon absorption cross section in this size of pure hydrocarbons. The present system is thus expected to be a promising candidate for highly efficient open-shell NLO molecules.