Theoretical Study on Open-Shell Singlet Character and Second Hyperpolarizabilities in Cofacial π-Stacked Dimers Composed of Weak Open-Shell Antiaromatic Porphyrins.

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 NiII 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.

Evaluation of Aromaticity for Open-Shell Singlet Dicyclopenta-Fused Acenes and Polyacenes Based on a Magnetically Induced Current.

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.

Benzonorcorrole NiII Complexes: Enhancement of Paratropic Ring Current and Singlet Diradical Character by Benzo-Fusion.

Fused benzene rings to antiaromatic compounds generally improve their stability but attenuate their antiaromaticity. The opposite case is now reported. NiII benzonorcorroles were synthesized and the effect of benzo-fusion on the antiaromaticity was elucidated. The benzo-fusion resulted in significant decrease of the HOMO-LUMO gaps and enhancement of the paratropic ring current effect. Furthermore, the introduction of the benzo groups induced singlet diradical character in the antiaromatic porphyrinoid.

Third-Order Nonlinear Optical Properties of One-Dimensional Quinoidal Oligothiophene Derivatives Involving Phenoxyl Groups.

The diradical characters (y) and third-order nonlinear optical (NLO) properties of open-shell quinoidal oligothiophene derivatives with phenoxyl groups, and the corresponding reduced (hydrogenated)-state oligomers, are investigated by using the broken-symmetry density functional theory method. The oxidized (dehydrogenated) states are predicted to have an open-shell singlet ground state and their y values increase with the number of units. Static second hyperpolarizabilities (γ) of the open-shell oligomers with intermediate y are shown to be enhanced significantly compared with those of the closed-shell analogues. Furthermore, owing to the effective diradical distances, the γ values of open-shell oligomers are found to exceed that of s-indaceno[1,2,3-cd;5,6,7-c'd']diphenalene, which is known as an organic molecule with the largest two-photon absorption cross-section in this size of the pure hydrocarbons. This feature extends the range of efficient open-shell third-order NLO materials to a novel class of one-dimensional conjugated oligomers with redox-based high tunability of third-order NLO properties.

Theoretical Study on the Open-Shell Singlet Nature and the Second Hyperpolarizabilities of Corannulene Derivatives with Two Phenoxyl Radicals.

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.

Origin of the Enhancement of the Second Hyperpolarizabilities of Metal-Carbon Bonds.

The spin-unrestricted coupled-cluster method was employed to investigate the origin of the second hyperpolarizabilities (γ) in model systems involving metal-carbon bonds with various bond lengths as a function of their diradical character (y) and charge transfer (CT). These systems exhibit unique features: (i) σ electrons give the dominant contribution to γ, (ii) the π electrons contribution to γ is negative, (iii) when the bond length increases, γ exhibits two positive extrema, which are associated with the CT nature and the intermediate diradical character, respectively, (iv) and one negative extremum corresponding to intermediate CT and diradical character, and (v) in the bond stretching process, the maximum γ amplitude per σ bond is about 7 times larger than that per π bond. These features are significantly different from those observed in pure organic systems.

Diradical Character Tuning for the Third-Order Nonlinear Optical Properties of Quinoidal Oligothiophenes by Introducing Thiophene-S,S-dioxide Rings.

To create a design guideline for efficient third-order nonlinear optical (NLO) molecules, the chain-length (n) dependences of the diradical character y and the longitudinal second hyperpolarizability γ of quinoidal oligothiophenes (QTs), from monomers to octamers, involving thiophene-S,S-dioxide rings are investigated by using the density functional theory method. It turns out that the diradical character of the modified QTs is reduced as compared to those of the pristine QTs. By introducing an appropriate number of oxidized rings into the QT framework, intermediate y values can be achieved even in the systems with large values of n, in which the pristine QTs are predicted to have pure diradical character. Such intermediate diradical oligomers are shown to exhibit enhanced γ values as compared to the pristine QTs with the same value for n. From the calculation results, the introduction of the optimal number of thiophene-S,S-dioxide rings is predicted to be an efficient chemical modification for optimizing the third-order NLO properties of open-shell QTs through tuning the diradical characters.

Interplay between Open-Shell Character, Aromaticity, and Second Hyperpolarizabilities in Indenofluorenes.

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.