Thiophene and its sulfur inhibit indenoindenodibenzothiophene diradicals from low-energy lying thermal triplets.

Many qualitative structure-property correlations between diradical character and emerging molecular properties are known. For example, the increase of diradical character further decreases the singlet-triplet energy gap. Here we show that inclusion of thiophenes within a quinoidal polycyclic hydrocarbon imparts appreciable diradical character yet retains the large singlet-triplet energy gap, a phenomenon that has no precedent in the literature. The low aromatic character of thiophene and its electron-rich nature are the key properties leading to these unique findings. A new indenoindenodibenzothiophene scaffold has been prepared and fully characterized by several spectroscopies, magnetic measurements, solid-state X-ray and state-of-the-art quantum chemical calculations, all corroborating this unique dichotomy between the diradical input and the emerging magnetic properties. New structure-property relationships such as these are not only extremely important in the field of diradical chemistry and organic electronics, but also provide new insights into the versatility of π-electron chemical bonding.

Tunability of Open-Shell Character, Charge Asymmetry, and Third-Order Nonlinear Optical Properties of Covalently Linked (Hetero)Phenalenyl Dimers.

Tunability of the open-shell character, charge asymmetry, and third-order nonlinear optical (NLO) properties of covalently linked (hetero)phenalenyl dimers are investigated by using the density functional theory method. By changing the molecular species X and substitution position (i, j) for the linker part, a variety of intermonomer distances R and relative alignments between the phenalenyl dimers can be realized from the geometry optimizations, resulting in a wide-range tuning of diradical character y and charge asymmetry. It is found that the static second hyperpolarizabilities along the stacking direction, γyyyy , are one-order enhanced for phenalenyl dimer systems exhibiting intermediate y, a feature that is in good agreement with the "y-γ correlation". By replacing the central carbon atoms of the phenalenyl rings with a boron or a nitrogen, we have also designed covalently linked heterophenalenyl dimers. The introduction of such a charge asymmetry to the open-shell systems, which leads to closed-shell ionic ground states, is found to further enhance the γyyyy values of the systems having longer intermonomer distance R with intermediate ionic character, that is, charge asymmetry. The present results demonstrate a promising potential of covalently linked NLO dimers with intermediate open-shell/ionic characters as a new building block of highly efficient NLO systems.

Synthesis of the Unknown Indeno[1,2-a]fluorene Regioisomer: Crystallographic Characterization of Its Dianion.

Of the five possible indenofluorene regioisomers, examples of a fully conjugated indeno[1,2-a]fluorene scaffold have so far remained elusive. This work reports the preparation and characterization of 7,12-dimesitylindeno[1,2-a]fluorene as a highly reactive species. Experimental and computational data support the notion of a molecule with pronounced diradical character that exists in a triplet ground state. As such, both NICS and ACID calculations suggest that the indeno[1,2-a]fluorene scaffold is weakly Baird aromatic. Reduction of the unstable red solid with Cs metal produces the dianion of the title compound, from which single crystals could be obtained and X-ray data acquired, thus fully corroborating the proposed indeno[1,2-a]fluorene hydrocarbon core.

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.

Intramolecular Pancake Bonding in Helical Structures.

We show that diradicaloid helical conjugated molecules can display strong through-space bonding interactions. These interactions are analogous to π-stacking pancake bonding widely observed for dimers and other aggregates of stable π-conjugated radicals. We show that these multicenter interactions can have a significant stabilizing effect, but they depend in subtle ways on the specific overlap and relative orientations of the radical carrying subunits. The specific through-space interactions between the radicaloid units occur at specific size ranges of the helical molecules.

Diradical and Ionic Characters of Open-Shell Singlet Molecular Systems.

The diradical and ionic natures of open-shell singlet systems have been investigated using new definitions of the diradical and ionic characters as well as of their densities within the valence configuration interaction (VCI) model with two electrons in two active orbitals. The two-site symmetric and asymmetric diradical models are examined by using these diradical/ionic characters. For realistic compounds, we investigate a diradicaloid diphenalenyl and a rectangular graphene nanoflake in the presence of an external static electric field, as well as π-stacked phenalenyl-derivative dimers with varying the intermonomer distance, where the central carbon atoms in the phenalenyl rings are substituted by boron (B) and nitrogen (N) atoms, respectively. It is found that the increase of charge asymmetricity induced by the static electric field decreases the diradical character and finally induces an ionic character in the ground state, while the first excited state is changed from pure ionic to diradical-dominant as the field amplitude increases. On the other hand, when increasing the intermonomer distance, the B/N substitution in the phenalenyl dimer changes the electronic state from open-shell singlet with small diradical character to closed-shell with large ionic character. These results indicate that the application of a static electric field to diradicaloids and the asymmetric substitution of a pancake bonded π-dimer combined with the variation of intermonomer distance could tune the diradical/ionic characters and therefore control the nonlinear optical responses.

Theoretical Study on the Second Hyperpolarizailities of Oligomeric Systems Composed of Carbon and Silicon π-Structures.

To explore the prospect of molecules involving silicon-silicon multiple bonds as nonlinear optical molecular systems, the relationship between the structure and the second hyperpolarizabilities γ of the oligomeric systems composed of carbon and silicon π-structures is investigated using the density functional theory method. It is found that these compounds indicate intramolecular charge transfer (ICT) from the silicon units to the carbon units together with nonzero diradical characters. The γ values of these compounds are shown to be 2-13 times as large as those of the carbon analogs. Although asymmetric carbon and silicon π-systems exhibit comparable enhancement to the corresponding symmetric systems, donor-π-donor structures exhibit remarkable enhancement of γ despite of their both-end short silicon π-chain moieties (donor units). Further analysis using the odd electron and γ densities clarifies that the intermediate diradical character also contributes to the enhancement of γ. These results predict that even short π-conjugated silicone moieties can cause remarkable enhancement of γ by introducing them into π-conjugated hydrocarbon structures.

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.

Theoretical study on the relationship between diradical character and second hyperpolarizabilities of four-membered-ring diradicals involving heavy main-group elements.

By using spin-unrestricted density functional theory methods, the relationship between the diradical character y and the second hyperpolarizability γ (the third-order nonlinear optical (NLO) properties at the molecular scale) for four-membered-ring diradical compounds, that is, cyclobutane-1,3-diyl, Niecke-type diradicals, and Bertrand-type diradicals, were investigated by focusing on the substitution effects of heavy main-group elements as well as of donor/acceptor groups on the y and γ values. It has been found that i) γ is enhanced in the intermediate y region for these four-membered-ring diradicals, ii) Niecke-type diradicals with intermediate y values, which are realized by tuning the combination of the main-group elements involved, exhibit larger γ values than Bertrand-type diradicals, and iii) the y value and thus γ value can be controlled by modifying the both-end donor/acceptor substituents attached to carbon atoms in Nicke-type C2 P2 diradicals. These results demonstrate that four-membered-ring diradicals involving heavy main-group elements exhibit high controllability of the y and γ, which indicates the potential applications of four-membered-ring diradicals as a building block of highly efficient open-shell NLO materials.

Third-order nonlinear optical properties of one-dimensional open-shell molecular aggregates composed of phenalenyl radicals.

The impact of intermolecular interactions on the third-order nonlinear optical (NLO) properties of open-shell molecular aggregates has been elucidated by considering one-dimensional aggregates of π-π stacked phenalenyl radicals with different intermolecular distances and the long-range corrected spin-unrestricted density functional theory method. In the phenalenyl dimer, which can be considered as a diradicaloid system, the diradical character strongly depends on the intermolecular distance, and the larger the intermolecular distance is, the larger the diradical character becomes. Then, around the equilibrium stacking distance that corresponds to an intermediate diradical character, its second hyperpolarizability (γ) is maximized and its value per monomer exhibits about a 30-fold enhancement with respect to the isolated phenalenyl monomer. This suggests that equilibrium is an optimal compromise between localization and delocalization of the radical electron pairs in such pancake bonding. No such effect was observed for the closed-shell coronene dimer. Moreover, when going from the dimer (diradical) to the tetramer (tetraradical), the γ-enhancement ratio increases nonlinearly with the aggregate size, whereas switching from the singlet to the highest spin (quintet) state causes a significant reduction of γ. Finally, for the tetramer, another one-order enhancement of γ is achieved for the dicationic singlet relative to its singlet neutral state. These results demonstrate the key role of intermolecular π-π stacking interactions and charge in open-shell (supra)molecular systems to achieve enhanced third-order NLO properties.

Open-shell character and second hyperpolarizabilities of one-dimensional chromium(II) chains: size dependence and bond-length alternation effect.

Using the long-range corrected spin-unrestricted density functional theory (LC-UBLYP) method, we have investigated the longitudinal third-order nonlinear optical (NLO) properties, i.e., the second hyperpolarizabilities γ of open-shell singlet one-dimensional (1D) extended metal atom chain (EMAC) systems, chromium(II) chains Cr(II)2n (n = 1-4), with different metal-metal bond lengths from the viewpoint of the open-shell character dependences of each d orbital contribution (dσ, dπ, dδ) to γ and of the chain-length dependence of γ. It turns out that the chain length dependences of the open-shell characters of dπ and dδ orbitals at any metal-metal bond length are negligible, while the dσ open-shell character decreases as a function of chain length. The systems display bell-shaped behaviors of γ as a function of the metal-metal bond length, in which the γ values attain maxima for intermediate dσ open-shell character. The maximum γ value (γmax) exhibits remarkable enhancement as a function of chain length. It is also found that the bond length alternation (BLA) significantly affects the γ values and their chain-length dependences. The present results provide the guiding principles for designing transition-metal complexes with open-shell singlet 1D metallic chains exhibiting large third-order optical nonlinearity.