Using strong‐correlated quantum chemical calculations, we have revealed the relationship between diradical character y and second hyperpolarizability γ third‐order nonlinear optical (NLO) property in ...alkaline earth metal inverse sandwich complexes, which have Mg or Ca atoms as an alkaline earth metal and a four‐ or eight‐membered ring as an organic ligand (4‐Mg, 4‐Ca, 8‐Mg, and 8‐Ca). Through detailed analysis of diradical character with the valence configuration interaction (VCI) model, we have found that the higher period metal leads to a larger metal–metal distance with larger y value 0.8–0.9, while a larger ring size of organic ligand leads to smaller diradical character values due to the larger transfer integral (smaller distance) between metals. These features are explained by orbital diagrams and VCI analysis. Indeed, it is found that 8‐Ca has the largest γ value, which is 4.94 times as large as that of the system with the smallest γ value (8‐Mg). From these results, we obtain a design guideline for efficient third‐order NLO systems based on alkaline earth metal inverse sandwich complexes: a combination of alkaline earth metal with a higher period number and larger organic antiaromatic (4nπ) ring tends to enhance the γ value due to the larger metal–metal distance with keeping an intermediate y value.
The diradical characters of alkaline earth metal inverse sandwich complexes are controlled by the metal species (Ca, Mg) and ring ligands (cyclopentadienyl, cyclooctatetraene). A combination of higher period alkaline earth metal and larger organic antiaromatic (4nπ) ring tends to enhance the second hyperpolarizability due to the intermediate diradical character and large effective diradical distance.
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.
All in a twist: Helical diradicaloid molecules can display strong through‐space π‐stacking pancake bonding. These multicenter two‐electron bonding interactions between the radicaloid terminal units occur at specific size ranges of the helical molecules.
Of the five possible indenofluorene regioisomers, examples of a fully conjugated indeno1,2‐afluorene scaffold have so far remained elusive. This work reports the preparation and characterization of ...7,12‐dimesitylindeno1,2‐afluorene 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 indeno1,2‐afluorene 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 indeno1,2‐afluorene hydrocarbon core.
Not a matter of IF but when: Described is the preparation of the last elusive indenofluorene (IF) regioisomer. While the body of circumstantial spectroscopic data support formation of the highly reactive triplet diradicaloid, definitive structural proof is provided by X‐ray diffraction analysis of crystals of the dianion, obtained by reduction of the indeno1,2‐afluorene with Cs metal.
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.
Close encounters of the third order: The impact of intermolecular interactions on the third‐order nonlinear optical (NLO) properties of one‐dimensional open‐shell molecular aggregates composed of phenalenyl radicals is theoretically investigated (see figure).
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 C2P2 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.
Relationship issues: The relationship between the diradical character (y) and second hyperpolarizability (γ; third‐order nonlinear optical property) for several four‐membered‐ring diradicals involving heavy main‐group elements was investigated (see figure). It is found that γ is enhanced in the intermediate y region, and that y and γ can be controlled by modifying the main‐group elements and the donor/acceptor groups substituted into the four‐membered ring.
Using the spin-unrestricted density functional theory method, we have investigated a novel class of open-shell singlet fused-ring molecules with helical scaffolds toward the development of highly ...efficient third-order nonlinear optical (NLO) systems. It turns out that the helical molecules possess pancake bonding with intermediate diradical character and thereby exhibit large enhancement of orientationally-averaged second hyperpolarizability γs values (third-order NLO properties at the molecular scale) as compared to their closed-shell analogues. It is also found that the asymmetric charge distribution between the cofacial radical sites located on both the terminal rings of the helical scaffold leads to further enhancement of the γ value in the intermediate open-shell character region as compared to the open-shell analogues without asymmetric charge distributions. These results indicate that the helical systems with intermediate diradical character are potential candidates for the building block of highly efficient open-shell singlet NLO materials, which are superior to the conventional closed-shell NLO materials.
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.
Tuning nonlinear optical dimers: Open‐shell characters, charge asymmetry, and third‐order nonlinear optical properties of covalently linked (hetero)phenalenyl dimers are investigated by density functional calculations. By changing the linker species, the diradical/ionic characters can be finely tuned to achieve significantly enhanced second hyperpolarizability (see scheme).
•Second hyperporizabilities (γ) of cyclic thiazyl diradicaloids (TZs) were studied.•The diradical character (y) depends on the size, and the positions of heteroatoms.•The increase in y with the size ...depends on the positions of heteroatoms.•The γ values of TZs show an enhancement in the intermediate y region.
Using the spin-unrestricted density functional theory method, the relationship between the diradical characters (y) and the longitudinal second hyperpolarizabilities (γ) has been investigated for several cyclic thiazyl compounds (TZs) and polyacenes (PAs) involving up to six fused rings (N=6). It turns out that y strongly depends on the substitution position of the nitrogen and sulfur atoms in the five-membered rings of TZs and that its increase with N depends on the substitution positions. The γ values of TZs show an enhancement for intermediate y values and are significantly larger than those of PAs of similar size.
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.
•Second hyperpolarizabilities γ of transition-metal dinuclear complexes.•Axial ligand effects on the diradical character (y) dependence of the γ.•The axial ligand coordinated complexes show larger y ...values than the bare system.•Open-shell dσ electrons enhance the |γ| as compared to the bare system.•Large negative γ values emerge in the small metal–metal bond-length region.
We investigate the axial ligand effects on the diradical character (y) dependences of the second hyperpolarizabilities (γ) of transition-metal dinuclear complexes, Mo(I)2(CO)2, with different bond lengths (R) using the spin-unrestricted coupled-cluster method. Mo(I)2(CO)2 exhibits intrinsic y–γ correlation and dominant dσ-electron contribution to the maximum γ (γmax), which are also observed in the bare dinuclear analogs. The axial-ligand coordination to Mo(I)2 is found to cause the increase of the diradical character of the dσ orbital, the emergence of large negative γ for small R, and an enhancement of |γmax| by a factor of ∼30 as compared to the bare analogs.
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