Local aromaticity of the lowest-lying singlet States of [N]acenes (N = 6-9)

The local aromaticities of the six-membered rings in the two lowest-lying singlet states of [n]acenes (n = 6-9) have been assessed by means of three probes of local aromaticity based on structural, magnetic, and electron delocalization properties. Important differences between the local aromaticities of the closed-shell and diradical singlet electronic states are found. Thus, while the inner rings have the largest aromatic character in the closed-shell singlet states, the outer rings become the most aromatic for the diradical singlet states.     

Second hyperpolarizabilities of singlet polycyclic diphenalenyl radicals: effects of the nature of the central heterocyclic ring and substitution to diphenalenyl rings

Adopting density functional theory and a hybrid exchange-correlation functional, the relationship between the second hyperpolarizability (gamma) and the diradical character has been investigated for diphenalenyl-based compounds containing different heterocyclic five-membered central rings (C(4)H(4)X, where X = NH, PH, O, S, CH(2), SiH(2), BH, GaH, C=O, C=S, and C=Se) or substituted by donor (NH(2))/acceptor(NO(2)) groups. It turns out that these structural modifications can tune the diradical character from 0.0 to 0.968 and lead to variations of gamma over more than 1 order of magnitude, demonstrating the controllability of gamma in this family of compounds. In particular, when the central ring is strongly aromatic, the diradical character is larger than 0.7, which is associated with pretty large gamma values except for almost the pure diradical case (y approximately 1). On the other hand, when the aromaticity decreases--or the antiaromaticity increases--the diradical character and the second hyperpolarizability get smaller. These relationships are correlated to structural (bond length alternation) and charge distribution (charge transfer between the phenalenyl rings and the central ring) properties, which account for the relative importance of the resonance diradical, zwitterionic, and quinoid forms. Therefore, the diradical character and the second hyperpolarizability can be controlled by the aromaticity of the ring while the paradigm of the enhancement of gamma for intermediate diradical character is globally verified. Then, upon introducing donor groups, the zwitterionic character increases, leading to closed-shell species and small second hyperpolarizabilities. In the case of substitution by acceptor groups, the charge transfer is reduced but the diradical character and the second hyperpolarizability hardly changes.     

Towards Magnetic Carbo‐meric Molecular Materials

Numerous studies have underlined the putative diradical character of π‐conjugated molecules that can be described by closed‐shell Lewis structures, for instance, p‐dimethylene p–n phenylenes, or long polyacenes. In the latter compounds, the only way to save the aromaticity of the six‐membered rings is to give up the Lewis electron pairing in the singlet biradical ground state. The present work considers the possibility of doing the same by using the basic C₂ units of carbo‐meric architectures. A series of acyclic and cyclic carbo‐meric architectures is studied by using UB3LYP DFT broken‐symmetry calculations, including spin decontaminations and subsequent geometry optimization of the singlet diradical. The C₂ units are shown to stabilize the singlet biradical by spin delocalization, two of them playing approximately the same role as one radical‐insulating 1,4 phenylene moiety. The results are generalized to the investigation of open‐shell polyradical singlet states of rigid hydrocarbon structures, the symmetry and rigidity of which can assist cooperativity and self spin polarization effect. Several synthesis targets with challenging magnetic/spin properties are suggested in the carbo‐mer series.     

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. Ni^II 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.     

A DFT study of the ground state multiplicities of linear vs angular polyheteroacenes

Unrestricted density functional calculations in combination with the broken-symmetry approach and spin-projection methods have been employed to study a series of formally 4n pi antiaromatic linear and angular polyheteroacenes. Calculations show that the linear polyheteroacene molecules have either stable singlet zwitterionic 6-9 or singlet diradical 5 ground states because they sacrifice the aromaticity of the central arene to form two independent cyanines. The corresponding angular compounds 10-14 have robust triplet states, since they cannot create independent cyanines to escape their overall antiaromaticity. An analysis based on the SOMO-SOMO energy splittings, their spatial distributions, and the spin density populations for the triplet states is presented to clarify the factors that determine their ground state multiplicities.     

The origin of global and macrocyclic aromaticity in porphyrinoids

The global and macrocyclic aromaticity of porphyrinoids was characterized using our graph theory of aromaticity. The sequential line plots of topological resonance energy (TRE) against the number of π-electrons (N(π)) for different porphyrinoids are similar with four major extrema to those for five-membered heterocycles. This supports the view that five-membered rings are the main origin of global aromaticity in porphyrinoids. Macrocyclic circuits contribute significantly to macrocyclic π-circulation but modestly to global aromaticity. Macrocyclic aromaticity/antiaromaticity in oligopyrrolic macrocycles can be predicted by formally applying Hückel's [4n + 2] rule to an annulene-like main macrocyclic conjugation pathway (MMCP). This bridged annulene model can be justified by examining the contribution of individual macrocyclic circuits to macrocyclic aromaticity. A Hückel-like rule of macrocyclic aromaticity was found for porphyrinoid species.     

Second hyperpolarizability (gamma) of singlet diradical system: dependence of gamma on the diradical character

The dependence of the second hyperpolarizability (gamma) on the diradical character (y) for singlet diradical systems is investigated using a model compound, the p-quinodimethane (PQM) molecule with different both-end carbon-carbon (C-C) bond lengths, by several ab initio molecular orbital and density functional theory methods. The diradical character based on UHF calculations indicates that at equilibrium geometry PQM is in a singlet ground state and primarily exhibits a quinoid structure, whereas the diradical character increases when increasing both-end C-C bond lengths. At the highest level of approximation, that is, using the UCCSD(T) method with the 6-31G+diffuse p (zeta = 0.0523) basis set, the longitudinal static gamma of PQM presents a maximum value for intermediate diradical character (y approximately 0.5) while the gamma values are larger for intermediate and large diradical character (y approximately 0.5-0.7) than for small diradical character (y < 0.2). This feature suggests that the gamma values of singlet diradical systems in the intermediate and somewhat strong correlation regimes are significantly enhanced as compared to those in the weak correlation regime. These results are substantiated by a complementary study of the variation in gamma upon twisted ethylene.     

The delocalization index as an electronic aromaticity criterion: application to a series of planar polycyclic aromatic hydrocarbons

This work introduces a new local aromaticity measure, defined as the mean of Bader's electron delocalization index (DI) of para-related carbon atoms in six-membered rings. This new electronic criterion of aromaticity is based on the fact that aromaticity is related to the cyclic delocalized distribution of pi-electrons. We have found that this DI and the harmonic oscillator model of aromaticity (HOMA) index are strongly correlated for a series of six-membered rings in eleven planar polycyclic aromatic hydrocarbons. The correlation between the DI and the nucleus-independent chemical shift (NICS) values is less remarkable, although in general six-membered rings with larger DI values also have more negative NICS indices. We have shown that this index can also be applied, with some modifications, to study of the aromaticity in five-membered rings.     

A DFT study on the magnetostructural property of ferromagnetic heteroverdazyl diradicals with phenylene coupler

We have theoretically designed five different m-phenylene coupled high-spin bis-heteroverdazyl diradicals and their analogous p-phenylene coupled low-spin positional isomers. The geometry-based aromaticity index, harmonic oscillator model of aromaticity (HOMA) values for both the couplers (local HOMA), and the whole diradicals (global HOMA) have been calculated for all the diradicals. We also qualitatively relate these HOMA values with the intramolecular magnetic exchange coupling constants (J), calculated using a broken symmetry approach within unrestricted density functional theory framework. Structural aromaticity index HOMA of linkage specific benzene rings in our designed diradical systems shows that the aromatic character depends on the planarity of the molecule and it controls the sign and magnitude of J. The predicted J values are explained on the basis of spin polarization maps, average dihedral angles, and magnetic orbitals. The effect of the spin leakage phenomenon on magnetic exchange coupling constant and that on HOMA values of certain phosphaverdazyl systems has been explicitly discussed. In addition, a similar comparison is made between the calculated exchange coupling constants and corresponding HOMA values. The main novelty of this work stands on the consideration of the aromatic behavior by means of the geometrical index HOMA. We also estimate another aromaticity index, nucleus independent chemical shift (NICS) values for the phenylene coupler in each diradical to measure aromaticity and compare its value with that of HOMA. The ground state stabilities of these diradicals have also been compared.     

From Open‐Shell Singlet Diradicaloid to Closed‐Shell Global Antiaromatic Macrocycles

A dithieno[a,h]‐s‐indacene‐ (DTI‐) based diradicaloid DTI‐2Br was synthesized and its open‐shell singlet diradical character was validated by magnetic measurements. On the other hand, its macrocyclic trimer DTI‐MC3 and tetramer DTI‐MC4 turned out to be closed‐shell compounds with global antiaromaticity, which was supported by X‐ray crystallographic analysis and NMR spectroscopy, assisted by ACID and 2D‐ICSS calculations. Such change can be explained by a subtle balance between two types of antiferromagnetic spin–spin coupling along the π‐conjugated macrocycles. The dications of DTI‐MC3 and DTI‐MC4 turned out to be open‐shell singlet diradical dications, with a singlet–triplet energy gap of ?2.90 and ?2.60 kcal mol^?1, respectively. At the same time, they are both global aromatic. Our studies show that intramolecular spin–spin interactions play important roles on electronic properties of π‐conjugated macrocycles.     

多环化合物的芳香性

介绍了简单判断多环化合物的芳香性、非芳香性、反芳香性、同芳香性及反同芳香性的方法及其在有机化学中的应用.     

Aromaticity of ring carbo-mers of [N]annulenes and [N]cycloalkanes

Maps of current density induced by a perpendicular external magnetic field are calculated at the ipsocentric CTOCD-DZ/6-31G**//B3PW91/6-31G** level for ring carbo-mers of [N]-annulenes (closed-shell singlet states of C(3N)H, N = 3 to 7, with q = -1, 0, +1, 0, -1, respectively, and also the triplet ground state for N = 4) and of [N]-cycloalkanes (C(3N)H(qN), N = 3, 4, 5). Strong four-electron diatropic ring currents indicate conventional pi aromaticity for all the singlet and triplet carbo-[N]annulenes studied, with the exception of C(12)H(4), where instead the strong two-electron paratropic ring current is the signature of pi antiaromaticity. The carbo-[N]cycloalkanes (also known as [N]pericyclynes) show only localized pi currents, consistent with non-aromaticity. There is no indication of a 'homo-aromatic' ring current attributable to the in-plane pi orbitals of the inserted C2 units in any of the maps. Consequences for the interpretation of ELF (electron localisation function) populations are discussed.     

Chemistry of the aromatic 9-germafluorenyl dianion and some related silicon and carbon species

Dipotassio-9-germafluorenyl dianion (3b) was synthesized by reduction of 9,9-dichloro-9-germafluorene (4b) with sodium/potassium alloy in tetrahydrofuran. The X-ray crystal structure of 3b, like that for the analogous silicon compound 3a, shows C-C bond length equalization in the five-membered metallole rings and C-C bond length alternation in the six-membered benzenoid rings, indicating aromatic delocalization of electrons into the germole ring of 3b. Calculated nucleus independent chemical shift (NICS) values indicate that the five-membered ring is more aromatic than the six-membered rings in 3a and 3b. Derivatization of 3b with Me(3)SiCl gave 9,9-bis(trimethylsilyl)-9-germafluorene (5). Controlled oxidation of 3b yielded dipotassio-9,9'-digerma-9,9'-bifluorenyl dianion (6). Reaction of 6 with MeOH yielded 9,9'-digerma-9,9'-bifluorene (7). The X-ray structure of 6 indicates C-C bond length alternation in the five-membered rings. Thus dianion 6, like its silicon analogue 8, has the negative charges localized at metal atoms and no aromatic character. Dipotassio-9,9'-bifluorenyl dianion (9), the carbon analogue of 6, exhibits aromaticity with its X-ray crystal structure showing the C-C bond length equalization in both the five- and six-membered rings. Derivatization of 9 with MeI gave 9,9'-dimethyl-9,9'-bifluorene (10). The structure of 10 shows that the two fluorenyl rings are cis to each other with a torsional angle of 59 degrees and a long C-C single bond (1.60 A) connecting them.     

Theoretical study on the second hyperpolarizabilities of phenalenyl radical systems involving acetylene and vinylene linkers: diradical character and spin multiplicity dependences

We have investigated the static second hyperpolarizabilities (gamma) of the singlet diradical systems with intermediate diradical character involving phenalenyl radicals connected by acetylene and vinylene pi-conjugated linkers, 1 and 2, using the hybrid density functional theory. For comparison, we have also examined the gamma values of the closed-shell and pure diradical systems with almost the same molecular size as 1 and 2. In agreement with our previous prediction of the diradical character dependence of gamma, it turns out that the gamma values of 1 and 2 are significantly enhanced compared to those of the closed-shell and pure diradical systems. In the present case, distinct differences in gamma values are not observed between the two pi-conjugated linkers, though the diradical character is found to depend on the kind of linker. Furthermore, we have investigated the spin multiplicity effect on gamma. Changing from the singlet to the triplet state, the gamma values of the systems with intermediate diradical character in the singlet state are quite reduced, though those of the pure diradical systems are hardly changed. Such spin multiplicity dependence of gamma is understood by considering the difference of diradical character between their singlet states together with the Pauli principle. The present results provide a possibility of a novel control scheme of gamma for phenalenyl radical systems involving pi-conjugated linkers by adjusting the diradical character through the change of the linked position of pi-conjugated linkers and the spin multiplicity.     

Theoretical evidence for the singlet diradical character of square planar nickel complexes containing two o-semiquinonato type ligands

Density functional theory and complete active space self-consistent field computations are applied to elucidate the singlet diradical character of square planar, diamagnetic nickel complexes that contain two bidentate ligands derived from o-catecholates, o-phenylenediamines, o-benzodithiolates, o-aminophenolates, and o-aminothiophenolates. In the density functional framework, the singlet diradical character is discussed within the broken symmetry formalism. The singlet-triplet energy gaps, the energy gained from symmetry breaking, the spin distribution in the lowest triplet state, and the form of the magnetic orbitals are applied as indicators for the singlet diradical character. Moreover, a new index for the diradical character is proposed that is based on symmetry breaking. All symmetry breaking criteria show that the complexes obtained from o-catecholates and o-benzodithiolates have the largest and the smallest singlet diradical character, respectively. The singlet diradical character should be intermediate for the complexes derived from o-phenylenediamines, o-aminophenolates, and o-aminothiophenolates. The diradical character of all complexes suggests the presence of Ni(II) central atoms. This is also indicated by the d-populations computed by means of the natural population analysis.     

Retaining Hückel Aromaticity in the Triplet Excited State of Azobenzene

The implication of the potential concept of aromaticity in the relaxed lowest triplet state of azobenzene, an efficient molecular switch, using elementary aromaticity indices based on magnetic, electronic, and geometric criteria has been discussed. Azobenzene exhibits a major Hückel aromatic character retained in the diradical lowest relaxed triplet state (T₁) by virtue of a twisted geometry with partial delocalization of unpaired electrons in the perpendicular p-orbitals of two nitrogen atoms to the corresponding phenyl rings. The computational analysis has been expanded further to stilbene and N-diphenylmethanimine for an extensive understanding of the effect of closed-shell Hückel aromaticity in double-bond-linked phenyl rings. Our analysis concluded that stilbene has Hückel aromatic character in the relaxed T₁ state and N-diphenylmethanimine has a considerable Hückel aromaticity in the phenyl ring near the carbon atom while a paramount Baird aromaticity in the phenyl ring near the nitrogen atom of the C=N double bond. The results reveal the application of excited-state aromaticity as a general tool for the design of molecular switches.     

Quantum master equation method based on the broken-symmetry time-dependent density functional theory: application to dynamic polarizability of open-shell molecular systems

A novel method for the calculation of the dynamic polarizability (α) of open-shell molecular systems is developed based on the quantum master equation combined with the broken-symmetry (BS) time-dependent density functional theory within the Tamm-Dancoff approximation, referred to as the BS-DFTQME method. We investigate the dynamic α density distribution obtained from BS-DFTQME calculations in order to analyze the spatial contributions of electrons to the field-induced polarization and clarify the contributions of the frontier orbital pair to α and its density. To demonstrate the performance of this method, we examine the real part of dynamic α of singlet 1,3-dipole systems having a variety of diradical characters (y). The frequency dispersion of α, in particular in the resonant region, is shown to strongly depend on the exchange-correlation functional as well as on the diradical character. Under sufficiently off-resonant condition, the dynamic α is found to decrease with increasing y and/or the fraction of Hartree-Fock exchange in the exchange-correlation functional, which enhances the spin polarization, due to the decrease in the delocalization effects of π-diradical electrons in the frontier orbital pair. The BS-DFTQME method with the BHandHLYP exchange-correlation functional also turns out to semiquantitatively reproduce the α spectra calculated by a strongly correlated ab initio molecular orbital method, i.e., the spin-unrestricted coupled-cluster singles and doubles.     

Cyclobis(7,8‐(para‐quinodimethane)‐4,4′‐triphenylamine) and Its Cationic Species Showing Annulene‐Like Global (Anti)Aromaticity

π‐Conjugated macrocycles containing all‐benzenoid rings usually show local aromaticity, but reported herein is the macrocycle CBQT , containing alternating para‐quinodimethane and triphenylamine units displaying annulene‐like anti‐aromaticity at low temperatures as a result of structural rigidity and participation of the bridging nitrogen atoms in π‐conjugation. It was easily synthesized by intermolecular Friedel–Crafts alkylation followed by oxidative dehydrogenation. X‐ray crystallographic structures of CBQT , as well as those of its dication, trication, and tetracation were obtained. The dication and tetracation exhibited global aromaticity and antiaromaticity, respectively, as confirmed by NMR measurements and theoretical calculations. Both the dication and tetracation possess open‐shell singlet ground states, with a small singlet–triplet gap.     

Second hyperpolarizabilities (gamma) of bisimidazole and bistriazole benzenes: diradical character, charged state, and spin state dependences

The second hyperpolarizabilities of bisimidazole- and bistriazole-benzene compounds have been calculated at different levels of approximation to unravel the effects of diradical character as well as of charge and spin multiplicity. The largest second hyperpolarizabilities are associated with intermediate diradical character, provided positive charging does not compensate for this effect. For the neutral diradical bisimidazole compound, the singlet diradical species possesses a second hyperpolarizability two to three times larger than the corresponding triplet, demonstrating the possibility of spin state control of the third-order NLO responses for diradical species.     

Cyclopenta Ring Fused Bisanthene and Its Charged Species with Open‐Shell Singlet Diradical Character and Global Aromaticity/ Anti‐Aromaticity

Cyclopenta ring fused bisanthene and its charged species were synthesized. The neutral compound has an open‐shell singlet ground state and displays global anti‐aromaticity. The dication also exhibits singlet diradical character but has a unique [10]annulene‐within‐[18]annulene global aromatic structure. The dianion is closed‐shell singlet in the ground state and shows global aromaticity with 22 π electrons delocalized on the periphery. These findings prrovide new insight into the design and properties of global aromatic/anti‐aromatic systems based on π‐conjugated polycyclic hydrocarbons.