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Experimental and theoretical rationalization of bond-shift valence tautomerization, characterized by double-well potential surfaces, is one of the most challenging topics of study among the rich electronic properties of antiaromatic molecules. Although the pseudo-Jahn–Teller effect (PJTE) is an essential effect to provide attractive characteristics of 4nπ systems, an understanding of the structure–property relationship derived from the PJTE for planar 4nπ electron systems is still in its infancy. Herein, we describe the synthesis and characterization of two regioisomers of the thiophene-fused diareno[a,f]pentalenes 6and 7. The magnetic and optoelectronic properties characterize these sulfur-doped diareno[a,f]pentalenes as open-shell antiaromatic molecules, in sharp contrast to the closed-shell antiaromatic systems of 3and 5, in which these main cores consist of the same number of π electrons as 6and 7. Notably, thiophene-fused 6band 7bshowed pronounced antiaromaticity, the strongest among the previous systems, as well as moderate open-shell characteristics. Our experimental and theoretical investigations concluded that these properties of 6band 7bare derived from the small energy barrier Ea‡for the bond-shift valence tautomerization. The energy profile of the single crystal of 6bshowed the temperature-dependent structural variations assigned to the dynamic mutual exchange between the two Cs-symmetric structures, which was also supported by changes in the chemical shifts of variable-temperature 1H NMR spectra in the solution phase. Both experimental and computational results revealed the importance of introducing heteroaromatic rings into 4nπ systems for controlling the PJTE and manifesting the antiaromatic and open-shell natures originating from the high-symmetric structure. The findings of this study advance the understanding of antiaromaticity characterized by the PJTE by controlling the energy barrier for bond-shift valence tautomerizations, potentially leading to the rational design of optoelectronic devices based on novel antiaromatic molecules possessing the strong contributions of their high-symmetric geometries.

An open-shell germylene 1stabilized by a phenalenyl-based bidentate ligand was synthesized and characterized. Because of the high thermal stability originating from spin delocalization over the phenalenyl moiety, it was possible to isolate compound 1in crystalline form by sublimation at ca. 300 °C. Electron spin resonance (ESR) spectra, crystallographic analysis, theoretical calculations, and reactivities with carbon radicals suggest that the spin of 1is distributed on the phenalenyl moiety, while 1reacted with C2Cl6, PhSSPh, and p-benzoquinone at the germanium center to form Ge–E (E = Cl, S, O) bonds. Furthermore, compound 1is featured by its reactivity as a “formal germylyne”, which allows for the formation of three new σ-bonds or one σ-bond with metal complexation on the germanium center.

Singlet fission (SF) occurs as a result of complex excited state relaxation dynamics in molecular aggregates, where a singlet exciton (FE) state is converted into a double-triplet exciton (TT) state through the interactions with several other degrees of freedom, such as nuclear motions. In this study, we combined quantum dynamics simulation based on the quantum master equation approach with all-atom-based classical molecular mechanics/molecular dynamics to examine the thermal structural fluctuation (i.e., static disorder) effects of intermolecular configuration on SF in pentacene crystal models. In particular, we considered two types of static-disordered models, in which excited states are assumed to interact with nuclear motions of intermolecular modes in the classical mechanical/statistical manner. We found that the introduction of static disorder effects leads to a faster decay of coherence between the FE and charge transfer (CT) states in the early stage of SF, contributing to the accelerations of several FE → TT relaxation pathways. Such acceleration in these models is shown to be attributed to fluctuations in the energies and electronic coupling of the CT states based on relative relaxation factor analysis. The present study is expected to contribute to further development of bottom-up materials design for efficient SF in condensed phases where the exitonic system interacts with nuclear motions in various coupling strengths.

Corminboeuf et al. theoretically predicted that closely π-stacked dimers of antiaromatic molecules tend to exhibit aromatic characters in the sense of magnetic and structural criteria due to the strong intermolecular orbital interactions. This phenomenon is usually called stacked-ring aromaticity. Several experimental and theoretical studies have been conducted to elucidate the aromaticity switching mechanism in the π-stacked dimers and proposed molecular systems realizing this type of phenomenon. So far, most of these studies focused on the aromatic characters of dimers. This paper aims to examine aromatic characters of π-stacked multimers of antiaromatic molecules where the number of monomers, N, is more than 2. We constructed theoretical and calculation models of π-stacked N-mers consisting of cyclobutadienes with different stacking distances d. Applying the theoretical analyses based on the Hückel theory, we clarified the mechanisms of N-, d-, and monomer position dependences of aromatic characters that are evaluated from the density functional theory calculations of these models. It is found that the terminal monomers in the π-stacked N-mer (N> 2) exhibit the most significant antiaromatic character, whereas the second terminal monomers show the most reduced antiaromatic characters at small d. These results demonstrate that, in addition to the stacking distance and configuration, the number and the positions of monomers can be useful factors in controlling the aromaticity switching in π-stacked assemblies of antiaromatic molecules.Graphical Abstract

We theoretically examined the energy stabilization mechanism of closely π-stacked dimers of antiaromatic molecules from the viewpoint of diradical character (y). Quantum chemical calculations for π-stacked dimer models of cyclobutadienes and Ni(II) norcorroles revealed that the balance between the destabilization due to structural deformation in each monomer and the stabilization due to intermolecular orbital interaction between 4nπ systems and dispersion force determined the stabilization in the π-dimer structures.Graphical Abstract

Stacking distance (d) dependence of the peak positions and intensities of one-photon absorption (OPA) and two-photon absorption (TPA) spectra of phenalenyl π-dimer models was investigated theoretically. Excitation energies and transition dipole moments required to simulate the OPA and TPA spectra were evaluated at the extended multiconfigurational quasi-degenerate second-order perturbation theory (XMC-QDPT2) level. The first TPA peak intensity for the model with d= 3.0 Å, related to the electronic transition along the stacking direction, was enhanced by a two-order magnitude compared with that for the model with d= 6.0 Å. We also obtained diradical character (y)-dependent behavior of the TPA property for the first TPA peak predicted from the valence-bond configuration interaction method based on the two-site model.Graphical AbstractTheoretical calculations predicted the appearance of a new two-photon absorption peak related to the intermolecular electronic polarization in phenalenyl π-dimer models when the stacking distance becomes sufficiently small.

A relationship between the single-molecule electron conductivity, spin states, and substituents is investigated on the paddlewheel-type dichromium(II,II) tetracarboxylate complexes as the simplest model of the extended metal atom chains. The electronic structures and single-molecule electron conductivity of some model complexes with different substituents are calculated by the broken-symmetry density functional theory and elastic scattering Green's functions methods, respectively. The calculated results indicate that the electron conductivity of the complexes is changed by the electron-donating/withdrawing groups introduced into the bridging ligands. In addition, it is also found that a ratio of the electron conductivities between the antiferromagnetic and ferromagnetic coupling states in the Cr(II)2unit can be changed by these substituents. These results suggest that the electron conductivity of these complexes can be controlled by changing the spin state.Graphical Abstract

We compare the calculated spin structures of magnetic metal-organic frameworks consisting of paddlewheel-type diruthenium complexes and tetracyano-p-quinodimethane derivatives using density functional theory calculations with Gaussian basis sets and DFT + U/plane-wave calculations under periodic conditions. The calculated results indicate that the asymmetricity of the spin density inside the [Ru2] unit disappears in the periodic systems. In addition, based on the partial spin density analysis, the electron conductivity would be switchable by changing the spin states of the metal-organic frameworks.Graphical Abstract

Bis-periazulene (cyclohepta[def]fluorene), which is an unknown pyrene isomer, was synthesized as kinetically protected forms. Its triaryl derivatives 1c–eexhibited the superimposed electronic structures of peripheral, polarized, and open-shell π-conjugated systems. In contrast to previous theoretical predictions, bis-periazulene derivatives were in the singlet ground state. Changing an aryl group controlled the energy gap between the lowest singlet–triplet states.

We report on our investigation of C–C bonding longer than 2.0 Å, which can be realized by perpendicularly facing two fluorenyl rings in the title compound. A small orbital overlap between the distantly positioned carbon atoms is observed as a small concentration of electrons on the X-ray electron density map. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the compound originate from the in-phase and out-of-phase interactions of the overlapping orbitals, respectively, with a gap of 2.39 eV. Solid-state 13C NMR spectroscopy shows a sharp peak at 82.9 ppm for the long-bonded carbons, and a CASSCF(6,6) calculation indicates small diradical character. The experimental and theoretical analyses reveal sufficient covalent-bonding interaction in the long-bonded carbon pair.

The preparation of a series of dibenzo- and tetrabenzo-fused fluoreno[3,2-b]fluorenes is disclosed, and the diradicaloid properties of these molecules are compared with those of a similar, previously reported series of anthracene-based diradicaloids. Insights on the diradical mode of delocalization tuning by constitutional isomerism of the external naphthalenes has been explored by means of the physical approach (dissection of the electronic properties in terms of electronic repulsion and transfer integral) of diradicals. This study has also been extended to the redox species of the two series of compounds and found that the radical cations have the same stabilization mode by delocalization that the neutral diradicals while the radical anions, contrarily, are stabilized by aromatization of the central core. The synthesis of the fluorenofluorene series and their characterization by electronic absorption and vibrational Raman spectroscopies, X-ray diffraction, SQUID measurements, electrochemistry, in situ UV–vis–NIR absorption spectroelectrochemistry, and theoretical calculations are presented. This work attempts to unify the properties of different series of diradicaloids in a common argument as well as the properties of the carbocations and carbanions derived from them.

The ability to alter optoelectronic and magnetic properties of molecules at a late stage in their preparation is in general a nontrivial feat. Here, we report the late-stage oxidation of benzothiophene-fused indacenes and dicyclopentanaphthalenes to their corresponding sulfone derivatives. We find that while such modifications increase the highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) energy gap to a small degree, other properties such as HOMO and LUMO energy levels, molecule paratropicity, and singlet-triplet energy gaps are influenced to a greater degree. The most surprising finding is a change of the bond alternation pattern within the s-indacene core of the sulfones. Computations corroborate the experimental findings and offer plausible explanations for these changes in molecular properties.

We theoretically investigated molecular charge populations of 1D π-stacked multimers consisting of π-conjugated molecules in the neutral and electron oxidation states based on the valence-bond (VB) theory. Qualitative analysis for a π-stacked trimer model based on the VB mixing diagram suggested that the inner monomer site tends to be more positively charged than the outer sites in the monocationic π-stacked trimer. Spatial expansion of each molecular site orbital toward the stacking direction is predicted to enhance the difference of positive charge populations between the inner and outer monomers. In contrast, an opposite tendency for the site charges was expected in the dicationic π-stacked trimer, primarily due to the hole–hole Coulomb repulsions. To generalize the results of the trimer to π-stacked N-mers, 1D N-site VB configuration interaction models were constructed considering the orbital expansion effects between the sites. We examined how the number of monomers (N), stacking distance (R), and characteristic orbital exponent for the monomers (ζ) affected the molecular charge populations in the monocationic and dicationic π-stacked N-mers through the parameters χijcharacterizing the orbital expansion effect. The results are expected to help establish design strategies for novel electronic functional materials based on discrete stacks of π-conjugated molecules.Based on the valence-bond configuration interaction models, we derived useful expressions for analyzing how the number of monomers, stacking distance, and characteristic orbital exponent for the monomers affect the molecular charge populations in the monocationic and dicationic π-stacked N-mers through the orbital expansion effect.

Inclusion of quinoidal cores in conjugated hydrocarbons is a common strategy to modulate the properties of diradicaloids formed by aromaticity recovery within the quinoidal unit. Here we describe an alternative approach of tuning of diradical properties in indenoindenodibenzothiophenes upon anti→ synisomerism of the benzothiophene motif. This alters the relationship of the S atom with the radical center from linear to cross conjugation yet retains the same 2,6-naphtho conjugation pattern of the rearomatized core. We conduct a full comparison between the antiand synderivatives based on structural, spectroscopic, theoretical, and magnetic measurements, showing that these systems are stable open-shell singlet diradicaloids that only access their triplet state at elevated temperatures.

This paper theoretically investigated the correlation between the open-shell electronic structure and third-order nonlinear optical (NLO) properties of one-dimensional (1D) stacked chains of π-radicals. By employing the finite N-mer models consisting of methyl or phenalenyl radicals with different stacking distances, we evaluated the average and standard deviation of diradical characters yifor N-mer models of π-radicals (yavand ySD). Then, we estimated these diradical characters at the limit of N→ ∞. These y-based indices were helpful in discussing the correlation between the open-shell electronic structures and the second hyperpolarizability per dimer at the limit N→ ∞, γ∞for the 1D chains with stacking distance alternation (SDA). The calculated γ∞values and the polymer/dimer ratio γ∞/γ(N= 2) were enhanced significantly when both the stacking distance and SDA are small. We also found that the spin-unrestricted long-range-corrected (LC−)UBLYP method with the range-separating parameter μ = 0.47 bohr–1well reproduced the trend of γ∞of this type of 1D chain estimated at the spin-unrestricted coupled-cluster levels. The present study is expected to contribute to establishing the design guidelines for future high-performance open-shell molecular NLO materials.

Understanding the structure–property relationships in antiaromatic molecules is crucial for controlling their electronic properties and designing new organic optoelectronic materials. Dibenzo[a,f]pentalene, a structural isomer of dibenzopentalene, displays open-shell and antiaromatic character harmonization, which is not shared by the well-known isomer, dibenzo[a,e]pentalene. The next questions of interest concern the topological effects of the π-extension on the harmonization of the open-shell and antiaromatic character in the dibenzo[a,f]pentalene π-system. Herein, we describe the synthesis and characterization of the π-extended (bis)annulated analogues, benzo[a]naphtho[2,1-f]pentalene 4and dinaphtho[2,1-a,f]pentalene 5. The solid-state structures and the magnetic and optoelectronic properties characterized these π-extended analogues as closed-shell antiaromatic molecules, in sharp contrast with dibenzo[a,f]pentalene 2. In these π-extended analogues, the open-shell character was annihilated whereas the antiaromatic character was retained. The fusion of additional hexagons into 2shifted the main 4nπ-conjugated circuit from a global to a local system. Further investigations into magnetic ring currents using gauge-including magnetically induced current (GIMIC) calculations suggested that an enhanced local paratropic ring current appeared in the pentalene core of 5. The preservation of the benzenoid character in the additionally fused hexagons confined the paratropicity to the pentalene subunit, and the inherent presence of an o-quinoidal structure highlighted the 4nπ-electron delocalization on the pentalene unit. The antiaromaticity of 4and 5was characterized by their small HOMO–LUMO energy gap. Both experimental and computational results demonstrated that the [a,f]-type ring fusion of the pentalene core effectively enhanced the antiaromatic character compared with the [a,e]-type ring fusion in the reported bisannulated[a,e]pentalenes. The findings of this study could potentially be used for the rational design of optoelectronic devices based on novel antiaromatic molecules.

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 p-electron chemical bonding.

Geometric features, electronic structures and third‐order nonlinear optical (NLO) properties of belt‐shaped hydrocarbons, namely, carbon nanobelts, are investigated by using the density functional theory (DFT) methods. A carbon nanobelt composed of five‐ and six‐membered rings (IF‐CNB, 42π), which involves repeating indenofluorene (IF) units, is expected to exhibit both open‐shell multiradical character and relatively strong aromatic nature in the singlet state, while that composed only of six‐membered rings (CNB, 48π) is shown to be a closed‐shell weak antiaromatic species. These features of electronic structure of IF‐CNB are shown to be closely related to its p‐quinodimethane (pQM)‐like substructures and several geometric features (bond‐length alternations and symmetry) of the system. Third‐order NLO properties of open‐shell IF‐CNB is expected to be enhanced more than three times as large as those of the closed‐shell CNB. These results indicate the possibility of further multi‐functionalizations of belt‐shaped hydrocarbons by fusing five‐membered rings. A theoretically designed carbon nanobeltcomposed of five‐ and six‐membered rings (IF‐CNB, 42π) involving repeating indeno[1,2‐b]fluorene units is found to have a potential for exhibiting open‐shell multiradical character, strong aromatic nature and large third‐order nonlinear optical properties in the singlet state based on broken symmetry density functional theory calculations.

The chain-length dependences of geometric and electronic structures and third-order nonlinear optical (NLO) properties of open-shell quinoidal oligothiophenes (QTs) are investigated from the viewpoint of diradical character (y) using the broken-symmetry density functional theory method. The results are compared with those of closed-shell oligothiophenes. The bond-length alternation and the nucleus-independent chemical shift values are evaluated to clarify the chain-length dependence of aromaticities of the terminal and middle thiophene rings in the oligomer chain, which is closely related to the variation in the diradical character through the quinoidal/aromatic resonance structure. The yvalues of these QTs ranging from monomer to hexamer are found to have a wide variety of yvalues [0 (closed-shell state) ≤ y≤ 1 (pure diradical state)]. The γ values per unit of the open-shell QTs having intermediate yare found to be significantly enhanced as compared to those of the closed-shell counterparts. The feature of ydependence of γ in open-shell QTs is found to be in good agreement with so-called “y–γ correlation”, which has been proposed on the basis of the simple two-site diradical model using the valence configuration interaction method. These results reveal the relationships among the terminal substituent group, molecular structure and size, and diradical character, which contribute to building design guidelines for highly efficient third-order NLO materials based on the open-shell one-dimensional oligomers.

Exciton recurrence motions in double-ring molecular aggregates are investigated using the quantum master equation approach. The rotatory and oscillatory recurrence behaviors are found to be controlled by changing the relative direction of the circular polarization of an incident two-mode laser field. These dynamics are understood by the relative phases among off-diagonal exciton density matrices, the feature of which is determined by the interaction between the circular-polarized field and the degenerate states of the double-ring structure. The results of exciton relaxation effects caused by the exciton−phonon coupling and static disorder also demonstrate the robustness of the exciton recurrence motions in double-ring molecular aggregates.

In this paper, we present a simple numerical approach to implement the modified Becke−Roussel (mBR) model for the purpose of developing an exchange density functional suitable for applications to atoms or molecules. Three steps constitute our approach. The first step is to model the exchange hole with the mBR distribution with the form of ρXσmBR= (α/π)3/2exp (−αr2) at each reference point, where α and rrepresent, respectively, the diffuseness and the distance of the model exchange hole from the reference point. We propose an iterative procedure to determine the values (α, r) during the Kohn−Sham DFT calculation. Second, we make a GGA correction to the functional obtained in the first step by adopting the conventional GGA formula to the gradients of the spin density as well as the mBR exchange hole (mBR-GGA). In the third step, mBR-GGA is combined with Dirac’s exchange functional to restore the exchange energy at the homogeneous electron gas limit (mBR-hyb). We demonstrate that the exchange energy densities of the mBR-based methods obey the −1/rasymptotic behaviors by virtue of the fact that the electron density in a hydrogenic atom is used as a prototypical exchange hole. Furthermore, we perform several test calculations for the properties of small molecules. For atomization energies for 35 molecules in the G2 set, the mean absolute deviation (MAD) with respect to the experiment is estimated to be 4.9 kcal/mol by the mBR-hyb functional, which is much smaller than the value of PBE functional (7.7 kcal/mol). The MAD for the enthalpies of formation of 68 molecules in the G3 set is evaluated as 9.4 kcal/mol by the present method, while that is given as 18.7 kcal/mol by the PBE functional. These results suggest the possibility of the present functional based on the mBR model for the applications to atoms or molecules.

The coherent exciton dynamics in molecular complexes composed of ring-shaped aggregates induced by linear- and circular-polarized laser fields has been investigated by using the quantum master equation (QME) approach. As shown in previous studies, near-degenerate states create the superposition states after irradiation of linear-polarized laser fields and thus cause the oscillatory exciton recurrence motion. In contrast, the rotatory exciton recurrence motion is found to be induced by circular-polarized laser field in a C3-symmetry complex composed of identical three ring-shaped aggregates. This exciton dynamics is predicted to originate in the superposition states between the two pairs of degenerate states, which are coherently excited by a circular-polarized laser field. The rotatory exciton recurrence motion induced by a two-mode laser field with mutually opposite circular polarizations also has been examined in the complex composed of two different-sized groups of ring-shaped aggregates. It turns out that the two-mode laser field induces mutually counter-rotatory exciton recurrence motions concurrently, which are generated separately on the two different groups of ring-shaped aggregates. These results suggest the possibility of controlling rotatory exciton recurrence motions by using the circular-polarized laser fields and ring-shaped aggregate complexes.

The exciton dynamics in molecular aggregate models composed of triangular lattice units have been investigated using the quantum master equation approach including relaxation terms originating in weak exciton−phonon coupling. We observe directed migration and recurrence motion of exciton after the irradiation of a laser field. It is found that the triangular lattice aggregates tend to suppress the decoherence behavior and thus to exhibit more distinguished longer-term exciton recurrence than the similar size dendritic aggregates, although the former show less efficient exciton migration, that is, light-harvesting behavior, than the latter. These dynamical features of exciton in the triangular lattice aggregate models turned out to be characterized by the strong interactions among spatially close-packed monomers through the branching points, originating in the equilateral triangular structure, as well as by the fractal, tournament-like, architecture.

Ab initio spin-flip configuration interaction (SF-CI) methods with the finite-field (FF) scheme are applied to the calculation of static second hyperpolarizabilities () of several singlet diradical systems, i.e., the model H2molecule under dissociation, p-quinodimethane, o-quinoid five-membered ring, and 1,4-bis(imidazole-2-ylidene)cyclohexa-2,5-diene (BI2Y) models. The SF-CI method using the UHF reference wave function provides the qualitatively correct diradical character (y) dependence of in a wide range of a diradical character region for H2under dissociation and p-quinodimethane as well as o-quinoid five-membered ring models. For BI2Y, which is a real diradical system, a non-negligible spin contamination is found in the spin-unrestricted Hartree−Fock (UHF) triplet state, which results in overestimations (SF-CIS) or underestimations (SF-CIS(D)) of . Such deficiencies are significantly reduced when using the pure spin state, i.e., the restricted open-shell HF (ROHF) triplet wave function as the reference wave function. These results indicate the applicability of the FF-SF-CI method starting with a pure or a nearly pure high-spin state to provide qualitative or semiquantitative for large-size diradical systems. For selected systems, these SF-CI results are also compared to the SF equation of motion coupled cluster singles and doubles (SF-EOM-CCSD) and to SF time-dependent density functional theory (SF-TDDFT) schemes. In particular, large amounts of Hartree−Fock exchange in the functional are required to obtain qualitatively correct dependence of on yin the case of p-quinodimethane.

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The cover picture showsopen‐shell and aromatic characters of a theoretically designed carbon nanobelt (CNB) composed of five‐ and six‐membered rings. Quantum chemical calculations and magnetically‐induced current density analysis have revealed that in the presence of repeating indeno[1,2‐b]fluorene (IF) substructures, the IF‐CNB bearing (4n+2)π electrons is expected to exhibit both intermediate open‐shell character and strong aromatic nature. Such features are suitable for applications to third‐order nonlinear optical systems. More information can be found in the Full Paper by Masayoshi Nakano et al. on page 2320 in Issue 11, 2018(DOI: 10.1002/ajoc.201800390).