Rotational Barrier in Phenalenyl Neutral Radical Dimer: Separating Pancake and van der Waals Interactions

Unlocking the Multistage Redox Property of Graphenic Radicals by π-Extension

Delocalized organic π-radicals are intrinsically amphoteric redox systems; however, achieving their multistage redox capability presents a challenge. In addition, their instability often hampers their synthesis, isolation, and characterization. Herein, we report the synthesis of a stable π-extended nanographene π-radical (NR1) and its isolation in the crystalline form. NR1 exhibits an unusual four-stage amphoteric redox behavior, as revealed by cyclic voltammetry measurements. The stable charged species, including a cation and a radical dication, are characterized using spectroscopic methods. This study demonstrates that π-extension could serve as a viable approach to unlock the multistage redox ability of delocalized organic radicals.

Theoretical Study on the Correlation between Open-Shell Electronic Structures and Third-Order Nonlinear Optical Properties in One-Dimensional Chains of π-Radicals

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 yi for N-mer models of π-radicals (yav and 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-1 well 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.

Charge Density Study of Two-Electron Four-Center Bonding in a Dimer of Tetracyanoethylene Radical Anions as a Benchmark for Two-Electron Multicenter Bonding

The dimer of the tetracyanoethylene (TCNE) radical anions represents the simplest and the best studied case of two-electron multicenter covalent bonding (2e/mc or pancake bonding). The model compound, N-methylpyridinium salt of TCNE•-, is diamagnetic, meaning that the electrons in two contiguous radicals are paired and occupy a HOMO orbital which spans two TCNE•- radicals. Charge density in this system is studied as a benchmark for comparison of charge densities in other pancake-bonded radical systems. Two electrons from two contiguous radicals indeed form a bonding electron pair, which is distributed between two central ethylene groups in the dimer, i.e., between four carbon atoms. The topology of electron density reveals two bond critical points between the central ethylene groups in the dimer, with maximum electron density of 0.185 e Å-3; the corresponding theoretical value is 0.118 e Å-3.

π-Extended 9b-Boraphenalenes: Synthesis, Structure, and Physical Properties

Boraphenalenes, compounds in which one carbon atom in the phenalenyl skeleton is replaced with a boron atom, have attracted attention for their solid-state and electronic structures; however, the construction of boraphenalene skeletons remains challenging because of the lack of suitable methods. Through this study, we showed that the tandem borylative cyclization of C3-symmetric dehydrobenzo[12]annulenes produces a new class of fully fused boron-atom-embedded polycyclic hydrocarbons possessing a 9b-boraphenalene skeleton. The obtained compounds exhibited high electron-accepting characteristics, and their two-step redox process was reversible in the reductive region, involving interconversion of 9b-boraphenalene between Hückel aromaticity and antiaromaticity. Notably, the benzo[b]fluorene-fused derivative exhibited a stepwise single-crystal-to-single-crystal (SCSC) phase transition triggered by thermal annealing. Intermolecular electron coupling calculation of the crystal structures suggested a significant improvement of charge transporting ability associated with the SCSC phase transition. Moreover, adequate photoconductivity was observed for the single crystals before and after the SCSC phase transition through flash photolysis-time-resolved microwave conductivity.

Structure and Bonding in π-Stacked Perylenes: The Impact of Charge on Pancake Bonding

Perylene (PER) is a prototype of polycyclic aromatic hydrocarbons (PAHs), which play a pivotal role in various functional and electronic materials due to favorable molecule-to-molecule overlaps, which enhance electronic transport. This study provides guidelines regarding the impact of molecular charge on pancake bonding, a form of strong π-stacking interaction. Pancake bonding significantly boosts interaction energies within the monopositive dimer ([(C20H12)2]•+ or PER2+), crucial for stabilizing aggregation and crystal formation. We discovered energetically feasible sliding and rotation pathways within the [(C20H12)2]•+ dimer, connecting different configurations found in the Cambridge Structural Database (CSD). The dimer's charge profoundly influences the pancake bond order (PBO) and the strength and structural preferences of pancake bonding. The most stable configuration is found in the monocationic state (PER2+), featuring a pancake bond order of 1/2 with one-electron multicenter bonding (1e/mc) with similar characteristics for charge -1. Increasing the total charge of the dimer to +2 or -2 leads to an unstable local minimum. Diverse distribution of pancake bonding types present in crystal structures is interpreted with modeling based on dimer computations with varying charges.

Stability and Reactivity of the Phenalene and Olympicene Isomers

The phenalene (triangulene) and olympicene molecules belong to the polycyclic aromatic hydrocarbon class, which have attracted substantial technological interest due to their unique electronic properties. Electronic structure calculations serve as a valuable tool in investigating the stability and reactivity of these molecular systems. In the present work, the multireference calculations, namely, the complete active space second-order perturbation theory and multireference averaged quadratic coupled cluster (MR-AQCC), were employed to study the reactivity and stability of phenalene and olympicene isomers, as well as their modified structures where the sp3-carbon at the borders were removed. The harmonic oscillator model of aromaticity (HOMA) and the nucleus-independent chemical shift as geometric and magnetic indexes calculated with density functional theory were utilized to assess the aromaticity of the studied molecules. These indexes were compared with properties such as the excitation energy and natural orbitals occupation. The reactivity analyzed using the HOMA index combined with MR-AQCC revealed the radical character of certain structures as well as the weakening of their aromaticity. Moreover, the results suggest that the removal of sp3-carbon atoms and the addition of hydrogen atoms did not alter the π network and the excitation energies of the phenalene molecules.

A theoretical study on π-stacking and ferromagnetism of the perylene diimide radical anion dimer and tetramer

Ferromagnetism is rare in pure organic materials. Recently, the perylene diimide radical anion (PDI-) salt prepared through solvothermal reduction by hydrazine hydrate has shown room-temperature ferromagnetism in our work [Jiang et al., Adv. Mater., 2022, 34, 2108103]. Based on this, herein we conduct a theoretical study based on density functional theory (DFT) to reveal the stacked geometries between two NH4PDI monomers for low-spin (LS) and high-spin (HS) states and their magnetic exchange interactions (JAB) using Yamaguchi's approximate spin projection. It is observed that the pancake-bonded dimer of NH4PDI is the most stable pimer compared to others on both LS and HS potential energy surfaces. A transition of magnetic properties from strong antiferromagnetic (-1333.9 cm-1) to moderate ferromagnetic (67.0 cm-1) appears after increasing the interplanar distance between monomers and their relative rotation angle to access the HS state. According to energy decomposition analysis, the enhanced hydrogen bond formation and decrease of Pauli repulsion is able to counteract the decrease of attraction induced by electron correlation after accessing the HS state. Stacking patterns of exchange-coupled chain consisting of the NH4PDI tetramer are obtained for the HS state after geometry optimization of the structure constructed by two most stable HS pimers. The exchange interactions (51.8 cm-1, 381.2 cm-1 and 53.2 cm-1) between adjacent NH4PDI monomers are ferromagnetic in the HS state, which is in accordance with the experimentally observed room-temperature ferromagnetism.

Polarizability characteristics of twisted bilayer graphene quantum dots in the absence of periodic moiré potential

Recent studies have documented a rich phenomenology in twisted bilayer graphene (TBG), which is significantly relevant to interlayer electronic coupling, in particular to the cases under an applied electric field. While polarizability measures the response of electrons against applied fields, this work adopts a unique strategy of decomposing global polarizability into distributional contributions to access the interlayer polarization in TBG, as a function of varying twisting angles (θ). Through the construction of a model of twisted graphene quantum dots, we assess distributional polarizability at the first-principles level. Our findings demonstrate that the polarizability perpendicular to the graphene plates can be decomposed into intralayer dipoles and interlayer charge-transfer (CT) components, the latter of which provides an explicit measurement of the interlayer coupling strength and charge transfer potential. Our analysis further reveals that interlayer polarizability dominates the polarizability variation during twisting. Intriguingly, the largest interlayer polarizability and CT driven by an external field occur in the misaligned structures with a size-dependent small angle corresponding to the first appearance of AB stacking, rather than the well-recognized Bernal structures. A derived equation is then employed to address the size dependence on the angle corresponding to the largest values in interlayer polarizability and CT. Our investigation not only characterizes the CT features in the interlayer polarizability of TBG quantum dots, but also sheds light on the existence of the strongest interlayer coupling and charge transfer at small twist angles in the presence of an external electric field, thereby providing a comprehensive understanding of the novel properties of graphene-based nanomaterials.

Extremely Long C-C Bonds Predicted beyond 2.0 Å

A number of conjugated molecules are designed with extremely long single C-C bonds beyond 2.0 Å. Some of the investigated molecules are based on analogues to the recently discovered molecule by Kubo et al. These bonds are analyzed by a variety of indices in addition to their equilibrium bond length including the Wiberg bond index, bond dissociation energy (BDE), and measures of diradicaloid character. All unrestricted DFT calculations indicate no diradical character supported by high-level multireference calculations. Finally, NFOD was computed through fractional orbital density (FOD) calculations and used to compare relative differences of diradicaloid character across twisted molecules without central C-C bonding and those with extremely elongated C-C bonds using a comparison with the C-C bond breaking in ethane. No example of direct C-C bonds beyond 2.4 Å are seen in the computational modeling; however, extremely stretched C-C bonds in the vicinity of 2.2 Å are predicted to be achievable with a BDE of 15-25 kcal mol-1.

Reimagining the Wave Function in Density Functional Theory: Exploring Strongly Correlated States in Pancake-Bonded Radical Dimers

Pancake bonding between π-conjugated radicals challenges conventional electronic structure approximations, due to the presence of both dispersion (van der Waals) interactions and "strong" electron correlation. Here we use a reimagined wave function-in-density functional theory (DFT) approach to model pancake bonds. Our generalized self-interaction correction extends DFT's reference system of noninteracting electrons, by introducing electron-electron interactions within an active space. We show that a small variation on our previous derivation recovers a DFT-corrected complete active space method proposed by Pijeau and Hohenstein. Comparison of the two approaches shows that the latter provides reasonable dissociation curves for single bonds and pancake bonds, including excited states inaccessible to conventional linear response time-dependent DFT. The results motivate broader adoption of wavefunction-in-DFT approaches for modeling pancake bonds.

Stable Crystalline Nanohoop Radical and Its Self-Association Promoted by van der Waals Interactions

A stable nanohoop radical (OR3) combining the structures of cycloparaphenylene and an olympicenyl radical is synthesized and isolated in the crystalline state. X-ray crystallographic analysis reveals that OR3 forms a unique head-to-tail dimer that further aggregates into a one-dimensional chain in the solid state. Variable-temperature NMR and concentration-dependent absorption measurements indicate that the π-dimer is not formed in solution. An energy decomposition analysis indicates that van der Waals interactions are the driving force for the self-association process, in contrast with other olympicenyl derivatives that favor π-dimerization. The physical properties in solution phase have been studied, and the stable cationic species obtained by one-electron chemical oxidation. This study offers a new molecular design to modulate the self-association of organic radicals for overcoming the spin-Peierls transition, and to prepare novel nanohoop compounds with spin-related properties.

A Triply Negatively Charged Nanographene Bilayer with Spin Frustration

We report on the largest open-shell graphenic bilayer and also the first example of triply negatively charged radical π-dimer. Upon three-electron reduction, bilayer nanographene fragment molecule (C₉₆ H₂₄ Ar₆ )₂ (Ar=2,6-dimethylphenyl) (1₂ ) was transformed to a triply negatively charged species 1₂ ^3.- , which has been characterized by single-crystal X-ray diffraction, electron paramagnetic resonance (EPR) spectroscopy and magnetic properties on a superconducting quantum interference device (SQUID). 1₂ ^3.- features a 96-center-3-electron (96c/3e) pancake bond with a doublet ground state, which can be thermally excited to a quartet state. It consists of 34 π-fused rings with 96 conjugated sp² carbon atoms. Spin frustration is observed with the frustration parameter f>31.8 at low temperatures in 1₂ ^3.- , which indicates graphene upon reduction doping may behave as a quantum spin liquid.

The Story of the Little Blue Box: A Tribute to Siegfried Hünig

The tetracationic cyclophane, cyclobis(paraquat-p-phenylene), also known as the little blue box, constitutes a modular receptor that has facilitated the discovery of many host-guest complexes and mechanically interlocked molecules during the past 35 years. Its versatility in binding small π-donors in its tetracationic state, as well as forming trisradical tricationic complexes with viologen radical cations in its doubly reduced bisradical dicationic state, renders it valuable for the construction of various stimuli-responsive materials. Since the first reports in 1988, the little blue box has been featured in over 500 publications in the literature. All this research activity would not have been possible without the seminal contributions carried out by Siegfried Hünig, who not only pioneered the syntheses of viologen-containing cyclophanes, but also revealed their rich redox chemistry in addition to their ability to undergo intramolecular π-dimerization. This Review describes how his pioneering research led to the design and synthesis of the little blue box, and how this redox-active host evolved into the key component of molecular shuttles, switches, and machines.

Semiconductive 2D arrays of pancake-bonded oligomers of partially charged TCNQ radicals

Multicentre two-electron (mc/2e or 'pancake bonding') bonding between 7,7,8,8-tetra-cyano-quinodi-methane (TCNQ) radical anions was studied on its 14 novel salts with planar organic cations. The formal charges of the TCNQδ- moieties are -1/2 and -2/3, and they form mc/2e bonded dimers, trimers and tetramers which are further stacked into extended arrays. Multicentre bonding within these oligomers is characterized by short interplanar separations of 2.9-3.2 Å; distances between the oligomers are larger, typically >3.3 Å. The stacks are laterally connected by C-H⋯N hydrogen bonding, forming 2D arrays. The nature of mc/2e bonding is characterized by structural, magnetic and electrical data. The compounds are found to be semiconductors, and high conductivity [10-2 (Ω cm)-1] correlates with short interplanar distances between pancake-bonded oligomers.

Phenalenyl Radical: Smallest Polycyclic Odd Alternant Hydrocarbon Present in the Graphene Sheet

Phenalenyl, a zigzag-edged odd alternant hydrocarbon unit can be found in the graphene nanosheet. Hückel molecular orbital calculations indicate the presence of a nonbonding molecular orbital (NBMO), which originates from the linear combination of atomic orbitals (LCAO) arising from 13 carbon atoms of the phenalenyl molecule. Three redox states (cationic, neutral radical, and anionic) of the phenalenyl-based molecules were attributed to the presence of this NBMO. The cationic state can undergo two consecutive reductions to result in neutral radical and anionic states, stepwise, respectively. The phenalenyl-based radicals were found as crucial building blocks and attracted the attention of various research fields such as organic synthesis, material science, computation, and device physics. From 2012 onward, a strategy was devised using the cationic state of phenalenyl-based molecules and in situ generated phenalenyl radicals, which created a new domain of catalysis. The in situ generated phenalenyl radicals were utilized for the single electron transfer (SET) process resulting in redox catalysis. This emerging range of applications rejuvenates the more than six decades-old phenalenyl chemistry. This review captures such developments ranging from fundamental understanding to multidirectional applications of phenalenyl-based radicals.

Doublet Open-Shell Graphene Fragments

The recent advances on neutral delocalized radical species based on polycyclic aromatic hydrocarbons with fused hexagonal rings, herein defined as doublet open-shell graphene fragments, are summarized in this review. A few simple yet useful theoretical approaches for structural analysis and molecular design were introduced at first. Then, based on the number of fused hexagonal rings, molecular systems with different size, symmetry and edge structure were discussed with emphasis on those isolated in the crystalline form. Their unique self-association behavior, chemical reactivity and physical properties were summarized and discussed, and insights on their functions and potential applications were provided.

π-Extended Doublet Open-Shell Graphene Fragments Exhibiting One-Dimensional Chain Stacking

The hitherto elusive benzo[c]anthanthrenyl radical derivatives composed of seven fused six-membered rings are synthesized and isolated in the crystalline form, representing a laterally π-extended doublet open-shell graphene fragment compared to the phenalenyl and olympicenyl radical structures. X-ray crystallographic analysis revealed one-dimensional chain stacking with relatively close intermolecular contacts, which is an important precondition for achieving single-component conductors. The magnetic, optical, and redox properties are investigated in the solution phase. In combination with the good stability, such open-shell molecular systems have potentials as functional electronic materials.

The Density Functional Theory Account of Interplaying Long-Range Exchange and Dispersion Effects in Supramolecular Assemblies of Aromatic Hydrocarbons with Spin

Aromatic hydrocarbons with fused benzene rings and regular triangular shapes, called n-triangulenes according to the number of rings on one edge, form groundstates with n-1 unpaired spins because of topological reasons. Here, we focus on methodological aspects emerging from the density functional theory (DFT) treatments of dimer models of the n = 2 triangulene (called also phenalenyl), observing that it poses interesting new problems to the issue of long-range corrections. Namely, the interaction comprises simultaneous spincoupling and van der Waals effects, i.e., a technical conjuncture not considered explicitly in the benchmarks calibrating long-range corrections for the DFT account of supramolecular systems. The academic side of considering dimer models for calculations and related analysis is well mirrored in experimental aspects, and synthetic literature revealed many compounds consisting of stacked phenalenyl cores, with intriguing properties, assignable to their long-range spin coupling. Thus, one may speculate that a thorough study assessing the performance of state-of-the-art DFT procedures has relevance for potential applications in spintronics based on organic compounds.

XEDA, a fast and multipurpose energy decomposition analysis program

A fast and multipurpose energy decomposition analysis (EDA) program, called XEDA, is introduced for quantitative analysis of intermolecular interactions. This program contains a series of variational EDA methods, including LMO-EDA, GKS-EDA and their extensions, to analyze non-covalent interactions and strong chemical bonds in various environments. XEDA is highly efficient with a similar computational scaling of single point energy calculations. Its efficiency and universality are validated by a series of test examples including van der Waals interactions, hydrogen bonds, radical-radical interactions and strong covalent bonds.

Periodic B- and N-doped phenalenyl π-aggregates: unexpected nonlinear optical properties by tuning pancake π-π bonding

Phenalenyl (PLY) and its derivatives could form one-dimensional π-aggregates through pancake π-π bonding, which would lead to exotic optoelectronic properties. We will highlight the key aspects of the PLY derivatives from the design strategies to exploration of the electronic properties. Here, we primarily construct alternating boron (B)- and nitrogen (N)-doped PLY π-aggregates: dimer[12], trimer[12-1], trimer[12-2], tetramer[12]₂, pentamer[12]₂-1, pentamer[12]₂-2, and hexamer[12]₃. The geometric and electronic structures show that the short intermolecular distances of the π-aggregates drive the formation of pancake π-π bonding. Significantly, the molecular structures show periodic changes in the π-aggregates, but the first hyperpolarizabilities (β_tot) present unexpected changes, which are found to increase sharply with increasing even layer thickness due to intermolecular charge transfer. The β_tot value of hexamer[12]₃ (5.72 × 10⁴ a.u.) is 6.4 times that of tetramer[12]₂ (8.95 × 10³ a.u.), and is 22.4 times that of dimer[12] (2.55 × 10³ a.u.). Thus, constructing π-aggregates can significantly improve the second-order NLO response, which is mainly due to intermolecular charge transfer through pancake π-π bonding of the interlayers.

Unexpected Charge Effects Strengthen π-Stacking Pancake Bonding

Phenalenyls (PLYs) are important synthons in many functional and electronic materials, which often display favorable molecule-to-molecule overlap for electron or hole transport. They also serve as a prototype for π-stacking pancake bonding based on two-electron multicenter bonding (2e/mc). Unexpected near-doubling of the binding energy is obtained for the positively charged PLY2 + dimer with an effect similar to that seen for the positively charged olympicenyl (OPY) radical dimer. This charge effect is reversed for the perfluorinated (PF) dimers, and the negatively charged perfluorinated (PF) dimers PF-PLY2 - and PF-OPY2 - become strongly bound. Long-range interactions reflect these differences. Also surprising is that in this case the pancake bonding corresponds to single-electron (1e/mc) or a three-electron (3e/mc) multicenter bonding in contrast to the 2e/mc bonding that occurs for the neutral radical dimers. The strong preference for a large intermolecular overlap is maintained in these charged dimers. Importantly, the preference for π-bonding in the charged dimers compared to σ-bonding is strongly enhanced relative to the neutral PLY dimers.

Exploring Curious Covalent Bonding: Raman Identification and Thermodynamics of Perpendicular and Parallel Pancake Bonding (Pimers) of Ethyl Viologen Radical Cation Dimers

Viologen radical cations can dimerize in solutions, and the resulting "pimers" were predicted to assemble into parallel and perpendicular conformers by density functional theory (DFT) calculations. Using resonance Raman, we could identify both perpendicular and parallel forms of ethyl viologen dimers. The distinction between the two forms was accomplished by studying the formation of a host-guest complex with γ-cyclodextrin. The dimer's perpendicular form was excluded due to the host cavity size, and γ-cyclodextrin addition caused a decrease in peak intensities at 1171, 1511, and 1602 cm^-1 that could be assigned to the perpendicular form. DFT modeling of the vibrational spectra under preresonance conditions allowed us to assign the remaining vibrational modes for the parallel and perpendicular forms. Using variable-temperature UV-vis, the bond dissociation energy (ΔH) for this pancake-bonded dimer was measured as 13.1 ± 0.2 kcal/mol. This type of covalent pancake bonding is a challenge to properly describe using DFT methods. Previously, B97D was found to best describe the ΔG of this dimerization (Angew. Chem. 2017, 129, 9563-9567), but this method underestimates the ΔH by 6 kcal/mol. Of the 11 functionals tested, we found that B3LYP with Grimme's D3 dispersion effect can best reproduce the ΔH. Energy decomposition analysis of the bonding energy showed that solvation effects were the most important contributor-polar solvents are needed to overcome the Coulomb repulsion between the two positively charged monomers. Dispersion effects are second in importance and appear larger than the favorable orbital interaction obtained by singly occupied molecular orbital (SOMO)-SOMO orbital overlap. This study brings forth important insights into the curious cases of covalent bonding between two π-delocalized radicals.

Rational design of organic semiconductors with low internal reorganization energies for hole and electron transport: position effect of aza-substitution in phenalenyl derivatives

Amphoteric-redox phenalenyl radical (PLY) is a suitable candidate used to design ambipolar organic materials. Because the singly occupied nonbonding molecular orbital (NBMO) of PLY has a perfect local nonbonding character, its internal reorganization energy (λ) for transporting holes (λ⁺) or electrons (λ^-) is known to be small. Herein, PLY is employed to study the position effect of the aza group on the λ. By adding or extracting an electron from the NBMO, the bond length alterations can be minute. Therefore, the PLY derivatives are also an excellent candidate to study the contributions from the bond angle alterations to the λ. Substituting the aza groups at the β- or α-positions of PLY shows two different trends. When consecutively substituting the aza group at the three β-positions of PLY, the λs are consistently decreased. Contrarily, a series of double functionalization of aza groups at the four α-positions of PLY, the λs are increased. It is because the local bonding or antibonding character in frontier orbitals (FMO) is observed in α2N-PLY and α4N-PLY. As the FMOs of the three β-substituted PLYs and α6N-PLY have perfect local nonbonding character, we found the bond angle alterations are the main contributors of λ. The λs for most aza-PLYs were smaller than 100 meV. Thus, we propose a design rule for substituting aza groups on the parent molecules with strong local nonbonding character in their FMOs. Based on the adiabatic ionization potential and electron affinity, two π-extended PLY derivatives with small λ were recommended for fabricating air-stable ambipolar OFET.

Intra- and Inter-Molecular Spin Coupling in Phenalenyl Dimeric Systems

Phenalenyl is a triangular aromatic molecule made of three fused benzene rings, carrying an unpaired electron, and many of its derivatives show crystal structures with stacked radicals. Here, we investigate the inter-molecular binding in phenalenyl dimers by state-of-the-art computational methods and phenomenological models. Aside from being important for the supramolecular assembly of such radical molecules, the theoretical insight is relevant in methodological aspects, due to the interplay of long-range exchange coupling effects and van der Waals forces. We used comparative wave function-based and density functional theories. Drawing the potential energy surfaces as a function of inter-planar separation and mutual rotation of the monomer units, we found an interesting pattern which is not discovered in previous computational reports on the title systems. The dependence can be nicely interpreted by a transparent phenomenological model based on an orbital overlap paradigm of exchange coupling. We also brought forth a simplified phenomenological valence bond (VB) model of inter-molecular coupling, which is realized on the background of the VB spin model inside of the aromatic monomers and calibrated with the corresponding ab initio data. As the systems can be considered good candidates with potential applications in spintronics and organic magnetism, the theoretical rationalization opens up prospective ways to realize such promises.

Radically Enhanced Dual Recognition

Complexation between a viologen radical cation (V^.+ ) and cyclobis(paraquat-p-phenylene) diradical dication (CBPQT^2(.+) ) has been investigated and utilized extensively in the construction of mechanically interlocked molecules (MIMs) and artificial molecular machines (AMMs). The selective recognition of a pair of V^.+ using radical-pairing interactions, however, remains a formidable challenge. Herein, we report the efficient encapsulation of two methyl viologen radical cations (MV^.+ ) in a size-matched bisradical dicationic host - namely, cyclobis(paraquat-2,6-naphthalene)^2(.+) , i.e., CBPQN^2(.+) . Central to this dual recognition process was the choice of 2,6-bismethylenenaphthalene linkers for incorporation into the bisradical dicationic host. They provide the space between the two bipyridinium radical cations in CBPQN^2(.+) suitable for binding two MV^.+ with relatively short (3.05-3.25 Å) radical-pairing distances. The size-matched bisradical dicationic host was found to exhibit highly selective and cooperative association with the two MV^.+ in MeCN at room temperature. The formation of the tetrakisradical tetracationic inclusion complex - namely, [(MV)₂ ⊂CBPQN]^{4( .+)} - in MeCN was confirmed by VT ¹ H NMR, as well as by EPR spectroscopy. The solid-state superstructure of [(MV)₂ ⊂CBPQN]^{4( .+)} reveals an uneven distribution of the binding distances (3.05, 3.24, 3.05 Å) between the three different V^.+ , suggesting that localization of the radical-pairing interactions has a strong influence on the packing of the two MV^.+ inside the bisradical dicationic host. Our findings constitute a rare example of binding two radical guests with high affinity and cooperativity using host-guest radical-pairing interactions. Moreover, they open up possibilities of harnessing the tetrakisradical tetracationic inclusion complex as a new, orthogonal and redox-switchable recognition motif for the construction of MIMs and AMMs.

Acene-Linked Zethrenes and Bisphenalenyls: A DFT Search for Organic Tetraradicals

Polycyclic aromatic hydrocarbons are of special interest due to their promising nonlinear optical and magnetic properties. A series of acene-linked zethrenes and bisphenalenyls comprising from five to nine benzene rings in the linker group have been computationally studied by the DFT UB3LYP/6-311++G(d,p) quantum-chemical modeling of their electronic structure, possible spin states, and exchange interactions. The zethrenes with octacene and nonacene linkers as well as bisphenalenyls comprising heptacene, octacene, and nonacene linker groups have been revealed to possess tetraradicaloid nature, which makes them promising building blocks for organic optoelectronic and spintronic devices. The results obtained open a way of constructing tetraradicaloid organic molecules characterized by the presence of two types of paramagnetic centers.

Radical-pairing-induced molecular assembly and motion

Radical-pairing interactions between conjugated organic π-radicals are relative newcomers to the inventory of molecular recognition motifs explored in supramolecular chemistry. The unique electronic, magnetic, optical and redox-responsive properties of the conjugated π-radicals render molecules designed with radical-pairing interactions useful for applications in various areas of chemistry and materials science. In particular, the ability to control formation of radical cationic or anionic species, by redox stimulation, provides a flexible trigger for directed assembly and controlled molecular motions, as well as a convenient means of inputting energy to fuel non-equilibrium processes. In this Review, we provide an overview of different examples of radical-pairing-based recognition processes and of their emerging use in (1) supramolecular assembly, (2) templation of mechanically interlocked molecules, (3) stimuli-controlled molecular switches and, by incorporation of kinetic asymmetry in the design, (4) the creation of unidirectional molecular transporters based on pumping cassettes powered by fuelled switching of radical-pairing interactions. We conclude the discussion with an outlook on future directions for the field.

Unveiling the Hidden σ-Dimerization of a Kinetically Protected Olympicenyl Radical

The σ-dimer of a kinetically protected olympicenyl radical, which evaded the experimental detection, was revealed by conversion into biolympicenylidene with E-configuration in a regioselective manner. The complicated stereochemistry and energetics of the σ-dimers derived from C_2v symmetry and uneven spin distribution of the olympicenyl radical were revealed by the theoretical calculations, and the energetic preference of π-dimer over σ-dimer by a minute gap was disclosed. The E-biolympicenylidene, a polycyclic ene structure previously considered as reactive intermediate in the phenalenyl radical system, exhibited exceptional stability, which allowed for a detailed investigation on its singlet diradical character and physical properties by means of X-ray crystallography, UV-vis-NIR absorption/emission spectroscopy and cyclic voltammetry, and assisted by theoretical calculations. The E-biolympicenylidene showed high resistance towards both thermal and photochemical ring-cyclization reactions, which was attributed to high activation energies for the rate-determining electrocyclization operated on both disrotatory and conrotatory mode, as well as a small spin density at the bonding sites for the radical-radical coupling process.

Charge transport properties of open-shell graphene fragments: a computational study of the phenalenyl tilings

Thinking outside the box of the phenalenyl radical: a systematic structure design strategy, phenalenyl tiling, is found to benefit the electron transport properties of open-shell graphene fragments with one free radical. Compared with the closed-shell species, phenalenyl-based π-radicals exhibit smaller intramolecular reorganization energies and larger intermolecular electronic couplings. However, the on-site Coulomb repulsion can be too strong and impedes the charge transport efficiency of such materials. The repulsion can be weakened in radical species by spin delocalization. In this paper, the extended π-radicals we studied are categorized into three types of open-shell structures: the zigzag, the armchair and the discotic odd alternant hydrocarbons. The latter two belong to phenalenyl tilings. We found that the phenalenyl tilings fully inherit the desirable features of the singly occupied molecular orbital of the phenalenyl radical in a predictable and delocalized fashion, and their on-site Coulomb repulsion is effectively reduced. The zigzag π-radicals are less satisfactory. Therefore, the phenalenyl tilings are favorable candidates for charge transporting materials.

Effects of structural variations on π-dimer formation: long-distance multicenter bonding of cation-radicals of tetrathiafulvalene analogues

The multicenter (pancake) bonding between cation-radicals of tetramethyltetraselenafulvalene, TMTSF⁺˙, tetramethyltetrathiafulvalene, TMTTF⁺˙, and bis(ethylenedithio)-tetrathiafulvalene, ET⁺,˙ was compared to that of tetrathiafulvalene, TTF⁺˙. To minimize counter-ion effects, the cation-radical salts with weakly coordinating anions (WCA), tetrakis(3,5-trifluoromethylphenyl)borate, dodecamethylcarborane and hexabromocarborane were prepared. Solid-state (X-ray and EPR) measurements revealed diamagnetic π-dimers in the TMTSF and ET salts and the separate monomers in the TTF salts with all WCAs, while TMTTF existed as a dimer in one and a monomer in two salts. The variable-temperature UV-Vis studies of these salts in solution showed that the thermodynamics of formation of the π-bonded dimers of TMTTF⁺˙ was close to that of TTF⁺˙, while TMTSF⁺˙ and ET⁺˙ showed a higher propensity for π-dimerization. These data indicated that the replacement of sulfur with heavier selenium or insertion of ethylenedithia-substituents into the TTF core increases the π-dimers' stability. Yet, computational analysis indicated that the weakly covalent component of π-bonding decreases in the order TTF > TMTTF > TMTSF > ET. The higher stability of the π-dimers of TMTSF⁺˙ and ET⁺˙ cation-radicals was related to a decrease of the electrostatic repulsion between cationic counter-parts and an increase of dispersion components in these associations.

How Much Dispersion Energy Is Included in the Multiconfigurational Interaction Energy?

We demonstrate how to quantify the amount of dispersion interaction recovered by supermolecular calculations with the multiconfigurational self-consistent field (MCSCF) wave functions. For this purpose, we present a rigorous derivation which connects the portion of dispersion interaction captured by the assumed wave function model-the residual dispersion interaction-with the size of the active space. Based on the obtained expression for the residual dispersion contribution, we propose a dispersion correction for the MCSCF that avoids correlation double counting. Numerical demonstration for model four-electron dimers in both ground and excited states described with the complete active space self-consistent field (CASSCF) reference serves as a proof-of-concept for the method. Accurate results, largely independent of the size of the active space, are obtained. For many-electron systems, routine CASSCF interaction energy calculations recover a tiny fraction of the full second-order dispersion energy. We found that the residual dispersion is non-negligible only for purely dispersion-bound complexes.

The generality of the GUGA MRCI approach in COLUMBUS for treating complex quantum chemistry

The core part of the program system COLUMBUS allows highly efficient calculations using variational multireference (MR) methods in the framework of configuration interaction with single and double excitations (MR-CISD) and averaged quadratic coupled-cluster calculations (MR-AQCC), based on uncontracted sets of configurations and the graphical unitary group approach (GUGA). The availability of analytic MR-CISD and MR-AQCC energy gradients and analytic nonadiabatic couplings for MR-CISD enables exciting applications including, e.g., investigations of π-conjugated biradicaloid compounds, calculations of multitudes of excited states, development of diabatization procedures, and furnishing the electronic structure information for on-the-fly surface nonadiabatic dynamics. With fully variational uncontracted spin-orbit MRCI, COLUMBUS provides a unique possibility of performing high-level calculations on compounds containing heavy atoms up to lanthanides and actinides. Crucial for carrying out all of these calculations effectively is the availability of an efficient parallel code for the CI step. Configuration spaces of several billion in size now can be treated quite routinely on standard parallel computer clusters. Emerging developments in COLUMBUS, including the all configuration mean energy multiconfiguration self-consistent field method and the graphically contracted function method, promise to allow practically unlimited configuration space dimensions. Spin density based on the GUGA approach, analytic spin-orbit energy gradients, possibilities for local electron correlation MR calculations, development of general interfaces for nonadiabatic dynamics, and MRCI linear vibronic coupling models conclude this overview.

Pancake-bonding of semiquinone radicals under variable temperature and pressure conditions

The effects of temperature (100-370 K) and pressure (0-6 GPa) on the non-localized two-electron multicentric covalent bonds (`pancake bonding') in closely bound radical dimers were studied using single-crystal X-ray diffraction on a 4-cyano-N-methylpyridinium salt of 5,6-dichloro-2,3-dicyanosemiquinone radical anion (DDQ) as the sample compound. On cooling, the anisotropic structural compression was accompanied by continuous changes in molecular stacking; the discontinuities in the changes in volume and b and c cell parameters suggest that a phase transition occurs between 210 and 240 K. At a pressure of 2.55 GPa, distances between radical dimers shortened to 2.9 Å, which corresponds to distances observed in extended π-bonded polymers. Increasing pressure further to 6 GPa reduced the interplanar separation of the radicals to 2.75 Å. This may indicate that the covalent component of the interaction significantly increased, in accordance with the results of DFT calculations reported elsewhere [Molčanov et al. (2019), Cryst. Growth Des. 19, 391-402].

Energy decomposition analysis based on broken symmetry unrestricted density functional theory

In this paper, the generalized Kohn-Sham energy decomposition analysis (GKS-EDA) scheme is extended to molecular interactions in open shell singlet states, which is a challenge for many popular EDA methods due to the multireference character. Based on broken symmetry (BS) unrestricted density functional theory with a spin projection approximation, the extension scheme, named GKS-EDA(BS) in this paper, divides the total interaction energy into electrostatic, exchange-repulsion, polarization, correlation, and dispersion terms. Test examples include the pancake bond in the phenalenyl dimer, the ligand interactions in the Fe(ii)-porphyrin complexes, and the radical interactions in dehydrogenated guanine-cytosine base pairs and show that GKS-EDA(BS) is a practical EDA tool for open shell singlet systems.

Storing redox equivalent in the phenalenyl backbone towards catalytic multi-electron reduction

Storing and transferring electrons for multi-electron reduction processes are considered to be the key steps in various important chemical and biological transformations. In this work, we accomplished multi-electron reduction of a carboxylic acid via a hydrosilylation pathway where a redox-active phenalenyl backbone in Co(PLY-O,O)2(THF)2, stores electrons and plays a preponderant role in the entire process. This reduction proceeds by single electron transfer (SET) from the mono-reduced ligand backbone leading to the cleavage of the Si-H bond. Several important intermediates along the catalytic reduction reaction have been isolated and well characterized to prove that the redox equivalent is stored in the form of a C-H bond in the PLY backbone via a ligand dearomatization process. The ligand's extensive participation in storing a hydride equivalent has been conclusively elucidated via a deuterium labelling experiment. This is a rare example where the ligand orchestrates the multielectron reduction process leaving only the metal to maintain the conformational requirements and fine tunes the electronics of the catalyst.

Spin splittings from first-order symmetry-adapted perturbation theory without single-exchange approximation

The recently proposed spin-flip symmetry-adapted perturbation theory (SF-SAPT) first-order exchange energy [Patkowski et al., J. Chem. Phys. 148, 164110 (2018)] enables the standard open-shell SAPT approach to treat arbitrary spin states of the weakly interacting complex. Here, we further extend first-order SF-SAPT beyond the single-exchange approximation to a complete treatment of the exchanges of electrons between monomers. This new form of the exchange correction replaces the single-exchange approximation with a more moderate single-spin-flip approximation. The newly developed expressions are applied to a number of small test systems to elucidate the quality of both approximations. They are also applied to the singlet-triplet splittings in pancake bonded dimers. The accuracy of the single-exchange approximation deteriorates at short intermolecular separations, especially for systems with few electrons and for the high-spin state of the complex. In contrast, the single-spin-flip approximation is exact for interactions involving a doublet molecule and remains highly accurate for any number of unpaired electrons. Because the single-exchange approximation affects the high-spin and low-spin states of pancake bonded complexes evenly, the resulting splitting values are of similar accuracy to those produced by the formally more accurate single-spin-flip approximation.

Towards understanding π-stacking interactions between non-aromatic rings

The first systematic study of π interactions between non-aromatic rings, based on the authors' own results from an experimental X-ray charge-density analysis assisted by quantum chemical calculations, is presented. The landmark (non-aromatic) examples include quinoid rings, planar radicals and metal-chelate rings. The results can be summarized as: (i) non-aromatic planar polyenic rings can be stacked, (ii) interactions are more pronounced between systems or rings with little or no π-electron delocalization (e.g. quinones) than those involving delocalized systems (e.g. aromatics), and (iii) the main component of the interaction is electrostatic/multipolar between closed-shell rings, whereas (iv) interactions between radicals involve a significant covalent contribution (multicentric bonding). Thus, stacking covers a wide range of interactions and energies, ranging from weak dispersion to unlocalized two-electron multicentric covalent bonding ('pancake bonding'), allowing a face-to-face stacking arrangement in some chemical species (quinone anions). The predominant interaction in a particular stacked system modulates the physical properties and defines a strategy for crystal engineering of functional materials.

Effect of Substitution on the Hysteretic Phase Transition in a Bistable Phenalenyl-Based Neutral Radical Molecular Conductor

The ability to tune the physical properties of bistable organic functional materials by means of chemistry can facilitate their development for molecular electronic switching components. The butylamine-containing biphenalenyl boron neutral radical, [Bu]₂ B, crystalline compound has recently attracted significant attention by displaying a hysteretic phase transition accompanied by simultaneous bistability in magnetic, electrical, and optical properties close to room temperature. In this report, substitutional doping was applied to [Bu]₂ B by crystallizing solid solutions of bistable [Bu]₂ B and its non-radical-containing counterpart [Bu]₂ Be. With increasing doping degree, the hysteretic phase transition is gradually suppressed in terms of reducing the height, but conserves the width of the hysteresis loop as observed through magnetic susceptibility and electrical conductivity measurements. At the critical doping level of about 6 %, the abrupt transformation of the crystal structure to that of the pure [Bu]₂ Be crystal packing was observed, accompanied by a complete collapse of the hysteresis loop. Further study of the structure-properties relationships of bistable neutral radical conductors based on the [Bu]₂ B host can be conducted utilizing a variety of biphenalenyl-based molecular conductors.

A Concise Synthetic Strategy for Accessing Ambient Stable Bisphenalenyls toward Achieving Electroactive Open-Shell π-Conjugated Materials

Open-shell, π-conjugated molecules represent exciting next-generation materials due to their unique optoelectronic and magnetic properties and their potential to exploit unpaired spin densities to engineer exceptionally close π-π interactions. However, prior syntheses of ambient stable, open-shell molecules required lengthy routes and displayed intermolecular spin-spin coupling with limited dimensionality. Here we report a general fragment-coupling strategy with phenalenone that enables the rapid construction of both biradicaloid (Ph₂- s-IDPL, 1) and radical [10(OTf)] bisphenalenyls in ≤7 steps from commercial starting materials. Significantly, we have discovered an electronically stabilized π-radical cation [10(OTf)] that shows multiple intermolecular closer-than-vdW contacts (<3.4 Å) in its X-ray crystal structure. DFT simulations reveal that each of these close π-π interactions allows for intermolecular spin-spin coupling to occur and suggests that 10(OTf) achieves electrostatically enhanced intermolecular covalent-bonding interactions in two dimensions. Single crystal devices were fabricated from 10(OTf) and demonstrate average electrical conductivities of 1.31 × 10^-2 S/cm. Overall, these studies highlight the practical synthesis and device application of a new π-conjugated material, based on a design principle that promises to facilitate spin and charge transport.

Nano-aggregates of furan-2-carbohydrazide derivatives displaying enhanced emission with a bathochromic shift

The non-fluorescent Schiff base compound C1 (N'-((4′-ethyl-3-hydroxy-[1,1′-biphenyl]-4-yl)methylene)furan-2-carbohydrazide) in organic solvent (e.g., THF) was found to produce yellow-green fluorescence emission upon addition of H₂O, and granular-shaped aggregates in a THF/H₂O mixed solution formed and exhibited obvious aggregation-induced emission (AIE). Especially its keto fluorescence band intensified dramatically, while the enol emission band remained almost unchanged. Hence, a change in fluorescence from no emission of light to emission of bright yellow-green light under a UV lamp was observed with the naked eye. In contrast, the reference compound C2 (N'-((4′-ethyl-3-methoxy-[1,1′-biphenyl]-4-yl)methylene)furan-2-carbohydrazide) showed no intensified fluorescence emission under the same experimental conditions. These results indicated the significant role played by intramolecular H-bonding in the formation of the C1 aggregates and the AIE process.

C1 exhibited obvious AIE phenomena. A change from a lack of fluorescence emission to the emission of yellow-green light under a UV lamp was observed upon the inclusion of water in the solvent.

Influence of organic cations on the stacking of semiquinone radical anions

A series of salts of tetrachloro- and tetrabromosemiquinone radical anions reveal four types of stacks: 1) pancake bonded dimers, 2) pancake-bonded trimers, 3) equidistant radicals and 4) a novel type of equidistant stacks of partially charged radicals.

Experimental and Computational Evidence for "Double Pancake Bonds": The Role of Dispersion-Corrected DFT Methods in Strongly Dimerized 5-Aryl-1λ2,3λ2-dithia-2,4,6-triazines

Crystal structures are reported for bicyclic 3-CF₃C₆H₄CN₅S₃ and monocyclic 3-CF₃C₆H₄CN₃S₂, the latter of which is strongly dimerized in a cis-cofacial geometry [3-CF₃C₆H₄CN₃S₂]₂. The title compounds have previously been characterized in solution by NMR, displaying spectra that are consistent with the structure of [3-CF₃C₆H₄CN₃S₂]₂ in the crystal with anti-oriented CF₃ substituents. The interannular binding was investigated using density functional theory (DFT) methods. However, the DFT-optimized geometry spreads the aryl rings too far apart (centroid-centroid distances of ≥4.353 Å versus experimental distance of 3.850 Å). Significant improvements are obtained with dispersion-corrected DFT functionals B3LYP-D3, B3LYP-D3BJ, M062X, and APFD using the 6-311+G(2d,p) basis set. However, all of these overbind the aryl rings with centroid-centroid distances of 3.612, 3.570, 3.526, and 3.511 Å, respectively. After selecting B3LYP-D3BJ/6-311+G(2d,p) as the best method, five alternative dimer geometries were tested, and all were found to be binding; however, anti cofacial-4 (matching the structure in the solid state) is the most stable. Computed energies of the remainder are as follows: +7.0 kJ mol^-1 (syn-cofacial-5), +26.7 kJ mol^-1 (anti-cofacial-64), +27.0 kJ mol^-1 (syn-cofacial-150), +102.0 kJ mol^-1 (S,S-antarafacial), and +103.7 kJ mol^-1 (S,N-antarafacial), where the suffixes are torsional angles around the CN₃S₂ thiazyl ring centroids. The binding in the four most stable cofacial dimers may be described by "double pancake bonding".

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 Ni^II 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.