Pancake Bond Orders of a Series of π‐Stacked Triangulene Radicals

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.

Close Stacking of Antiaromatic Ni(II) Norcorrole Originating from a Four-Electron Multicentered Bonding Interaction

A π-conjugated molecule with one electronic spin often forms a π-stacked dimer through molecular orbital interactions between two unpaired electrons. The bonding is recognized as a multicentered two-electron interaction between the two π-conjugated molecules. Here, we disclose a multicentered bonding interaction between two antiaromatic molecules involving four electrons. We have synthesized an antiaromatic porphyrin analogue, Ni(II) bis(pentafluorophenyl)norcorrole. Its dimer adopts a face-to-face stacked structure with an extremely short stacking distance of 2.97 Å. The close stacking originates from a multicenter four-electron bonding interaction between the two molecules. The bonding electrons were experimentally observed via synchrotron X-ray diffraction analysis and corroborated by theoretical calculations. The intermolecular interaction of the molecular orbitals imparts the stacked dimer with aromatic character that is distinctly different from that of its monomer.

Triply Bonded Pancake π-Dimers Stabilized by Tetravalent Actinides

Aromatic π-stacking is a weakly attractive, noncovalent interaction often found in biological macromolecules and synthetic supramolecular chemistry. The weak nondirectional nature of π-stacking can present challenges in the design of materials owing to their weak, nondirectional nature. However, when aromatic π-systems contain an unpaired electron, stronger attraction involving face-to-face π-orbital overlap is possible, resulting in covalent so-called "pancake" bonds. Two-electron, multicenter single pancake bonds are well known, whereas four-electron double pancake bonds are rare. Higher-order pancake bonds have been predicted, but experimental systems are unknown. Here, we show that six-electron triple pancake bonds can be synthesized by a 3-fold reduction of hexaazatrinaphthylene (HAN) and subsequent stacking of the [HAN]3- triradicals. Our analysis reveals a multicenter covalent triple pancake bond consisting of a σ-orbital and two equivalent π-orbitals. An electrostatic stabilizing role is established for the tetravalent thorium and uranium ions in these systems. We also show that the electronic absorption spectrum of the triple pancake bonds closely matches computational predictions, providing experimental verification of these unique interactions. The discovery of conductivity in thin films of triply bonded π-dimers presents new opportunities for the discovery of single-component molecular conductors and other spin-based molecular materials.

Radical Cations of Bilayer Nanographenes

Chemical redox reactions of bilayer nanographene complexes, (C96H24Ar6)2 (Ar = 2,6-dimethylphenyl) (12) and (C42H12R6)2 (R = tBu) (22), were investigated. Upon two-electron oxidation reactions, 12 and 22 were transformed to radical cations 122•+ and 222•+, respectively. SQUID and EPR measurements on 122•+ and 222•+ indicate that they possess an open-shell singlet ground state with antiferromagnetic interactions between two layers. The shortest separation distance between bilayers in 222•+ (3.30 Å) is shorter than that in 22 (3.44 Å) and 22•+ (3.40 Å), illustrating stronger interaction upon loss of electrons.

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.

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.

Unraveling two distinct polymorph transition mechanisms in one n-type single crystal for dynamic electronics

Cooperativity is used by living systems to circumvent energetic and entropic barriers to yield highly efficient molecular processes. Cooperative structural transitions involve the concerted displacement of molecules in a crystalline material, as opposed to typical molecule-by-molecule nucleation and growth mechanisms which often break single crystallinity. Cooperative transitions have acquired much attention for low transition barriers, ultrafast kinetics, and structural reversibility. However, cooperative transitions are rare in molecular crystals and their origin is poorly understood. Crystals of 2-dimensional quinoidal terthiophene (2DQTT-o-B), a high-performance n-type organic semiconductor, demonstrate two distinct thermally activated phase transitions following these mechanisms. Here we show reorientation of the alkyl side chains triggers cooperative behavior, tilting the molecules like dominos. Whereas, nucleation and growth transition is coincident with increasing alkyl chain disorder and driven by forming a biradical state. We establish alkyl chain engineering as integral to rationally controlling these polymorphic behaviors for novel electronic applications.

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.

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 TCNQ^δ- 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.

A Redox-active Microporous Organosiloxane Containing a Stable Neutral Radical, Trioxotriangulene

A new silyl-substituted trioxotriangulene ( TOT ) neutral radical and corresponding porous organosiloxanes (POSs) were synthesized. The neutral radical exhibited a peculiarly high stability and formed a diamagnetic π-dimer characteristic to TOT neutral radicals stabilized by the strong multiple SOMO-SOMO interaction in both solution and solid states. POSs including TOT units within the organosiloxane-wall were prepared by polycondensation of the silyl groups, and formed microporous structures with ~1 nm-size diameters. Redox ability of TOT units in the POS was demonstrated by the treatment of oxidant/reductant in heterogeneous suspension condition, where the TOT units were reversibly converted between reduced and neutral radical species. Furthermore, the solid-state electrochemical measurements of the POS revealed the reversible multi-stage redox ability of TOT units involving polyanionic species within the organosiloxane-wall.

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.

Synthesis and Physical Properties of Trioxotriangulene Having Methoxy and Hydroxy Groups at α-Positions: Electronic and Steric Effects of Substituent Groups and Intramolecular Hydrogen Bonds

New 4,8,12-trioxotriangulene (TOT) neutral radical derivatives having three methoxy and hydroxy groups at the α-positions were synthesized, and the substituent effects on the electronic spin and redox properties were elucidated in the theoretical and experimental methods. Due to the small SOMO coefficients at the α-positions of TOT, the methoxy groups in the TOT neutral radical had negligible effects on the electronic spin structure and redox ability. On the other hand, methoxy groups greatly increased the LUMO energy having large coefficients at α-positions and, thus, caused a remarkable negative-potential shift of the redox wave of anion species involving the dianion and trianion species. Converting the methoxy groups to hydroxy groups caused a dramatic change in the electronic structure of TOT, where the intramolecular hydrogen bonds between hydroxy groups and oxo groups strongly attracted a minus charge on the TOT skeleton. The HOMO energy of the monoanion species was significantly reduced, causing a blue shift of the HOMO-LUMO transition and an anodic shift of the redox potential. In addition, due to the steric repulsion smaller than that of the methoxy group, the hydroxy derivative showed a more planar molecular structure and a strong π-stacking ability.

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.

On-Surface Hydrogenation of Buckybowls: From Curved Aromatic Molecules to Planar Non-Kekulé Aromatic Hydrocarbons

Functionalization of surfaces with derivatives of Buckminsterfullerene fragment molecules seems to be a promising approach toward bottom-up fabrication of carbon nanotube modified electrode surfaces. The modification of a Cu(100) surface with molecules of the buckybowl pentaindenocorannulene has been studied by means of scanning tunneling microscopy, carbon monoxide-modified noncontact atomic force microscopy, time-of-flight secondary mass spectrometry, and quantum chemical calculations. Two different adsorbate modes are identified, in which the majority is oriented such that the bowl cavity points away from the surface and the convex side is partially immersed into a four-atom vacancy in the Cu(100) surface. A minority is oriented such that the convex side points away from the surface with the five benzo tabs oriented basically parallel to the surface. Thermal annealing leads to hydrogenation and planarization of the molecules in two steps under specific C-C bond cleavage. The benzo tabs of the convex side up species serve as a hydrogen source. The final product has an open-shell electron structure that is quenched on the surface.

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].

Intramolecular Magnetic Interaction of Spin-Delocalized Neutral Radicals through m-Phenylene Spacers

A new diradical having two 4,8,10-trioxotriangulene (TOT) neutral radical units linked through an m-phenylene moiety was synthesized and characterized by ESR measurements. An electrochemical study showed that the diradical undergoes two one-electron reductions to generate corresponding dianion species, suggesting the electronic interaction between two TOT units through the π-conjugated spacer. A strong intramolecular interaction between the two TOT units gives rise to the spin-projected small hyperfine couplings in comparison with those of the monomer. Furthermore, the temperature dependent ESR measurement revealed that the dimer behaves as an S=1 species in the ground state with a ferromagnetic interaction of 2 J/k_B =+7±3 K.

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.

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".

Dimethylcethrene: A Chiroptical Diradicaloid Photoswitch

We describe the synthesis and properties of 13,14-dimethylcethrene, a prototype of a chiral diradicaloid photochemical switch that can be transformed reversibly via conrotatory electrocyclization to its more stable closed form by light (630 nm) or heat and back to its open form by light (365 nm). This system illustrates how the chemical reactivity of a diradicaloid molecule can be translated into a switching function, which alters substantially all electronic parameters, namely, the HOMO-LUMO and the singlet-triplet (ST) energy gaps, and the degree of helical twist. As a result, distinct changes in the optical and chiroptical properties of this system were observed, which allowed us to monitor the switching process by a variety of spectroscopic techniques, including NMR, UV-vis, and CD. In comparison to the previously reported parent molecule cethrene, this system benefits from two methyl substituents installed in the fjord region, which account for the stability of the closed form against oxidation and racemization. The methyl substituents increase the ST energy gap of 13,14-dimethylcethrene by ∼4 kcal mol-1 in comparison to cethrene. Our DFT calculations reveal that the larger ST gap is a result of electronic and geometric effects of the methyl substituents and show the potential of related systems to act as magnetic switches at room temperature.

Deciphering Stability of Five-Membered Heterocyclic Radicals: Balancing Act Between Delocalization and Ring Strain

Computational studies on five-membered heterocycles with single heteroatom and their isomeric dehydro-borole 1a-1c, cyclopentadiene 2a-2c, pyrrole 3a-3c, furan 4b-4c, phosphole 5a-5c, and thiophene 6b-6c radicals have been carried out. Geometrical aspects through ground state electronic structures and stability aspects using bond dissociation energies (BDE) and radical stabilization energies (RSE) have been envisaged in this regard. Spin densities, electrostatic potentials (ESP), and natural bond orbital (NBO) analysis unveiled the extent of spin delocalization. The estimated nucleus-independent chemical shifts (NICS) values revealed the difference in aromaticity characteristics of radicals. Particularly the heteroatom centered radicals exhibit odd electron π-delocalized systems with a quasi-antiaromatic character. Various factors such as, the relative position of the radical center with respect to heteroatoms, resonance, ring strain and orbital interactions influence the stability that follows the order: heteroatom centered > β-centered > α-centered radicals. Among the influences of various factors, we confirmed the existence of a competition between delocalization and the ring strain, and the interplay of both decides the overall stability order.

Pancake Bonding in π-Stacked Trimers in a Salt of Tetrachloroquinone Anion

The crystal structure of [4-damp])₂ [Cl₄ Q]₃ (4-damp=4-dimethylamino-N-methylpyridinium, Cl₄ Q=tetrachloroquinone) salt is built up from slipped columnar stacks of quinoid rings composed of closely bound trimers with the intra-trimer separation distance of 2.84 Å and total charge of -2 whereas the inter-trimer distance is 3.59 Å. The individual rings exhibit partial negative charges that are distributed unevenly among the three Cl₄ Qs in the trimer. The strong interactions within a trimer (Cl₄ Q)₃^2- have a partially covalent character with two-electron/multicentered bonding, that is extended over three rings, plausibly termed as "pancake bonding". The electron pairing within this multicentre bond leads to the fact that the crystals are diamagnetic and act as insulators. The studies of the structure and nature of bonding are based on X-ray charge density analysis and density functional theory.

Probing semiconductivity in crystals of stable semiquinone radicals: organic salts of 5,6-dichloro-2,3-dicyanosemiquinone (DDQ) radical anions

The structural parameters and semiconductivity of crystals with stacked 5,6-dichloro-2,3-dicyanosemiquinone (DDQ) radicals were studied for a series of nine salts of DDQ with substituted N-ethyl- and N-methylpyridinium cations.

Validation of density functionals for pancake-bonded π-dimers; dispersion is not enough

π-Stacking pancake bonding between radicals poses special challenges to density functional theories (DFTs) due to their shorter than van der Waals contact distances, their multireference singlet ground states and the concurrently important dispersion interactions.