Electronic Structure of Open-Shell Singlet Molecules: Diradical Character Viewpoint

On Entangled Singlet Pure Diradicals

This work addresses a class of conjugated hydrocarbons that are expected to be singlet diradicals according to the topological Hückel Hamiltonian while possibly satisfying full on-bond electron pairing. These systems possess two degenerate singly occupied molecular orbitals (SOMOs), but aromaticity brought by properly positioned six-membered rings does prevent Jahn-Teller distortions. Density functional theory (DFT) calculations performed on two emblematic examples confirm the strong bond-length alternation in the closed-shell solutions and the clear spatial symmetry in the open-shell spin-unrestricted determinants, the latter solution always being found to have significantly lower energy. Since the SOMOs are here of different symmetry, the wave function is free from ionic valence-bond component, and spin decontamination of the unrestricted DFT solutions and wave function calculations at the CASSCF-plus-second-order-perturbation level confirm the expected pure diradical character of such molecules. In contrast to disjoint diradicals, the SOMOs of present systems have large amplitudes on neighbor atoms, and we propose to name them entangled pure diradicals, further providing some prescription rules for their design. Additional calculations point out the qualitative contrast between these molecules and the related diradicaloids.

N-Heterocyclic Carbene Analogues of Wittig Hydrocarbon

N-Heterocyclic carbene (NHC) analogues of Wittig hydrocarbon, [(NHC)(Stil)(NHC)] (3a-c) (NHC = SIPr (1a) = C[N(Dipp)CH2]2, Dipp = 2,6-iPr2C6H3; IPr (1b) = C[N(Dipp)CH]2; Me-IPr (1c) = C[N(Dipp)CMe]2 and Stil = C6H4CHCHC6H4) have been reported as crystalline solids. 3a-c are prepared by two-electron reductions of the corresponding bis-1,3-imidazoli(ni)um bromides [(NHC)(Stil)NHC)](Br)2 (2a-c) with KC8 in >94 % yields. 2a-c are accessible by the nickel catalyzed direct C-C coupling of NHCs (1a-c) with (E)-4,4'-dibromostilbene. One-electron oxidation of 3a,b yields the corresponding radical cations [(NHC)(Stil)NHC)]B(C6F5)4 4a,b. All compounds have been characterized by UV-Vis/NMR/EPR spectroscopy as well as 2a, 3a, and 3b by single crystal X-ray diffraction. The electronic structures of representative systems have been analyzed by quantum chemical calculations.

Synthesis and Reactivity of a Dialane-Bridged Diradical

Radicals of the lightest group 13 element, boron, are well established and observed in numerous forms. In contrast to boron, radical chemistry involving the heavier group 13 elements (aluminum, gallium, indium, and thallium) remains largely underexplored, primarily attributed to the formidable synthetic challenges associated with these elements. Herein, we report the synthesis and isolation of planar and twisted conformers of a doubly CAAC (cyclic alkyl(amino)carbene)-radical-substituted dialane. Extensive characterization through spectroscopic analyses and X-ray crystallography confirms their identity, while quantum chemical calculations support their open-shell nature and provide further insights into their electronic structures. The dialane-connected diradicals exhibit high susceptibility to oxidation, as evidenced by electrochemical measurements and reactions with o-chloranil and a variety of organic azides. This study opens a previously uncharted class of dialuminum systems to study, broadening the scope of diradical chemistry and its potential applications.

Unlocking Biradical Character in Diborepins

Systems that possess open- and closed-shell behavior attract significant attention from researchers due to their inherent redox and charge transport properties. Herein, we report the synthesis of the first diborepin biradicals. They display tunable biradical character based on the steric and electronic profile of the stabilizing ligand and the resulting geometric deviation of the diborepin core from planarity. While there are numerous all-carbon-based biradical systems, boron-based biradical compounds are comparatively rare, particularly ones in which the radical sites are disjointed. Calculations using density functional theory (DFT) and multireference methods demonstrate that the fused diborepin scaffold exhibits high biradical character, up to 95%. Use of a nonsterically demanding diaminocarbene promotes the planarization of the pentacyclic framework, resulting in the synthetic realization of a diborepin containing a dibora-quinoidal core, which possesses a closed-shell ground state and thermally accessible triplet state. The biradicals were structurally authenticated and characterized by both solution and solid-state electron paramagnetic resonance (EPR) spectroscopy. Half-field transitions were observed at low temperatures (about 170 K), confirming the presence of the triplet state. Initial reactivity studies of the biradicals led to the isolation and structural characterization of bis(borepin hydride) and bis(borepin dianion).

Fused Indacene Dimers

Polycyclic hydrocarbons consisting of two or more directly fused antiaromatic subunits are rare due to their high reactivity. However, it is important to understand how the interactions between the antiaromatic subunits influence the electronic properties of the fused structure. Herein, we present the synthesis of two fused indacene dimer isomers: s-indaceno[2,1-a]-s-indacene (s-ID) and as-indaceno[3,2-b]-as-indacene (as-ID), containing two fused antiaromatic s-indacene or as-indacene units, respectively. Their structures were confirmed by X-ray crystallographic analysis. 1 H NMR/ESR measurements and DFT calculations revealed that both s-ID and as-ID have an open-shell singlet ground state. However, while localized antiaromaticity was observed in s-ID, as-ID showed weak global aromaticity. Moreover, as-ID exhibited a larger diradical character and a smaller singlet-triplet gap than s-ID. All the differences can be attributed to their distinct quinoidal substructures.

Ambipolar Charge Transport in Organic Semiconductors: How Intramolecular Reorganization Energy Is Controlled by Diradical Character

The charged forms of π-conjugated chromophores are relevant in the field of organic electronics as charge carriers in optoelectronic devices, but also as energy storage substrates in organic batteries. In this context, intramolecular reorganization energy plays an important role in controlling material efficiency. In this work, we investigate how the diradical character influences the reorganization energies of holes and electrons by considering a library of diradicaloid chromophores. We determine the reorganization energies with the four-point adiabatic potential method using quantum-chemical calculations at density functional theory (DFT) level. To assess the role of diradical character, we compare the results obtained, assuming both closed-shell and open-shell representations of the neutral species. The study shows how the diradical character impacts the geometrical and electronic structure of neutral species, which in turn control the magnitude of reorganization energies for both charge carriers. Based on computed geometries of neutral and charged species, we propose a simple scheme to rationalize the small, computed reorganization energies for both n-type and p-type charge transport. The study is supplemented with the calculation of intermolecular electronic couplings governing charge transport for selected diradicals, further supporting the ambipolar character of the investigated diradicals.

Multiple stable redox states and tunable ground states via the marriage of viologens and Chichibabin's hydrocarbon†

Chichibabin's hydrocarbon and viologens are among the most famous diradicaloids and organic redox systems, respectively. However, each has its own disadvantages: the instability of the former and its charged species, and the closed-shell nature of the neutral species derived from the latter, respectively. Herein, we report that terminal borylation and central distortion of 4,4′-bipyridine allow us to readily isolate the first bis-BN-based analogues (1 and 2) of Chichibabin's hydrocarbon with three stable redox states and tunable ground states. Electrochemically, both compounds exhibit two reversible oxidation processes with wide redox ranges. One- and two-electron chemical oxidations of 1 afford the crystalline radical cation 1˙⁺ and dication 1²⁺, respectively. Moreover, the ground states of 1 and 2 are tunable with 1 as a closed-shell singlet and the tetramethyl-substituted 2 as an open-shell singlet, the latter of which could be thermally excited to its triplet state because of the small singlet-triplet gap.

Herein, we report the isolation of bis-BN-based species 1 and 2 with multiple stable redox states. Their ground states are tunable with 1 as a closed-shell singlet and 2 as an open-shell singlet with a small singlet-triplet gap.

Controlling Diradical Character of Photogenerated Colored Isomers of Phenoxyl-Imidazolyl Radical Complexes

We propose a rational method for evaluating the diradical character of the photochromic phenoxyl-imidazolyl radical complex (PIC) derivatives based on their radical-radical coupling reaction rates. PIC consists of an imidazole ring, a phenoxyl ring, and a bridging unit that structurally connects them. The C-N bond formed between the imidazole and phenoxyl rings can be dissociated photochemically in a homolytic manner. The photochromism of PIC differs significantly from other photochromic molecules in that the transient colored open-ring isomer has a diradical character. The colored open-ring isomer returns promptly to the initial colorless closed-ring isomer by the intramolecular radical recombination reaction. By changing the aromaticity and substitution position of the bridging unit, it is possible to control the degree of contribution of the open-shell diradical and closed-shell quinoidal structures to the open-ring isomer. Systematic investigation of the photochromic reactions of several PIC derivatives revealed that the half-life of the open-ring isomers reflects the diradical character. Thus, the radical recombination reaction rate of the open-ring isomer of the PIC derivatives is an excellent parameter of the diradical character.

Minimal Active Space for Diradicals Using Multistate Density Functional Theory

This work explores the electronic structure as well as the reactivity of singlet diradicals, making use of multistate density functional theory (MSDFT). In particular, we show that a minimal active space of two electrons in two orbitals is adequate to treat the relative energies of the singlet and triplet adiabatic ground state as well as the first singlet excited state in many cases. This is plausible because dynamic correlation is included in the first place in the optimization of orbitals in each determinant state via block-localized Kohn–Sham density functional theory. In addition, molecular fragment, i.e., block-localized Kohn–Sham orbitals, are optimized separately for each determinant, providing a variational diabatic representation of valence bond-like states, which are subsequently used in nonorthogonal state interactions (NOSIs). The computational procedure and its performance are illustrated on some prototypical diradical species. It is shown that NOSI calculations in MSDFT can be used to model bond dissociation and hydrogen-atom transfer reactions, employing a minimal number of configuration state functions as the basis states. For p- and s-types of diradicals, the closed-shell diradicals are found to be more reactive than the open-shell ones due to a larger diabatic coupling with the final product state. Such a diabatic representation may be useful to define reaction coordinates for electron transfer, proton transfer and coupled electron and proton transfer reactions in condensed-phase simulations.

Can a Wanzlick-like equilibrium exist between dicoordinate borylenes and diborenes?

Boron chemistry has experienced tremendous progress in the last few decades, resulting in the isolation of a variety of compounds with remarkable electronic structures and properties. Some examples are the singly Lewis-base-stabilised borylenes, wherein boron has a formal oxidation state of +I, and their dimers featuring a boron-boron double bond, namely diborenes. However, no evidence of a Wanzlick-type equilibrium between borylenes and diborenes, which would open a valuable route to the latter compounds, has been found. In this work, we combine DFT, coupled-cluster, multireference methods, and natural bond orbital/natural resonance theory analyses to investigate the electronic, structural, and kinetic factors controlling the reactivity of the transient CAAC-stabilised cyanoborylene, which spontaneously cyclotetramerises into a butterfly-type, twelve-membered (BCN)4 ring, and the reasons why its dimerisation through the boron atoms is hampered. The computations are also extended to the NHC-stabilised borylene counterparts. We reveal that the borylene ground state multiplicity dictates the preference for self-stabilising cyclooligomerisation over boron-boron dimerisation. Our comparison between NHC- vs. CAAC-stabilised borylenes provides a convincing rationale for why the reduction of the former always gives diborenes while a range of other products is found for the latter. Our findings provide a theoretical background for the rational design of base-stabilised borylenes, which could pave the way for novel synthetic routes to diborenes or alternatively non-dimerising systems for small-molecule activation.

Generation and Characterization of the Charge-Transferred Diradical Complex CaCO2 with an Open-Shell Singlet Ground State

The CaCO₂ complex is generated via the reaction of excited-state calcium atom with carbon dioxide in a solid neon matrix. Infrared absorption spectroscopy and quantum chemical calculations reveal that the complex has a planar four-membered ring structure with a strongly bent CO₂ ligand side-on coordinated to the calcium center in an η^2-O, O manner. The complex has an open-shell singlet ground state, which can be described as the bonding interactions between a Ca⁺ (4s¹) cation in the doublet ground state and a doublet ground state CO₂^- anion. The analysis of the bonding situation suggests that the Ca-O₂C bonds have a large (75%) electrostatic character. The covalent (orbital) interactions come from the coupling of the unpaired electrons of Ca⁺ and CO₂^- giving rise to electron-sharing bonding and a stronger contribution from dative bonding (Ca⁺)←(CO₂^-). The atomic orbitals (AOs) of Ca⁺ that are engaged in the covalent bonds are the 4s AO for the electron-sharing bonds and the 3d AOs for the dative bonds. This is further evidence for the assignment of the heavier alkaline-earth atoms as transition metals rather than main-group elements.

Tuning the magnetic properties of a diamagnetic di-Blatter's zwitterion to antiferro- and ferromagnetically coupled diradicals

In the quest of obtaining organic molecular magnets based on stable diradicals, we have tuned the inherent zwitterionic ground state of tetraphenylhexaazaanthracene (TPHA), a molecule containing two Blatter's moieties, by adopting two different strategies. In the first strategy, we have increased the length of the coupler between the two radical moieties and observed a transition from the zwitterionic ground state to the diradicalized state. With a larger coupler, ferromagnetic interactions are realized based on density functional theory (DFT) and wave-function theory (WFT) based complete active space self-consistent field (CASSCF)-N-electron valence state perturbation theory (NEVPT2) methods. An analysis based on the extent of spin contamination, diradical character, CASSCF orbital occupation number, Head-Gordon's index, HOMO-LUMO and SOMOs energy gaps is demonstrated that marks the transition of the ground state in these systems. In another approach, we systematically explore the effect of push-pull substitution on the way to obtain molecules based on a TPHA skeleton with diradicaloid state and, in some cases, even a triplet ground state.

Simulating X-ray photoelectron spectra with strong electron correlation using multireference algebraic diagrammatic construction theory

A new theoretical approach for the simulations of X-ray photoelectron spectra of strongly correlated molecular systems that combines multireference algebraic diagrammatic construction theory (MR-ADC) with a core–valence separation (CVS) technique.

Influence of the Radicaloid Character of Polyaromatic Hydrocarbon Couplers on Magnetic Exchange Interactions

The molecular properties of the conjugated spacers, such as the π-conjugation, aromaticity, length of the couplers, etc., that couple two localized spin-centers influence the intramolecular magnetic exchange interactions (2J) mediated...

Antiaromatic Dicyclopenta[b,g]/[a,f]naphthalene Isomers Showing an Open-Shell Singlet Ground State with Tunable Diradical Character

Since the first isolation of 1,3,5,7-tetra-tert-butyl-s-indacene in 1986, core-expanded s- and as-indacenes have attracted intensive interest. However, there is no reported synthesis of such type of molecules due to their high reactivity for over 30 years. Herein, we report the successful synthesis of two relatively stable, core-expanded indacene isomers, dicyclopenta[b,g]-naphthalene (5) and dicyclopenta[a,f]naphthalene (6). X-ray crystallographic analyses reveal that the backbone of 5 adopts a bond-delocalized structure, while that of 6 exhibits a bond-localized character. Variable-temperature ¹H NMR/ESR measurements, electronic absorption spectra, and theoretical calculations confirm that both molecules are globally antiaromatic and have an open-shell singlet ground state. However, 6 shows stronger antiaromaticity, a larger diradical character (y₀ = 48%), and a smaller singlet-triplet energy gap (ΔE_S-T = -0.99 kcal mol^-1) compared to 5 (y₀ = 30%, ΔE_S-T = -6.88 kcal mol^-1), which can be explained by their different quinoidal structures.

Dynamic Spin-Spin Interaction Observed as Interconversion of Chemical Bonds in Stepwise Two-Photon Induced Photochromic Reaction

Biradicaloids in π-conjugated organic molecules have been extensively studied in recent years because of the fundamental insights into the chemical bonds and unique optical, electrical, and magnetic properties. Several studies have reported that the spin-spin interactions of biradicaloids with flexible molecular frameworks dynamically evolve correlating with molecular structural changes. Although these dynamic behaviors will provide important insights into the relationship between molecular structures and spin properties, studies on such behaviors have been limited to two-spin systems. Here, we investigated the stepwise photochromic properties of biphotochromic molecules involving multiple spin interactions by double-pulse laser flash photolysis. The one-photon photochromic reaction generates the o-biradical form as the open-closed form, which thermally isomerizes to the o-quinoidal form and reaches the thermal equilibrium state between them. The additional absorption of a photon by the open-closed form leads to the photochromic reaction of the other photochromic unit, resulting in the generation of unpaired spins at the p-position of the central aromatic bridge of the biradical or quinoidal form. Under the situation, while the interaction between the unpaired spins and the o-biradical preferentially produces the p-quinoidal form in which the antiferromagnetic interaction at the p-position is dominant, that between the spins and the o-quinoidal form kinetically produces the bis(o-quinoidal) form followed by the thermal isomerization to the thermodynamically stable p-quinoidal form. These dynamic spin-spin interactions along with the rearrangement of chemical bonds will give a deeper understanding of the singlet biradicaloids and that to bridge organic multiradicals in molecular systems to cooperative spin behaviors in bulk materials.

Taming the Antiferromagnetic Beast: Computational Design of Ultrashort Mn-Mn Bonds Stabilized by N-Heterocyclic Carbenes

The development of complexes featuring low-valent, multiply bonded metal centers is an exciting field with several potential applications. In this work, we describe the design principles and extensive computational investigation of new organometallic platforms featuring the elusive manganese-manganese bond stabilized by experimentally realized N-heterocyclic carbenes (NHCs). By using DFT computations benchmarked against multireference calculations, as well as MO- and VB-based bonding analyses, we could disentangle the various electronic and structural effects contributing to the thermodynamic and kinetic stability, as well as the experimental feasibility, of the systems. In particular, we explored the nature of the metal-carbene interaction and the role of the ancillary η6 coordination to the generation of Mn2 systems featuring ultrashort metal-metal bonds, closed-shell singlet multiplicities, and positive adiabatic singlet-triplet gaps. Our analysis identifies two distinct classes of viable synthetic targets, whose electrostructural properties are thoroughly investigated.

The Interplay between Diradical Character and Stability in Organic Molecules

The number of scientific papers on the unique properties and the potential for various applications of compounds with a diradical character is growing constantly. The diradical character enhances and even engenders certain desired optical properties and its modulation is a modern molecular design strategy. Nowadays, molecules with a non-zero diradical character are regarded as promising materials for new-generation and highly efficient solar cells and photonics devices. What is the price, however, of the unique properties of open-shell compounds? Alongside all the benefits, the diradical character is usually associated with low stability and high reactivity—unwanted molecular qualities for practical purposes. Thus, from a fundamental and applied point of view, it is important to investigate the correlation between the diradical character and laboratory stability, which is the goal of the present paper. Here, we report a combined quantum–chemical study (conceptual DFT and spin-projected HF theory) and multivariate analysis of the diradical character of a series of o- and p-quinomethides, for the stability of which experimental data are available. Our results reveal that a compromise between the diradical character and laboratory stability of a molecule is feasible and that the relationship between these two quantities can be understood in the framework of Clar’s sextet theory.

Fused Quinoidal Dithiophene-Based Helicenes: Synthesis by Intramolecular Radical-Radical Coupling Reactions and Dynamics of Interconversion of Enantiomers

A series of fused quinoidal dithiophene-based double and triple helicenes (1-M, 2-M, 2-M-Cl, 3-M, 3-M-Cl) were synthesized by intramolecular radical-radical coupling followed by oxidative dehydrogenation reaction. These helical molecules show dynamic interconversion of enantiomers in solution as revealed by variable-temperature NMR measurements, and the energy barriers are correlated to the substituents and topological structures. Notably, dynamic high performance liquid chromatography was used to quantitatively investigate the room-temperature racemization process between the (P,P,M)- and (P,M,M)- enantiomers of the triple helical 3-M-Cl, which gave an interconversion energy barrier in consistent with density functional theory calculations. Their optical and electrochemical properties are dependent on the fusion mode. Our studies provide both new synthetic strategy and new dynamic analytical method for helicenes with unique electronic structure.

Twisting versus Delocalization in CAAC- and NHC-Stabilized Boron-Based Biradicals: The Roles of Sterics and Electronics

Twisted boron-based biradicals featuring unsaturated C2 R2 (R=Et, Me) bridges and stabilization by cyclic (alkyl)(amino)carbenes (CAACs) were recently prepared. These species show remarkable geometrical and electronic differences with respect to their unbridged counterparts. Herein, a thorough computational investigation on the origin of their distinct electrostructural properties is performed. It is shown that steric effects are mostly responsible for the preference for twisted over planar structures. The ground-state multiplicity of the twisted structure is modulated by the σ framework of the bridge, and different R groups lead to distinct multiplicities. In line with the experimental data, a planar structure driven by delocalization effects is observed as global minimum for R=H. The synthetic elusiveness of C2 R2 -bridged systems featuring N-heterocyclic carbenes (NHCs) was also investigated. These results could contribute to the engineering of novel main group biradicals.

Theoretical Study on Third-Order Nonlinear Optical Properties for One-Hole-Doped Diradicaloids

We investigate the relationships between open-shell character and longitudinal static second hyperpolarizabilities γ for one-hole-doped diradicaloids using the strong-correlated ab initio molecular orbital methods and simple one-dimensional (1D) three-site two-electron (3s-2e) models. As examples of one-hole-doped diradicaloids, we examine H₃ ⁺, methyl radical trimer cation ((CH₃)₃ ⁺), silyl radical trimer cation ((SiH₃)₃ ⁺), and 1,2,3,5-dithiadizolyl trimer cation (DTDA₃ ⁺). For H₃ ⁺, the static γ exhibits negative values and shows a monotonic increase in amplitude with an increase in the open-shell character defined by a neighbor-site interaction (y _S). On the other hand, it is found for (CH₃)₃ ⁺, (SiH₃)₃ ⁺, and DTDA₃ ⁺ that the static γ value exhibits similar behavior to that for H₃ ⁺ up to an intermediate y _S value, while it takes the negative maximum at a large y _S value, followed by a decrease in γ amplitude, and subsequently, γ changes to positive values with a drastic increase for larger y _S values. For example, in DTDA₃ ⁺, the negative/positive γ values, -69 × 10⁵/700 × 10⁵ au at y _S = 0.75/0.87, exhibit significant enhancements in amplitude, 2.4/24 times as large as that (-29 × 10⁵ au) at intermediate y _S = 0.59 as is often the case in DTDA₂. Using the 1D 3s-2e valence-bond configuration interaction model, these sign inversions and drastic increase in the amplitude of γ are found to originate in the differences in Coulomb interactions between valence electrons, between valence and core electrons, and between valence electrons and nuclei. These results contribute to pave the way for the construction of novel control guidelines for the amplitude and sign of γ for one-hole-doped diradicaloids.

On-surface synthesis of graphene nanostructures with π-magnetism

Graphene nanostructures (GNs) including graphene nanoribbons and nanoflakes have attracted tremendous interest in the field of chemistry and materials science due to their fascinating electronic, optical and magnetic properties. Among them, zigzag-edged GNs (ZGNs) with precisely-tunable π-magnetism hold great potential for applications in spintronics and quantum devices. To improve the stability and processability of ZGNs, substitutional groups are often introduced to protect the reactive edges in organic synthesis, which renders the study of their intrinsic properties difficult. In contrast to the conventional wet-chemistry method, on-surface bottom-up synthesis presents a promising approach for the fabrication of both unsubstituted ZGNs and functionalized ZGNs with atomic precision via surface-catalyzed transformation of rationally-designed precursors. The structural and spin-polarized electronic properties of these ZGNs can then be characterized with sub-molecular resolution by means of scanning probe microscopy techniques. This review aims to highlight recent advances in the on-surface synthesis and characterization of a diversity of ZGNs with π-magnetism. We also discuss the important role of precursor design and reaction stimuli in the on-surface synthesis of ZGNs and their π-magnetism origin. Finally, we will highlight the existing challenges and future perspective surrounding the synthesis of novel open-shell ZGNs towards next-generation quantum technology.

Impact of the macrocyclic structure and dynamic solvent effect on the reactivity of a localised singlet diradicaloid with π-single bonding character

Localised singlet diradicals are key intermediates in bond homolysis processes. Generally, these highly reactive species undergo radical–radical coupling reaction immediately after their generation. Therefore, their short-lived character hampers experimental investigations of their nature. In this study, we implemented the new concept of “stretch effect” to access a kinetically stabilised singlet diradicaloid. To this end, a macrocyclic structure was computationally designed to enable the experimental examination of a singlet diradicaloid with π-single bonding character. The kinetically stabilised diradicaloid exhibited a low carbon–carbon coupling reaction rate of 6.4 × 10³ s⁻¹ (155.9 μs), approximately 11 and 1000 times slower than those of the first generation of macrocyclic system (7.0 × 10⁴ s⁻¹, 14.2 μs) and the parent system lacking the macrocycle (5 × 10⁶ s⁻¹, 200 ns) at 293 K in benzene, respectively. In addition, a significant dynamic solvent effect was observed for the first time in intramolecular radical–radical coupling reactions in viscous solvents such as glycerin triacetate. This theoretical and experimental study demonstrates that the stretch effect and solvent viscosity play important roles in retarding the σ-bond formation process, thus enabling a thorough examination of the nature of the singlet diradicaloid and paving the way toward a deeper understanding of reactive intermediates.

An extremely long-lived localised singlet diradical with π-single bonding character is found in a macrocyclic structure that retards the radical–radical coupling reaction by the “stretch and solvent-dynamic effects”.

Paradoxical design of a serendipitous pyrazolate bridging mode: a pragmatic strategy for inducing ineluctable ferromagnetic coupling

In this contribution we have carried out a systematic magnetostructural investigation to establish a robust one-to-one correlation between the quasi-orthogonal bridging mode of a pyrazolate ring and ferromagnetic coupling. Generating a complex with an elusive quasi-orthogonal pyrazolate bridging is a challenging task but would ineluctably result in a ferromagnetic exchange pathway. Notwithstanding the rarity, we report herein a series of bis-pyrazolato copper complexes. We have successfully exploited a so-called hypothetical-deductive model on a particular set of ligand systems that forced the pyrazolate moiety to adopt an unusual bridging mode with the M-Npz-Npz-M torsion angles in the range from 49.7° to 72.8°. The corroborating variable temperature direct current (DC) magnetic susceptibility data unequivocally confirm the ferromagnetic coupling for the complexes with the torsion angles greater than 71.37°. Furthermore, the experimental results are in excellent agreement with theoretical calculations. Based on density functional theory (DFT) calculations, again a one-to-one correspondence is made between the ligand structure and magnetic behaviour. The diradical character (y0) of the complexes is correlated with the extent of bonding interactions between the Cu centers and hence, their ferromagnetic or antiferromagnetic nature. The broken symmetry (BS) calculations on the magnetically active molecular orbitals indicate the essential magnetic behaviour of the complexes, while the EPR g-tensor calculations confirm that dx2-y2 is the magnetic orbital.

Theoretical study on aromatic and open-shell characteristics of carbon nanobelts composed of indeno[1,2-b]fluorene units: dependence on the number of units and charge states

In this study, we theoretically investigate the aromatic and open-shell characteristics of carbon nanobelts (CNBs) composed of five- and six-membered rings. We have designed nanobelts composed of indeno[1,2-b]fluorene ([1,2-b]IF) units, which are referred to as [N]IF-CNB (N: the number of five-membered rings). The number of π-electrons, n π, in neutral [N]IF-CNB is 7N, and thus depending on N and charge states, n π can be 4n + 2 and 4n. Quantum chemical calculations on neutral [6]IF-CNB and [8]IF-CNB and dicationic [8]IF-CNB2+ have revealed that they are expected to exhibit unique aromatic and open-shell characteristics depending on n π, there are several analogies of the electronic structures in [N]IF-CNB to those in [N]annulene. Delocalized and intermediate open-shell electronic structures of [N]IF-CNB are also useful to drastically change the third-order nonlinear optical properties. These results suggest that theoretically designed [N]IF-CNB can be attractive and challenging targets of organic synthesis for realizing novel open-shell functional conjugated macrocycles.

Boron-Doped Polycyclic Aromatic Hydrocarbons: A Molecular Set Revealing the Interplay between Topology and Singlet Fission Propensity

We demonstrate the relationship between the topology (the way in which the atoms are connected), open-shell character, and singlet fission (SF) propensity in a series of diboron-doped anthracenes and phenanthrenes. The study is performed by using high-level wave-function-based quantum-chemical calculations. The results show that the molecular topology plays a crucial role for the optical properties and, respectively, for the SF propensity of the studied compounds. The topology-derived correlations between the structure and properties are interpreted in the light of the Kekulé hydrocarbons concept and serve as molecular design guidelines for the discovery of new SF materials. Finally, several boron-doped polycyclic aromatic hydrocarbons are proposed as SF chromophores for organic solar cells.

Dynamic solvent effects in radical-radical coupling reactions: an almost bottleable localised singlet diradical

Localised singlet diradicals are key intermediates in bond homolysis, which plays a crucial role in chemical reactions. However, thorough experimental analyses of the reaction dynamics and chemical properties are generally difficult because bond formation is rapid, even under low-temperature matrix conditions. In this study, the effects of solvent and pressure on the lifetimes of long-lived singlet diradicals with bulky substituents were investigated. The solvent dynamic effect was revealed to provide control over the rate constant of radical-radical coupling reactions, and an almost bottleable singlet diradical with a lifetime of ∼2 s at 293 K was obtained.

Lewis-Base Stabilization of the Parent Al(I) Hydride under Ambient Conditions

Aluminum(III) is inherently electron deficient and therefore acts as a prototypical Lewis acid. Conversely, Al(I) is a rare, nucleophilic variant of aluminum that is thermodynamically unstable under ambient conditions. While attempts to stabilize and isolate Al(I) species have become increasingly successful, the parent Al(I) (i.e, Al-H) remains accessible only under extreme temperatures/pressures or matrix conditions. Here, we report the isolation of the parent Al(I) hydride under ambient conditions via the reduction of a Lewis-base-stabilized alkyldihaloalane. Computational and spectroscopic analyses indicate that the ground-state electronic configuration of this monomeric aluminum species is best described as an Al(I) hydride with non-negligible open-shell Al(III) singlet diradical character. These findings are also supported by reactivity studies, which reveal both the p-centered lone pair donating ability and the hydridic nature of the parent aluminene.

Singlet-Fission-Induced Enhancement of Third-Order Nonlinear Optical Properties of Pentacene Dimers

Using quantum chemical calculations and exciton dynamics simulations, we investigate the static second hyperpolarizability γ [the third-order nonlinear optical (NLO) property at the molecular scale] of slip-stacked pentacene dimer models in the correlated-triplet-pair [¹(TT)] state created from the singlet excited state in the singlet fission (SF) process. It is found that the SF induces significant (∼20 times at maximum) enhancement of γ/monomer in the ¹(TT) state as compared to that in the singlet ground state. The origin of the remarkable enhancement of γ/monomer is revealed by analyzing the γ density distribution and the intermolecular orbital interaction. Furthermore, we clarify molecular packings suitable for highly efficient SF and largely enhanced γ values of a novel class of SF-induced NLO systems, which have promising potential to surpass the conventional NLO systems.

Monte Carlo Wavefunction Approach to Singlet Fission Dynamics of Molecular Aggregates

We have developed a Monte Carlo wavefunction (MCWF) approach to the singlet fission (SF) dynamics of linear aggregate models composed of monomers with weak diradical character. As an example, the SF dynamics for a pentacene dimer model is investigated by considering the intermolecular electronic coupling and the vibronic coupling. By comparing with the results by the quantum master equation (QME) approach, we clarify the dependences of the MCWF results on the time step (Δt) and the number of MC trajectories (MC). The SF dynamics by the MCWF approach is found to quantitatively (within an error of 0.02% for SF rate and of 0.005% for double-triplet (TT) yield) reproduce that by the QME approach when using a sufficiently small Δt (~0.03 fs) and a sufficiently large MC (~10⁵). The computational time (treq) in the MCWF approach also exhibits dramatic reduction with increasing the size of aggregates (N-mers) as compared to that in the QME approach, e.g., ~34 times faster at the 20-mer, and the size-dependence of treq shows significant reduction from N5.15 (QME) to N3.09 (MCWF). These results demonstrate the promising high performance of the MCWF approach to the SF dynamics in extended multiradical molecular aggregates including a large number of quantum dissipation, e.g., vibronic coupling, modes.

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.

Thiophene and its sulfur inhibit indenoindenodibenzothiophene diradicals from low-energy lying thermal triplets

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 π-electron chemical bonding.

Exploring the novel donor-nanotube archetype as an efficient third-order nonlinear optical material: asymmetric open-shell carbon nanotubes

Contrary to the enormous number of previous studies on carbon nanotubes (CNTs), herein, we realized the origin of the intrinsic open-shell diradical character and second hyperpolarizability γ using a broken symmetry approach. This study was inspired by our recent findings (S. Muhammad, et al., Nanoscale, 2016, 8, 17998 and Nakano, et al., J. Phys. Chem. C, 2016, 120, 1193). We performed structural modifications through a unique asymmetric donor-nanotube framework, which led to a novel paradigm of modified CNTs with tunable open-shell diradical character and remarkably superior NLO response properties. Interestingly, asymmetry and diradical character were found to be the crucial factors to modulate the second hyperpolarizability γ. We initially performed a comparative analysis of the diradical characters and γ amplitudes of boron nitride nanotubes (BNNTs) and CNTs possessing significant ionic characters and covalent characters, respectively. The basic findings for these simple configurations were further extended to the donor-acceptor CNT paradigm, which finally led to excellent asymmetric donor-CNT configurations with remarkably larger γ amplitudes. Furthermore, among the CNTs, finite length zigzag CNT(6,0)3 were modified with different donor-acceptor configurations. Interestingly, for the first time, unique donor-nanotube configurations [1,4-(NH2)2CNT-(6,0)3 and 1,4-(NH2)2CNT-(6,0)5] were found; they showed significantly robust γ amplitudes as large as 2519 × 103 and 4090 × 103 a.u. at the LC-UBLYP(μ = 0.33)/6-31G* level of theory. Additionally, several molecular level insights have been obtained for these novel donor-nanotube configurations using their odd electron densities, molecular electrostatic maps, densities of states and γ density analyses to highlight the realization of these novel materials for highly efficient optical and NLO applications.

Isomerism, Diradical Signature, and Raman Spectroscopy: Underlying Connections in Diamino Oligophenyl Dications

A diradical dication of a 4,4'-di(bis(1,4-methylphenyl)amino)-p-terphenyl oligomer has been characterized in solid-state by Raman spectroscopy and thermo-spectroscopy together with quantum chemical calculations. The diradical character has been evaluated on the basis of the Raman spectra and as a function of temperature. A complete understanding of the nature of the changes in solid state has been provided based on a pseudo-Jahn-Teller effect, which is feasible owing to the fine balance between quinoidal/aromatic extension among consecutive rings and steric crowding. This study contributes to the further comprehension of the molecular and electronic structures of these particular diradical molecules with strong implications on the understanding of the nature of chemical bonds in the limits of high electronic correlation or π-conjugation.

Computational Modeling of Cobalt-Based Water Oxidation: Current Status and Future Challenges

A lot of effort is nowadays put into the development of novel water oxidation catalysts. In this context, mechanistic studies are crucial in order to elucidate the reaction mechanisms governing this complex process, new design paradigms and strategies how to improve the stability and efficiency of those catalysts. This review is focused on recent theoretical mechanistic studies in the field of homogeneous cobalt-based water oxidation catalysts. In the first part, computational methodologies and protocols are summarized and evaluated on the basis of their applicability toward real catalytic or smaller model systems, whereby special emphasis is laid on the choice of an appropriate model system. In the second part, an overview of mechanistic studies is presented, from which conceptual guidelines are drawn on how to approach novel studies of catalysts and how to further develop the field of computational modeling of water oxidation reactions.

Tunability of Open-Shell Character, Charge Asymmetry, and Third-Order Nonlinear Optical Properties of Covalently Linked (Hetero)Phenalenyl Dimers

Tunability of the open-shell character, charge asymmetry, and third-order nonlinear optical (NLO) properties of covalently linked (hetero)phenalenyl dimers are investigated by using the density functional theory method. By changing the molecular species X and substitution position (i, j) for the linker part, a variety of intermonomer distances R and relative alignments between the phenalenyl dimers can be realized from the geometry optimizations, resulting in a wide-range tuning of diradical character y and charge asymmetry. It is found that the static second hyperpolarizabilities along the stacking direction, γ_yyyy , are one-order enhanced for phenalenyl dimer systems exhibiting intermediate y, a feature that is in good agreement with the "y-γ correlation". By replacing the central carbon atoms of the phenalenyl rings with a boron or a nitrogen, we have also designed covalently linked heterophenalenyl dimers. The introduction of such a charge asymmetry to the open-shell systems, which leads to closed-shell ionic ground states, is found to further enhance the γ_yyyy values of the systems having longer intermonomer distance R with intermediate ionic character, that is, charge asymmetry. The present results demonstrate a promising potential of covalently linked NLO dimers with intermediate open-shell/ionic characters as a new building block of highly efficient NLO systems.

Synthesis of the Unknown Indeno[1,2-a]fluorene Regioisomer: Crystallographic Characterization of Its Dianion

Of the five possible indenofluorene regioisomers, examples of a fully conjugated indeno[1,2-a]fluorene scaffold have so far remained elusive. This work reports the preparation and characterization of 7,12-dimesitylindeno[1,2-a]fluorene as a highly reactive species. Experimental and computational data support the notion of a molecule with pronounced diradical character that exists in a triplet ground state. As such, both NICS and ACID calculations suggest that the indeno[1,2-a]fluorene scaffold is weakly Baird aromatic. Reduction of the unstable red solid with Cs metal produces the dianion of the title compound, from which single crystals could be obtained and X-ray data acquired, thus fully corroborating the proposed indeno[1,2-a]fluorene hydrocarbon core.