π-Conjugated polycyclic hydrocarbons (PHs) can either accommodate π-electrons in the bonding orbitals to form a closed-shell ground state or show open-shell ground state due to the existence of one or more unpaired electrons . Monoradical PH is comprised of an unpaired electron in neutral molecule in the ground state . Existence of two unpaired electrons (radicals) in a molecule can be classified by either diradical or biradical . In the spin-restricted (R) molecular orbital (MO) representation , diradical character tends to increase as the highest occupied molecular orbital (HOMO)– lowest unoccupied molecular orbital (LUMO) gap gets reduced, causing a variation in bond nature from the stable bond regime to the bond dissociation regime through increasing the weight of doubly excited configuration from HOMO to LUMO. In a stable bond limit, i.e., closed-shell, no diradical character exists while in the bond dissociation limit, the perfect biradical or a pure open-shell configuration emerges. Any intermediate state is referred to as “diradicaloid” (diradical-like). Diradicals are even-electron molecules that have one bond less than the number permitted by the standard rule of valence and the two electrons occupy two near-degenerate MOs. The spin multiplicity (2S + 1) of monoradicals is doublet, whereas for diradicals, two spins can orient in parallel or antiparallel fashion, producing triplet biradical or singlet diradical species. Singlet diradical, as a molecular species, has all the electrons paired but a pair of these electrons, being weakly coupled through anti-ferromagnetic interaction, occupies different parts of the space with a small shared region. PHs with moderate to strong singlet diradical character generally show a broad electron spin resonance (ESR) signal due to the reduced singlet–triplet energy gap, which is believed to increase the population of the magnetically active triplet species. However, the ground state of such species is still singlet as at least one Kekulé structural formula can be drawn (e.g., p-quinodimethane (p-QDM)- and o-quinodimethane (o-QDM)-based PHs, Figure 1(a)). On the other hand, a pure biradical PH (e.g., m-quinodimethane (m-QDM)-based PHs, Figure 1(a)) is a molecular species with two electrons occupying two degenerate or nearly degenerate MOs, and there exists no Kekulé structural formula for this type of system [3a].
Aromaticity is a key concept for chemistry in the electronic ground state, and reactions in which aromaticity is gained are normally highly favorable. Antiaromatic molecules like parent cyclobutadiene can be categorized as delocalized diradicals according to their MO diagram as two electrons occupy two degenerate non-bonding MOs which are “spin-up” unpaired, making them strongly reactive species and thus their synthesis is highly elusive. In fact, later it was found that cyclobutadiene derivatives prefer a rectangular shape in its singlet ground state instead of delocalized square geometry caused by the Jahn–Teller effect . In the proaromatic concept (Figure 1(b)) for the formation of diradicals [5b], the driving force for such structure is the recovery of aromaticity from consecutive non-aromatic rings (quinoidal structure). A net energy minimization that can eventually surpass the energy required to break a C–C double bond is the key in generation of an open-shell diradical ground state. The smaller proaromatic tetracyano-quinoidal-thiophene oligomers are closed shell, whereas the ESR spectra of the 5QT and 6QT constitute the first reports on the unquestionable diradical character due to the population of thermally (room temperature (rt)) excited magnetically active species as a result of aromatization of the thiophene rings .
Acenes can be regarded as one-dimensional fragments of graphene and belong to a class of PHs consisting of linearly fused benzene rings. Bendikov et al. showed that the RB3LYP wave function becomes unstable for oligoacenes as small as hexacene and all higher oligoacenes, implying that the calculated energies for singlet states are unbelievably high. Re-optimization by using the broken-symmetry (BS) UB3LYP/6-31G* method, it was shown that acenes, larger than hexacene, possess a nonzero bandgap with a large amount of diradical character in a singlet open-shell ground state and the singly occupied molecular orbital (SOMO) is largely populated on the zigzag edges . Later, Hachmann et al. also showed that the ground state of linear polyacenes is singlet for all chain lengths from naphthalene to dodecacene, and acenes larger than dodecacene were found to exhibit singlet polyradical character in their ground state . Interestingly, experimental observations already established the closed-shell ground states (as evident from clear and sharp 1H nuclear magnetic resonance (NMR) signal) of higher-order acenes except for the first isolated crystalline nonacene derivative  that apparently showed low HOMO–LUMO gap of 1.2 eV which is a criterion for the origin of diradical character in PH. Absence of NMR signal and the presence of ESR signal with ge = 2.0060 for nonacene derivative were reported, although no clear conclusion regarding the ground state electronic structure was given in the report as the ESR signal may also come from some monoradical impurities.
Theoretically, diradical character is estimated by a complete active space self-consistent field (SCF) calculation using the restricted Hartree–Fock and two-configuration SCF calculations. A BS approach , later modified with spin-projection technique  to discard spin contamination in BS approach, using the unrestricted Hartree–Fock wave function  can define the occupation number of the lowest unoccupied natural orbital (LUNO) as the extent of diradical character. As simplified by Nakano , for a two-electron two-orbital model the ground state closed-shell molecule has the natural orbital (NO) occupation numbers 2 (occupied) or 0 (unoccupied). So the LUNO is 0 for closed shell, whereas in the open-shell singlet molecules, the NO occupation number can be an intermediate value between 0 and 2, depending on the diradical character; therefore, the occupation number of the LUNO should increase with the increase in the diradical character and eventually approaches 1 for a pure diradical. This implies that the diradical character, which is denoted by y (0 ≤ y ≤ 1 where y = 0 is closed shell and y = 1 is pure open-shell biradical), can be defined by the occupation number of the LUNO. Experimentally, diradical character can also be determined using the following equation : where ES1u,S1g and ES2g,S1g correspond to the energy of the lowest energy peaks in the one- and two-photon absorption (TPA) spectra, and ET1u,S1g corresponds to the energy gap between the triplet and the singlet ground state.
2 Quinodimethane-Based Open-Shell Polycyclic Hydrocarbons
The most basic, yet powerful, approach to generate a diradicaloid PH is to embed an o-QDM or p-QDM subunit into a π-conjugated framework. This approach has been a topic of intense interest due to their inherent diradical character arising from the recovery of the aromaticity of the central benzenoid ring of the respective quinoidal subunits, in the ground state. Comparatively, o-QDM derivatives such as pleiadene  are extremely reactive compared to p-QDM derivatives. Unlike o- and p-QDM, the m-QDM (i.e., m-xylylene biradical) cannot have a closed-shell quinoidal structure and thus is classified into non-Kekulé PH. Embedding of an m-xylylene biradical subunit into a planarized polycyclic benzenoid hydrocarbon generates open-shell π-conjugated triplet PH systems such as triangulenes (vide infra), with large spin densities at the edge sites.
2.1 o-QDM-Embedded Diradicaloids
Tobe et al. reported  the synthesis and crystallographic structure of an indeno-[2,1-a]fluorene (1) derivative 5 which could show diradical resonance contribution due to recovery of one additional Clar’s sextet (highlighted in gray color) in the ground state, with radical sites mainly located on the five-membered rings (Figure 2). Mesityl groups were introduced to kinetically protect the reactive sites, by adding mesitylmagnesium bromide to the diketone 3 to afford the diol 4 which on treatment with tin(II)chloride gave 5 as a stable, purple-colored solid. The unaffected 1H NMR spectra of 5 at higher temperature and a significant bond-length alternation in o-QDM core, as per crystal structure analysis, indicate a large singlet–triplet energy gap with small diradical contribution, which was also supported by theory. The singlet diradical character of 1 and 5 estimated by the Yamaguchi scheme was 0.33 and 0.21, respectively. Nucleus-independent chemical shift calculation further supports that 5 is weakly antiaromatic as a result of the as-indacene moiety. The vertical π-extension of o-QDM can lead to Kekulé structure 2 which can also have two diradical resonance forms and the spin density may distribute to the inner naphthalene ring. A similar synthetic approach was conducted to prepare the vertically extended o-QDM derivative 8 which was confirmed by X-ray crystallographic analysis . This compound is reported to be quite reactive in air affording an endoperoxide 9 (Figure 2). Compound 8 showed sharp signals at rt and broadening of the signals at higher temperatures was observed due to thermally accessible triplet state because of a reduced singlet–triplet energy gap of –7.46 kcal mol–1, indicating an enhanced diradical character in 8 compared to 5. The index y was estimated to be 0.63 which was considerably larger when compared to that of 1 (0.33).
2.2 m-Xylylene-Based Systems
An unsuccessful attempt by Clar to synthesize an m-xylylene derivative, triangluene, was explained by the triplet ground state in neutral state . Nakasuji et al. treated a dihydrotriangulene 10 precursor with p-chloranil to obtain a highly reactive triangulene derivative 11, although being protected by bulky tert-butyl groups on the three vertexes (Figure 3) . Variable temperature (VT) ESR measurement was conducted to monitor the chemical oxidation step and rapid freezing of the sample at intermediate stage gave a superposition of a doublet monoradical species and a fine-structure ESR spectrum of a typical triplet state which was attributed to compound 11, a true hydrocarbon with three-fold rotation axis. 11 is highly reactive and tends to polymerize to give oligomer/polymer 12.
Two naphthalene units bridged by an m-xylylene moiety cannot have a Kekulé structure and can only be drawn in its open-shell biradical form with two spins aligned parallel to each other leading to a reactive triplet biradical (Figure 4). A kinetically protected high-spin derivative 14 was synthesized by deprotonation of 13 using lithium diisopropylamide and subsequent oxidation of the dianion with iodine in dry 2-methyltetrahydrofuran at –78°C. This in situ generated triplet biradical was persistent at –78°C under nitrogen protection for at least one day .
An m-xylylene unit, incorporated into indeno[2,1-b]fluorene framework, can be drawn into both closed- and open-shell resonance forms (Figure 5). More resonance stabilization energy in the diradical resonance form of indeno[2,1-b]fluorene (1 sextet in closed shell vs. 3 aromatic sextets in open shell) compared to indeno-[2,1-a]fluorene (2 sextets in closed shell vs. 3 sextets in open shell) is supposed to increase its diradical character. Indeed, the mesityl-substituted isomer 17, prepared by addition of mesitylmagnesium bromide to the diketone 15 and subsequent reduction of the diol 16, turned out to be a singlet diradical in the ground state . Absence of rt 1H NMR signal and only broad NMR signals at low temperature down to –93°C indicate the existence of the thermally active triplet species. The ESR signal intensity decreased with decreasing temperature, indicating a singlet open-shell ground state. However, the singlet–triplet energy gap estimated experimentally, –4.2 kcal mol–1, was relatively higher compared to the theoretical value of –2.46 kcal mol–1. X-ray crystallographic analysis indeed showed the bond lengths of bond a (1.437 Å) and b (1.431 Å) are similar and lie between the lengths of the C(sp2)–C(sp2) bond in benzene (1.39 Å) and the C(sp2)–C(sp3) bond in fluorene (1.468 Å), supporting significant diradical contribution (y = 0.68) in ground state.
2.3 p-QDM-Embedded Systems and Its π-Extended Derivatives
Substitution of the terminal methylene sites in p-QDM by four phenyl groups resulted in the reasonably stable Thiele’s hydrocarbon 18 due to a quinoidal closed-shell ground state with a strong bond-length alternation in the p-QDM core (1.346 and 1.449 Å) (Figure 6) . Electron-withdrawing cyano (CN) groups, at the terminal methylene sites (radical centers), can help stabilize the p-QDM derivatives and, indeed, the tetracyanoquinodimethane (TCNQ, 21) is stable and commercially available. Incorporation of a p-QDM moiety into a fused π-conjugated PH framework has been an efficient approach to generate singlet diradicaloids, and typical examples include the bis(phenalenyl)s like indacenodiphenalene (IDPL) and heptazethrenes, to be discussed later. p-QDM-embedded indenofluorene congeners have been reported as typical closed-shell antiaromatic systems with negligible diradical character . Indeno-[1,2-b]fluorene 27 derivatives have shown their promise as electron-transporting materials, although no open-shell characteristics are found in the ground state . Similarly, indeno[1,2-c]fluorene 28 derivative was also found to be closed shell in the ground state . A fluoreno[4,3-c]fluorene (29) derivative, comprising of a laterally π-extended p-QDM architecture (2,6-naphthoquinodimethane), also exhibited no diradical characteristics in the ESR spectrum on heating or any line broadening in NMR spectrum as the triplet state was theoretically found to be 16.1 kcal mol–1 above the singlet ground state, thereby confirming a stable closed-shell ground state . In contrast, linearly π-extended p-QDM derivative, the tetracyano-substituted diphenoquinodimethane 22, had been reported to be very reactive and underwent instantaneous polymerization . The bond distance in the central part of the π-extended p-QDM derivative 19 with four phenyl protected at the terminal methylene (Tschitschibabin’s hydrocarbon) is intermediate between double- and single-bond values (1.420 and 1.372 Å), indicating significant diradical contribution in the ground state . A more enhanced diradical character was observed in π-extended Müller’s hydrocarbon 20 (Figure 6) that showed an ESR signal typical for triplet species at 153 K . The biphenoquinone 23 is a quinoidal closed-shell system, and terphenoquinone 24 also showed a strong bond length alternation in the ground state , whereas the more para-extended quaterphenoquinone 25  and quinquephenoquinone 26  are ESR active both in the solution and solid states, indicating significant diradical contribution in the ground state. These findings, indeed, lead to a new observation that the diradical character in π-conjugated planar PHs should emerge with the increasing number of proaromatic units, simply because more aromatic sextet rings can be recovered from a closed-shell quinoid to an open-shell diradical form.
Nakamura et al. used palladium catalyzed Takahashi coupling on the iodo-derivatives 30 and 32 to generate air and thermally stable tetracyano-substituted oligo-(para-phenylene vinylenes) 31 and 33, respectively (Figure 7) . Compound 33 displayed temperature-dependent broadening of its 1H NMR spectrum and a quite small singlet–triplet gap of 2.12 kcal/mol was estimated by superconducting quantum interference device (SQUID) measurements, suggesting the population of thermally excited triplet species causing an NMR line broadening and an ESR signal at g e = 2.003 at 340 K. In contrast, the closed-shell compound 31 exhibited sharp NMR signals and a relatively large HOMO–LUMO energy gap (1.58 eV) compared to 33 (1.02 eV).
A closed-shell diindeno[1,2-b:20,10-n]perylene 35, consisting a Tschitschibabin’s hydrocarbon framework, comprised of two indene groups being simultaneously fused at the peri- and β- position of a perylene core was synthesized from the corresponding diol precursor 34 by treating tin(II)chloride . No extra aromatic sextet rings can be drawn in its diradical resonance form (Figure 8) and thus it behaves as a closed-shell quinoidal hydrocarbon and was used as semiconductor in ambipolar field effect transistors.
Wu et al. had developed a series of tetracyano-terminated, quinoidal N-annulated perylene (NP)-based diradicaloids 37 comprising of extended p-QDM framework (Figure 9) . These oligomers were synthesized by Takahashi coupling from the dibromo-oligomers 36 followed by oxidation with p-chloranil. It was found that upon extension of the chain length, the monomer possesses a closed–shell quinoidal structure while the dimer, trimer and tetramer are open-shell singlet diradicals, and pentamer and hexamer become weakly coupled biradicals in the ground state. The enhanced diradical character in the higher-order oligomers is due to the large steric repulsion between the neighboring NPs causing a strain release from the rigid quinoidal structure to the more flexible diradical form. In addition, the recovery of aromaticity of the quinoidal perylene units in the diradical form helps the longer oligomers to gain more stability, and hence the diradical character approaches nearly 1 for the pentamer and hexamer.
To minimize the influence of strain release, planarized tetracyano-quaterylenequinodimehtane (40, m = 0) and hexarylenequinodimethane (40, m = 1) were prepared from respective dibromo-rylenes 38 (Figure 10) . In contrast to the unfused perylene dimer 37 (n = 2), the fused dimer 40 (m = 0) is closed shell due to the strong intramolecular antiferromagnetic coupling of the two spins via a double-spin polarization mechanism. The fused trimer 40 (m = 1) has an open-shell singlet diradical ground state due to the stabilization through the recovery of six aromatic naphthalene units in the open-shell form, although the diradical character, theoretically, was found to be quite smaller (y = 0.064) with a large singlet–triplet energy gap of –4.21 kcal/mol. This comparison leads to a valuable conclusion that the dihedral angle between the rylene cores plays a critical role in fine-tuning the electronic configuration of quinoidal molecules.
Incorporation of one thiophene unit between the rylene and the dicyanomethylene site in closed-shell 37 (n = 1) and 40 (m = 0) can readily turn on their diradical states, making 42 and 44 singlet diradical in the ground state with diradical character estimated as 0.81 and 0.93, respectively . The larger diradical contribution for 43 is in agreement with the stronger ESR signal and small singlet–triplet energy gaps of –0.16 kcal/mol as compared to –4.71 kcal/mol for 42, determined by SQUID measurements. Such a strong diradical contribution can be attributed to the recovery of two additional aromatic thiophene rings in the diradical resonance forms together with the conformational flexibility around the thiophene-rylene connections (Figure 11).
Nakano et al., theoretically, predicted that the asymmetric open-shell singlet systems with intermediate diradical characters could exhibit further enhancement of static first and second hyperpolarizabilities as compared to conventional asymmetric closed-shell systems or symmetric open-shell singlet systems with similar conjugation size . In order to achieve such systems, Wu et al. reported the first push–pull type quinoidal NP oligomers with two terminal sites substituted by benzo-1,3-dithiol-2-ylidene (donor) and dicyanomethylene (acceptor), respectively (Figure 12) . 46a and 46b represent the smallest derivatives with different substituents at the amine site, while 47 and 48 are the higher-order analogues. The bulky 2,6-dioctoxytolyl group in 46b suppressed the strong aggregation observed in 46a. Their synthesis was achieved by Pd-catalyzed Takahashi coupling from the corresponding bromo- and benzo-1, 3-dithiol-2-yl-substituted oligo- or (N-annulated perylenes) 45, followed by p-chloranil treatment to ensure complete dehydrogenation. The 1H and 13C NMR spectrum of 46b in CDCl3 exhibited sharp peaks at rt and even at elevated temperature, confirming its closed-shell ground state. In contrast, the higher series 47 and 48 showed NMR silence even at the low temperature (e.g., –100°C), implying their open-shell diradical ground state. Accordingly, ESR measurements on both displayed a broad spectrum both in solid and solution state with ge = 2.0017. The VT ESR measurements on the powder disclosed that the ESR intensity decreased as the temperature decreased, indicating that both 47 and 48 have an open-shell singlet ground state. ΔES-T values were estimated by SQUID to be –0.348 kcal mol–1 and –0.114 kcal mol–1 for 47 and 48, respectively, indicating an increased diradical character with increasing chain length. The contribution of the diradical form to the ground state in the push–pull type systems is slightly smaller than the pull–pull type framework 37 (n = 2) (–0.341 kcal mol–1) and 37 (n = 3) (–0.107 kcal mol–1) with the same conjugation length. The monomer 46b gave a maximum TPA cross-section value of about 1,000 GM at 1,500 nm compared to the values of about 660 GM and 670 GM at 1,900 nm for 47 and 48, respectively. This observation was reasoned for the enhancement of diradical character from closed-shell monomer (y = 0.123) to nearly pure open-shell 47 (y = 0.899) and 48 (y = 0.995) that does not benefit the non-linear optical (NLO) response. This abrupt increase of y from monomer to dimer is because of the reasonably large steric repulsion between the NP units in the rigid quinoidal structure, which tends to relax back to more flexible diradical/ionic form. To evaluate the intramolecular charge transfer character in the derivatives, the Hirshfeld charges of the central NP units and the terminal regions were calculated and it was found that with an extension of the chain length, the contribution of the zwitterion character decreases while the diradical character increases, and thus their physical properties become less solvent dependant. As a result, solvent polarity has a significant effect on the ground state and physical properties of the monomer only, but insignificant on the dimer and trimer.
An unorthodox approach to stabilize the Tschitschibabin’s hydrocarbon is benzannulation of the central biphenyl unit, reported by Wu et al., to generate the tetrabenzannulated hydrocarbons 50 and 52 (Figure 13) which should favor a closed-shell ground state (50-CS and 52-CS) as two aromatic Clar’s sextets are lost in their respective diradical resonance forms . However, the closed-shell forms of 50 and 52 adopt a contorted geometry with a larger steric hindrance among the anthryl peri-hydrogens, which could make the corresponding orthogonal diradical structures (50-OS and 52-OS) more favorable. A thorough experimental investigation assisted with theoretical calculation supported a closed-shell quinoidal ground state for 50 while 52 can be regarded as a weakly coupled triplet biradical in the ground state. The better thermodynamic stability of the diradical ground state in 52 can be credited to the efficient spin delocalization on the fluorenyl units. 4-tert-Butylphenyl-substituted compound 50 favors a closed–shell ground state (i.e., 50-CS) and a diradical excited state which was chemically obtained by reduction of the diol precursor 49, and the diradical excited state gradually decayed to the closed-shell ground state 50-CS with a half-life time of 495 min overcoming the large energy barrier (22.7 kcal mol–1) for the transition from the orthogonal diradical form to a butterfly-like quinoidal form. On the other hand, the triplet biradical ground state of 52 (i.e., 52-OS) was confirmed by the absence of NMR signal and presence of strong ESR signal with a singlet–triplet energy gap of 0.334 kcal mol–1 from SQUID measurements. An attempt to isolate the closed–shell form of 52 (i.e., 52-CS) was failed as the intermediate quickly relaxed back to the more stable open-shell form.
3 Open-Shell Anthenes and Peri-Fused Acenes
Anthenes and peri-fused acenes (periacenes) are rectangular polycyclic aromatic hydrocarbons (PAHs) comprising both zigzag and armchair edges with extended zigzag edges (Figure 14). As the conjugation is extended to a certain point (n > 0 for anthenes and m > 2 for periacenes), a remarkable open-shell diradical character may emerge which originates from a narrow bandgap and stabilization through recovery of Clar’s sextet in the diradical resonance form. Anthracene units fused together by three single bonds between neighboring anthryls generates extended graphene-like molecules called bisanthene (n = 0, m = 1), teranthene (n = 1, m = 1), quarteranthene (n = 2, m = 1) and so on. Closed-shell bisanthene is an unstable material and stabilization of closed-shell bisanthene was achieved by introduction of electron-withdrawing imide groups onto the zigzag edges or by substitution at the meso-positions with aryl or alkyne groups .
Teranthene  and quarteranthene  derivatives have been prepared and isolated in the crystalline form by Kubo’s group, thus allowing a detailed investigation on their ground-state molecular structure, chemical behavior and physical properties (Figure 15). Treatment of 53 with 2-mesitylmagnesium bromide in the presence of CeCl3 followed by NaI/NaH2PO2 generated a partially cyclized hydrocarbon 55 which upon ring-closure reaction by 2,3-Dichloro-5,6-dicyano-1,4-benzoquinone (DDQ)/Sc(OTf)3 afforded teranthene 57 . The quarteranthene was synthesized using an identical synthetic approach . Treatment of 54 with respective arylmagnesium bromides in the presence of CeCl3 and subsequent reductive aromatization with SnCl2/acetic acid afforded the partially ring-closed hydrocarbons 56a and 56b. Upon DDQ/Sc(OTf)3 treatment, 56a/56b gave the desired quarteranthenes 58a/58b. The CD2Cl2 solution of 57 was 1H NMR silent at rt while progressive line sharpening was observed as the temperature was lowered which is attributed to the lower population of triplet species at low temperature. A small singlet−triplet energy gap of –3.81 kcal mol–1 was estimated from SQUID. In contrast, the NMR baseline of 58a remained flat even when the temperature was lowered to 183 K. The absence of NMR signals for 58a accounts for the large population of thermally accessible triplet species. The singlet−triplet energy gap for 58a was found to be 0.689 kcal mol–1 from SQUID which indicates that 58a was easily activated to a triplet state with nearly 50 % populated triplet species at rt. The crystallographic data gave further information about the bond length alternation as a bond in 58a is 1.412 Å, much shorter than teranthene 57 (1.424 Å), which is considerably shorter than length of a C(sp2)–C(sp2) single bond (1.467 Å) and the corresponding one in bisanthene (1.447 Å), resulting from the significant diradical contribution. In addition, the highest harmonic oscillator model of aromaticity (HOMA) values of outer six-membered rings in quarteranthene indicates more benzenoid character at the peripheral rings and, hence, a larger diradical character compared to bisanthene. According to the desnsity functional theory (DFT) calculation, the singlet diradical character values are estimated to be 0.07 for bisanthene, 0.54 for teranthene and 0.91 for quarteranthene . The diradical character of these molecules in terms of the energy balance between the formal loss of a double bond and the aromatic stabilization was well explained by Kubo. The aromatic stabilization energy of benzene, based on the homodesmic stabilization energy, is ~21.5 kcal mol–1 which is around three times less than the C–C π-bond energy of ~64.53 kcal mol–1. Upon transformation to the diradical form, bisanthene contains only two additional sextets; therefore, the destabilization energy due to the π-bond cleavage cannot be fully compensated, so electron pairing is favored. In contrast, teranthene and quarteranthene both include three and four additional Clar sextets, respectively, in its diradical resonance form; hence the diradical forms contribute a lot to their ground state.
Perylene (59) and bisanthene (60) can be subcategorized as another class of PAHs, peri-fused acenes or periacenes (Figure 16), because they look like two naphthalenes or anthracenes have been peri-fused, respectively. The synthesis of the higher-order periacenes, namely peritetracene (61) and peripentacene (62), is quite challenging due to the extremely high reactivity, presumably originating from the more diradical/polyradical contribution (Figure 16), and the lack of proper synthetic methodology. Theoretical calculations conducted by Jiang et al. pointed out a crossover from nonmagnetic phase to antiferromagnetic phase for both periacenes and anthenes starting from bisanthene onward, and an open-shell ground state is therefore expected for these types of graphene-like molecules . Synthesis of peritetracene derivative is yet to be reported, and only one potential precursor, i.e., monobromo-tetracene dicarboximide, was reported by Wu’s group . The only experimental evidence of peripentacene was the mass spectroscopic peak of gas-phase disproportionation products .
A partially fused tetracene dimer was very recently reported by Müllen et al. The intermediate compound 63 was first prepared in 8 steps and was subjected to Grignard treatment followed by a ring fusion and oxidative dehydrogenation to afford the tetrabenzo[a,f,j,o]perylene (a bistetracene analogue) derivative 65 as green powder (Figure 17) . The diradical contribution to the ground state, arising from the 5 Clar sextets in open-shell form compared to 2 sextets in closed shell, was derived by the VT NMR measurement where progressive line broadening from 213 K to 298 K was attributed to the population of the thermally excited triplet species which was –3.4 kcal mol–1 (derived from VT ESR) higher than the singlet diradical ground state. Theoretically (at B3LYP/6-31G(d,p) level), the compound has been shown to have y = 0.615, even though a large singlet–triplet energy gap of –6.7 kcal mol–1 was deduced.
In contrast, a bistetracene derivative 66 (Figure 18) with high-charge carrier mobility of 6.1 cm2 V−1 s−1 was reported  to exhibit closed-shell ground state as in the open-shell form only one extra Clar’s sextet was recovered which may not be high enough to compensate the breaking of one C–C double bond energy.
There are a couple of synthetic approaches toward peripentacene reported in literatures; however, none of them succeeded (Figure 19(a)). One of them, contributed by Wu’s group, involves the oxidative photocyclization of 67 to obtain partially fused bis-pentacenequinone 68 . However, the subsequent nucleophilic reaction did not generate the desired 1, 2-addition adduct; instead an unexpected 1, 4-Michael addition product 69 was obtained when compound 68 was treated with excess Grignard reagent of 1-bromo-3,5-di-tert-butylbenzene in anhydrous tetrahydrofuran (THF) followed by acidification in air. Further treatment of 69 with excess Grignard reagent followed by acidification in air gave the tetraaryl-substituted fused bispentacenequinone 70. Crystallographic analysis revealed an α, β-unsaturated ketone structure in the fused bispentacenequinones 68 and 69, which may account for the unusual Michael addition reactions. Another synthetic approach, documented by Müllen et al. (Figure 19(b)), involves the cyclization of tetracyano pyrene derivative 71 to afford the tetraketone 72 which unfortunately didn’t undergo further photocyclization . Adopting an alternative path by oxidative cyclodehydrogenation of 71 in the presence of PIFA/BF3 (PIFA: phenyliodine bis(trifluoroacetate)) and subsequent acid-promoted acylation afforded the peripentacenetetraketone 73 in trace amount with very poor solubility and no further reactions were conducted. It concludes that periacenes beyond bisanthene are still elusive.
A tetrabenzo-peripentacene derivative 76  was recently reported by Yamada et al., utilizing another pyrene derivative, in 17 % yield by oxidation of 74 with FeCl3 following a quick separation and further oxidation with DDQ/Sc(OTf)3 in a microwave at 130°C . This compound is better be described as a tetrabenzo-peripentacene rather than a “peripentacene” derivative because HOMA analysis revealed localized aromaticity as defined by the eight aromatic sextet rings in the core, with a closed-shell ground state (Figure 20). The structure was established by mass spectrum and single-crystal X-ray crystallographic analysis. The rigid framework of the compound is well reflected by the fine and sharp UV-vis absorption structure and a small stokes shift of 10 cm–1.
4 Phenalenyl-Based Open-Shell PHs
Phenalenyl (77) is regarded as rigid π-conjugated neutral radical composed of a triangular fusion of three benzene rings and is also the smallest “open-shell graphene fragment” (Figure 21). Research on phenalenyls could lead to a better understanding of the intriguing electronic and magnetic properties of nanographene . The planar structure of phenalenyl with the radical spin delocalized over the entire molecule, and high redox amphotericity grabbed attention of chemists, and earlier, Haddon claimed its potential use as single-component molecular electroconductors . The kinetic instability of phenalenyl stimulated a great deal of synthetic efforts for the stabilization of the phenalenyl by chemical modifications to suppress its immediate dimerization by intermolecular σ-bond formation as well as reactivity toward oxygen. In the following sections, the significant progress in neutral monoradicals and diradicaloids based on the phenalenyl system is discussed.
4.1 Phenalenyl-Based Monoradicals
Introduction of three tert-butyl groups at the β-positions of phenaleny helped Nakasuji with the isolation of 82 in the solid state in air in 1999 (Figure 22) . Formylation on 4-bromo-2,7-di-tert-butylnaphthalene (78) by lithiation and then Reformatsky reaction followed by a reductive elimination of hydroxyl group, subsequent hydrolysis and Friedel–Crafts acylation, gave the phenalanone derivative 80. The radical precursor 81 was obtained as pale yellow crystals by reduction of 80 with LiAlH4 and subsequent dehydration in p-TsOH. Oxidation of the phenalene 81 by p-chloranil in degassed toluene afforded phenalenyl 82 as deep blue crystals. The bulky substituents not only successfully suppress the σ-bond dimerization, but are also possessed with a minimal perturbation to the electronic structure of the parent phenalenyl in that the connection positions were β positions with negligible spin densities. Crystal structure showed the formation of π-dimer in a herringbone packing motif with interplanar distance ranging from 3.201 to 3.323 Å, much shorter than the sum of the Van der Waals radius of the carbon atoms. A strong antiferromagnetic interaction within the π-dimer as evidenced by a large antiferromagnetic intermolecular exchange interaction (2J/k B = –2,000 K) from SQUID measurements corroborates well with such short distance that eventually opened the area of multicenter bonding . Interestingly, spectroscopic study showed the same dimeric behavior (pancake bonding) in solution (similar to crystal) as the red purple solution of 82 gradually turned to blue upon cooling which is in accordance with the increase of absorbance in 530–670 nm region . More definite evidence was provided by low-temperature 1H and 13C NMR measurements. The molecular weight of the π-dimer was also detected by cold-spray ionization mass spectrometry (MS) which allows substance ionized at lower temperatures, and this result represented the first detection of a radical dimer with NMR and MS techniques.
Perchlorophenalenyl radical 88 with all α- and β-positions substituted by chlorine atom was first prepared by Haddon et al. , and the X-ray crystallographic structure (Figure 23) was obtained in 2001 . The key starting material perchloroacenaphthylene 85 was obtained as mixture with 84 from chlorination of acenaphthene 83. Conversion of 85 from 84 also was realized by thermolysis or treatment with PPh3. Addition of dichlorocarbene to 85 afforded 86 which underwent subsequent allyl rearrangement in the presence of Lewis acid to yield phenalenyl cation 87. Reduction of 87 afforded the air stable 88 as a shiny black hexagonal crystal. X-ray analysis revealed a propeller-shaped 88 due to the bulky chlorine atom-induced deformation from the planar structure, and nonuniform stacking was also observed. This molecule stacked in columns separated by 3.78 Å, in sharp contrast to the tert-butyl phenalenyl 82 which was dimeric in the solid state with a much closer intermolecular distance. The reason for the long intermolecular distance of 88 was due to the non-planarity which inhibited the formation of 60o-rotated stacking motif. The magnetic susceptibility measurements disclosed that the solid 88 exhibited Curie paramagnetism at 100–380 K and antiferromagnetic ordering below 100 K. A rt conductivity of 10–10 S cm–1 was reasoned for the isolation of individual molecules, making 88 a Mott–Hubbard insulator.
In 2014, Kubo et al. tried to create an ideal 1D chain by utilizing the strong electrostatic interaction of pentafluorophenyl groups that were introduced at the β-positions of phenalenyl. A hydro precursor 89 was prepared in ten steps from a commercially available 2,8-dibromonaphthalene and dehydrogenation with DDQ in final step resulted in the formation of a σ-dimer (90) of pentafluorophenyl-substituted phenalenyl radical, and not the desired 2,5,8-tris(pentafluorophenyl)phenalenyl radical 91 . The single-crystal X-ray analysis is the first structural characterization of a σ-dimer of an electronically unperturbed phenalenyl compound. The σ-dimer featured a long s-bond 1.636(7) Å between two phenalenyl rings, thereby implying the weakness of the σ bond. Indeed, a solution of the σ-dimer in toluene at rt showed a well-resolved multiline ESR spectrum that corresponded to compound 91; therefore, compound 91 and its s-dimer existed as an equilibrium mixture in solution. The ESR signals decreased in intensity with decreasing temperature and almost disappeared at 230 K. The σ-dimer in solid form was further heated at 300°C in a degassed tube. The heating resulted in melting to a liquid accompanied by a color change from yellow to purple and, surprisingly, cooling the liquid afforded relatively large X-ray quality needles that at 10 K showed the distinctive feature that 91 forms a 1D chain with equidistant stacking of the molecule. It exhibited bimodal (σ and π) association modes. In the π mode, a consecutive multicenter bonding interaction led to electron delocalization in a uniform 1D stack of the radicals and a covalent bonding interaction of about –600 K (2J/k B). High thermodynamic stability of the phenalenyl moiety decreased the stability of the s-dimer, whilst its planar structure adequately stabilized the p-association, owing to a multicenter bonding interaction, which resulted in a small energy difference between the s- and p-modes (Figure 24).
Bis(phenalenyl)s linked through a five-membered ring to produce a monoradical system 93a, obtained as black powder by the reduction of precursor 92 with decamethylferrocene, was reported by Kubo et al.  to be highly stable in the solid state sans steric protection due to extensive delocalization (thermodynamically stabilized) (Figure 25). The extensive delocalization of unpaired electron also suppressed the formation of σ-dimer as evident from the unchanged multiline ESR signal intensity from rt to –90°C. The X-ray crystallographic analysis of the n-butyl-substituted compound 93b indicated the formation of π-dimers in the solid state with multicenter bonding, and the strength of antiferromagnetic coupling interaction was measured as –1,600 K (2J/k B) within the π-dimer, which would split the SOMO of 93b into bonding and antibonding MOs within the π-dimer. The half-life in air determined at rt was almost 60 h, which is in contrast to the rapid reaction of the phenalenyl radical with oxygen, suggesting that spin delocalization is very important for the stabilization of organic radicals. Fusion of three phenalenyl units onto one benzene ring was supposed to lead to a highly delocalized monoradical system (Figure 25), but the very low solubility of the synthetic intermediates and, furthermore, the oxygen-sensitive trihydro precursor of 94a hampered its characterization . Tert-butyl groups were then introduced to improve the solubility and stability, and subsequent reactions eventually afforded a hexa-tert-butyl-tribenzodecacyclenyl derivative 94b which showed six reversible one-electron redox waves, providing evidence for formation of stable mono-, di- and tri-valent species, making 94b one of the rare examples of compounds with six-stage amphoteric redox behavior.
With the aim to obtain stable neutral radicals with less steric hindrance and extended delocalization, Haddon et al. designed a series of phenalenyl radicals with a disulfide bridge across two neighboring active positions (Figure 26). The dithiophenalenyl 98 was firstly prepared in 1978 by reduction of the corresponding cationic species 97 and it survived in solid state in air for up to 24 h but decomposed quickly in solution . In the crystalline phase, 98 stacked in a sandwich herringbone motif of face-to-face π-dimers with 180° rotation between two radicals (Figure 26). The intermolecular distance in this π-dimer (3.13–3.22 Ǻ) is even shorter than that of 82, indicating a stronger intermolecular interaction. Notably, in spite of the absence of bulky substituents, no σ-dimerization was formed in the solid state as the spin is largely delocalized even on the two sulfur atoms stabilizing the neutral radical thermodynamically. An almost complete superposition of the α carbon atoms can be observed from a perpendicular view, maximizing the overlap of SOMOs. Other contacts in the lattice, such as S–S interactions between different π-dimers, were also observed, but the dimers remain isolated with electrons trapped within dimer pairs, which was further demonstrated by the conductivity measurements revealing it as insulator . The attempt to prepare a more spin-delocalized radical analogue of tetrathiophenalenyl was performed; however, the reduction of the cation 100 led to formation of a closed-shell dimer 101 with a S–S σ-bond (Figure 26), and only a weak ESR signal can be observed in solution .
Modifications within the phenalenyl moiety, instead of around the phenalenyl unit, were also investigated to stabilize the open-shell system; for example, incorporation of heteroatoms such as nitrogen atom is an effective way to stabilize phenalenyl radical , and a chiral diazaphenalenyl having helicene structure was also reported as stable radical .
4.2 Phenalenyl-Based Diradicaloids
Pentalenodiphenalene 102 , a pentalene subunit bridging two phenalenyl moieties, was first reported by Nakasuji et al. (Figure 27) and showed interesting amphoteric multistage redox properties. However, the neutral state was substantially destabilized by the electronic contribution from 8π-electron antiaromatic pentalene subunit. Afterward, an IDPL 103a with one benzenoid ring fused in the center was developed, and various substituents were introduced to improve the solubility (Figure 27) . The line broadening in the 1H NMR spectra at elevated temperature as well as emergence of sharp peaks at lower temperature together with solid-state ESR peak clearly indicated a thermally accessible triplet species at rt, and the energy separation between ground singlet state to excited triplet state was further determined as ~4.87 kcal mol–1. The crystallographic structure of 103d demonstrated one-dimensional chains in staggered stacking mode with an average π–π distance of 3.137 Å, which is significantly shorter than the van der Waals contact of carbon atoms (3.4 Å). This packing mode will maximize the SOMO–SOMO overlapping between the radicals, leading to stabilized intermolecular orbitals corresponding to intermolecular covalency . A naphthalene-linked bis(phenalenyl) 104a with enhanced diradical character than 103 was also reported  to feature a smaller HOMO–LUMO and singlet–triplet gap of 1.04 eV and –3.77 kcal mol–1 (by SQUID), respectively, than 103d (1.15 eV and ΔES-T = –4.37 kcal mol–1). The crystal packing of 104b adopted similar stepped mode to 103d in the one-dimensional chain, and the intermolecular bonding was stronger than the intramolecular one due to the spin-localized nature on the phenalenyl moieties, which can be more adequately described as multicenter bonding. Bis(phenalenyl)s linked by anthracene unit 105 (Figure 27) were also reported by Kubo et al.  and have even larger diradical contribution (y = 0.68) compared to their naphthalene (y = 0.50) and benzene (y = 0.30) counterparts. The enhanced diradical contribution of 105 was further supported by crystallographic analysis where the bond a in 105b is more elongated (1.467(3) Å) compared to that of 104a (1.465(7) Å) and 103e (1.457(2) Å). A similar intermolecular covalent bonding interaction in 105a with a distance of 3.122 Å, which is considerably stronger between molecules compared to within a molecule in a one-dimensional stack, was observed. The significant diradical contribution of 105 was attributed to the high aromatic stabilization energy of the anthracene bridge. These compounds are featured by a singlet diradical ground state as two factors play major role in stabilization of the systems: (1) the intrinsic delocalization of phenalenyl moiety and (2) the aromatic stabilization through the recovery of additional aromatic ring from quinoidal resonance form to the diradical resonance form.
A thiophene-fused bis(phenalenyl) 106 (Figure 28) was reported to show y = 0.35 and DFT calculation at UB3LYP/6-31G(d,p) level predicted a singlet diradical ground state which lies 1.7 kcal mol–1 below the singlet closed-shell state. The single crystal analysis revealed two kinds of dimeric pairs with substantially short nonbonding contacts of about 3.1 Å between each thiophene ring . Accommodation of a doubly excited configuration into the ground state configuration stabilized this system by suppressing four-electron repulsion arising from interaction between fully occupied orbitals. Fusion of phenalenyl to ortho- positions of phenyl ring led to compounds 107a and 107b (Figure 28), and 107b with tert-butyl substituents was reported to be extremely air-sensitive and decomposed in the air compared to several week long stable 103c . The absence of 1H NMR signals gave no useful information about 107b, however, dissolution of 107b in D2SO4 gave clear spectra assignable to the dicationic species 107b 2+, thereby supporting the formation of 107b. The singlet open-shell form was stabilized by 8.45 kcal mol–1 than the singlet closed shell, supporting a diradical ground state .
A head-to-head fusion of two phenalenyl moieties will generate a Z-shape graphene fragment, called zethrene 108, which looks like two naphthalene units are fixed by a trans-1,3-butadiene unit (Figure 29) . The diradical form of zethrene cannot be stabilized by recovery of additional aromatic sextet ring, therefore, they could show closed-shell ground state, although, remarkable open-shell diradical character y = 0.407 was predicted by Nakano et al., based on the occupancy numbers of spin-unrestricted Hartree–Fock natural orbitals (UNOs) . However, synthesis and experimental investigations of 7, 14-bis(phenylethynyl)zethrene 109 by Tobe et al. , the phenyl-substituted zethrene derivative 110 by Y. -T. Wu et al. , a zethrene biscarboximide derivative 111 by Wu et al. , and a parent zethrene derivative 108 by Miao et al.  were in favor of a closed-shell ground state. A diphenyl-substituted 1,2:8,9-dibenzozethrene 114 , prepared by adopting a similar approach used by Y. -T. Wu , exhibits larger diradical character index of 0.210 compared to that of 0.128 for unsubstituted 1,2:8,9-dibenzozethrene, most probably due to the distorted geometry and extended delocalization. However, the large singlet–triplet gap (–7.32 kcal mol–1) didn’t allow any thermally promoted magnetic activity, making it behave like a typical closed-shell PH.
Extension of the butadiene unit gives higher-order zethrenes such as heptazethrene 115, octazethrene 116, and nonazethrene 117 (not reported yet) in which two naphthalene units are bridged by a p-QDM, 2,6-naphthoquinodimethane, and 2,6-anthraquinodimethane unit, respectively (Figure 30). Unlike zethrene, diradical resonance form of heptazethrene (y = 0.537) and higher homologues (octazethrene, y = 0.628) are stabilized by the recovery of aromaticity of the aromatic linker ring in the center together with the thermodynamic stabilization through radical delocalization on entire hydrocarbon backbone. Vertical fusion of two benzenoid rings onto the heptazethrene core, in different modes, can lead to two isomeric structures, 1,2:9,10-dibenzoheptazethrene 118 and 5,6:13,14-dibenzoheptazethrene 119 (Figure 30).
Theoretical prediction of a larger diradical character in heptazethrene stimulated our group to synthesize the first relatively stable heptazethrene derivative, heptazethrenebis(dicarboximide) 121 (Figure 31(a)). This compound was synthesized by using a transannular cyclization approach from 120 involving simultaneous cyclization of an octadehydronaphthoannulene intermediate . 1H NMR spectrum showed a line broadening at rt due to the existence of thermally accessible triplet species and progressive line sharpening upon cooling due to the shift of the equilibrium to the singlet state. On the basis of DFT calculations, the energy of singlet diradical state of 121 was located 5.8 and 7.9 kcal/mol lower than the closed-shell quinoidal state and open-shell triplet biradical state, respectively, supporting an open-shell singlet diradical ground state with a homogeneously distributed spin density on the entire hydrocarbon backbone. A low electrochemical bandgap of 0.99 eV associated with lower-energy UV-vis-NIR absorption band that originated from admixing of the doubly excited electronic configuration (H,H-L,L) into the ground state further supports the open-shell character of 121. Compound 121 showed reasonable photostability in solution; however, the material slowly decomposed during storage either as solution or in solid state. In order to improve the stability without compromising the solubility, kinetic blocking at the most reactive radical sites was necessary. With the aim to improve the stability and tune the bandgap and diradical character, an extended-heptazethrenebis(dicarboximide) (a p-QDM-bridged perylene monoimide dimer) 123 was synthesized which was kinetically blocked by t-butyl phenyl groups at the most reactive radical sites (Figure 31(b)) . BF3·OEt2-mediated intramolecular ring-cyclization of the dimethoxy derivative 122 followed by oxidative dehydrogenation by DDQ gave the target compound 123, which is soluble in common organic solvents and stable under ambient conditions. An absorption spectrum characteristic to admixture of a doubly excited electronic configuration with low HOMO–LUMO gap of 0.99 eV, absence of NMR signal at rt and presence of broad ESR signal due to thermally populated triplet species (ΔES-T = –2.97 kcal mol–1, from SQUID) were in favor of its singlet diradical character (y = 0.465) in ground state. It is worth to mention that a different regio-selectivity for the ring cyclization reaction was observed with NP derivative 124 leading to eventual isolation of a closed-shell s-indacene-bridged perylene dimer 125 with negligible diradical character (y = 0.009), instead of the extended heptazethrene derivative (Figure 31(c)) . This observation was attributed to the activation of the β-position of electron-rich NP unit (in 124) along with formation of two five-membered rings rather than six-membered rings which is thermodynamically more favorable. The structures of 123 and 125 are both confirmed by X-ray crystallographic analysis (Figure 31(d)).
To improve the stability of the higher-order zethrenes, bulky triisopropylsilylethynyl (TIPS)-blocked heptazethrene 126 and octazethrene 127 were prepared from the corresponding diketone precursors (Figure 32) . Compound 126 showed a typical p-band similar to closed-shell PHs, while 127 displayed an absorption pattern similar to the 121 and 123 indicating a probable open-shell character for 127. The open-shell nature of 127 was further supported by the broadened 1H NMR spectrum and the appearance of ESR signal at rt due to presence of thermally excited triplet species as a consequence of small singlet–triplet energy gap (−3.87 kcal/mol based on SQUID). Both 126 and 127 were packed into a 1D infinite chain via intermolecular π−π interactions, with an average π-stacking distance of 3.38 and 3.35 Å, respectively, which is larger than intermolecular covalent π-bonding interaction seen in Kubo’s bis(phenalenyl)-based diradicaloids.
Using a similar synthetic strategy, nucleophilic addition of TIPS-magnesium chloride to the corresponding diketone precursor 128 following reduction with SnCl2 provided a dibenzoheptazethrene derivative 129 (a derivative of 119) which appeared to have an open-shell singlet diradical ground state (Figure 33). Another dibenzoheptazethrene isomer 131 (a derivative of 118) was also obtained using a DDQ-mediated oxidative dehydrogenation of a dihydro precursor 130. Experimental and theoretical investigation revealed 129 to possess a larger diradical contribution (y = 0.576) in the ground state compared to isomeric 131 (0.309) . This difference in diradical character between two isomeric structures was explained by the different number of aromatic sextet rings in the respective diradical resonance forms (Figure 30). Hence, benzenoid PHs with the same chemical composition, the molecule with more aromatic sextet rings in the diradical resonance forms, exhibits greater diradical character. This can be regarded as an extension of Clar’s aromatic sextet rule in the benzenoid PH-based singlet diradicaloids.
5 Miscellaneous Open-Shell PHs
A potential tetraradicaloid hydrocarbon 132 (Figure 34), tetracyclopenta-[def,jkl,pqr,vwx]tetraphenylene, was successfully prepared by Tobe et al., which on NMR timescale rapidly equilibrated between its two D2h structures through valence tautomerization in solution . It exhibited an intense absorption maximum at 475 nm together with a broad band centered at 909 nm with the lowest energy absorption band shifted to much longer wavelengths because of the extended conjugation. Using a long-range-corrected LC-UBLYP/6-311+G(d,p) method, the diradical and tetraradical characters were measured where (y0, y1) = (1, 0) indicated a pure diradical character while (y0, y1) = (1, 1) indicated pure tetraradical character. Theoretical calculation, on three different models with D2h, D4h symmetry and the crystal structure, predicted the (y0, y1) as (0.095, 0.032) for D2h structure, (1.00, 0.166) for D4h structure and (0.258, 0.085) for the crystallographic structure. However, a clear and sharp 1H NMR can’t experimentally validate the open-shell ground state which also corroborates the strong bond length alternation from crystallographic bond length analysis as the relatively short bonds a (1.371 Å), c (1.349 Å), e (1.373 Å) and g (1.359 Å), and longer bonds b (1.433 Å) and d (1.440 Å) bonds were in favor of the presence of a p-QDM subunit. Notably, 1H NMR signal broadening at 50°C was observed which was indicative of thermally accessible triplet state, although vertical singlet–triplet energy gap was theoretically found to be quite large. So, this compound is better regarded as a singlet diradicaloid with a moderate diradical character and minor tetraradical character.
Stable fluorenyl-based monoradicals were recently reported by Kubo (Figure 35) . The attachment of the 9-anthryl group at the most reactive site of the fluorenyl moiety efficiently stabilizes the radicals as anthracene can effectively protect the spin centers  with large spin density from σ-dimerization and oxygen attack, and benzannulation of the fluorenyl center increases the stability of the radicals through extended delocalization. All three radicals showed significant stabilities with the half lives of 7, 3.5 and 43 days for 133, 134 and 135, respectively. Compound 134 was isolated as an unassociated monoradical in crystalline form, whereas 133 gave crystalline σ-dimers and 135 existed in both unassociated monoradical and σ-dimer forms in its solid state. The dimerization in solution for 133 was evident from decrease in ESR signals at low temperature, whereas 134 and 135 did not show such ESR behavior. Solid UV measurements disclosed mechanochromic properties of crystals of 1332 and 1352 (σ-dimers) that indicated the dissociation of σ-dimer to monoradical could be a mechanochemical process.
As said by Lambert , “the future of these biradical PAHs clearly lies in materials science” and therefore efforts have to be made to realize their importance in materials sciences. Open-shell systems with moderate diradical contribution, theoretically, showed impressive third-order NLO properties [4, 87] which was justified experimentally (large TPA cross section was observed) by several groups including ours [3e]. Their role in future photovoltaic devices had also been investigated in terms of singlet-fission process [4, 88] and lately, promising results for organic light emitting device material have also been reported . Furthermore, investigations of molecular-sized open-shell graphene fragments showed promise in molecule-based batteries , field-effect transistors , and as electroconductor . Such advancement is believed to make path for the open-shell PHs as the next-generation spintronic materials  given that realistic synthetic approaches evolve from a clear understanding on the stabilization issues of such systems in the molecular level.
The project at Singapore was financially supported by AcRF MOE Tier 2 grants (MOE2014-T2-1-080), Tier 3 grant (MOE2014-T3-1-004) and A*STAR JCO grant (1431AFG100). We also would like to say special thanks to other major collaborators, Professor D. Kim in Yonsei University, Professor J. Casado and Professor J. T. Lopéz Navarrete in University of Malaga, Professor J. Ding in National University of Singapore, Professor K. -W. Huang in KAUST, Professor K. Furukawa in Niigata University, Professor Masayoshi Nakano in Osaka University, and Professor R. D. Webster in Nanyang Technological University for their valuable contributions.
This article is also available in: Muellen, Feng, Chemistry of Carbon Nanostructures. De Gruyter (2016), isbn 978-3-11-028450-8.
Sun Z, Wu J. Closed-shell and open-shell 2D nanographenes, in Polyarenes I: topics in current chemistry. Siegel JS, Wu YT, editors. Springer-Verlag Berlin Heidelberg, 2014:197–248. Google Scholar
Morita Y, Nishida S. Phenalenyls, cyclopentadienyls, and other carbon-centered radicals, in Stable radicals: fundamentals and applied aspects of odd-electron compounds. Hicks RG, editor. Germany, 2010:81–145. Google Scholar
(a) Abe M. Diradicals. Chem Rev 2013;113:7011–88. (b) Sun Z, Wu J. Open-shell polycyclic aromatic hydrocarbons. J Mater Chem 2012;22:4151–60. (c) Sun Z, Ye Q, Chi C, Wu J. Low bandgap polycyclic hydrocarbons: from closed-shell near infrared dyes and semiconductors to open-shell radicals. Chem Soc Rev 2012;41:7857–89. (d) Sun Z, Zeng Z, Wu J. Benzenoid polycyclic hydrocarbons with an open-shell biradical ground state. Chem Asian J 2013;8:2894–904. (e) Sun Z, Zeng Z, Wu J. Zethrenes, extended p-QDMs, and periacenes with a singlet biradical ground state. Acc Chem Res 2014; 47:2582–91. (f) Kubo T. Phenalenyl-based open-shell polycyclic aromatic hydrocarbons. Chem Rec 2015;15:218–32. (g) Kubo T. Recent progress in quinoidal singlet biradical molecules. Chem Lett 2015;44:111–122. (h) Das S, Wu J. Open-shell benzenoid polycyclic hydrocarbons, in: Polycyclic arenes and heteroarenes: synthesis, properties, and applications. Qian M, editor. John Wiley & Sons Inc., 2015:1–36. PubMedCrossrefGoogle ScholarGoogle ScholarGoogle ScholarGoogle ScholarGoogle ScholarGoogle ScholarGoogle ScholarGoogle Scholar
Nakano M. Excitation energies and properties of open-shell singlet molecules: applications to a new class of molecules for nonlinear optics and singlet fission, Springer International Publishing, 2014. DOI: . CrossrefGoogle Scholar
(a) Senn P. A simple quantum mechanical model that illustrates the Jahn–Teller effect. J Chem Educ 1992;69:819. (b) Zeng Z, Shi X, Chi C, López Navarrete JT, Casado J, Wu J. Pro-aromatic and anti-aromatic π-conjugated molecules: an irresistible wish to be diradicals. Chem Soc Rev 2015;44:6578–96. CrossrefGoogle ScholarGoogle Scholar
Takahashi T, Matsuoka K, Takimiya K, Otsubo T, Aso Y. Extensive Quinoidal oligothiophenes with dicyanomethylene groups at terminal positions as highly amphoteric redox molecules. J Am Chem Soc 2005;127:8928. CrossrefPubMedGoogle Scholar
Bendikov M, Duong HM, Starkey K, Houk KN, Carter EA, Wudl F. Oligoacenes: theoretical prediction of open-shell singlet diradical ground states. J Am Chem Soc 2004;126:7416–17. PubMedCrossrefGoogle Scholar
(a) Yamaguchi K. Self-consistent field: theory and applications. Carbo R, Klobukowski M, editors. Amsterdam: Elsevier, 1990:727–823. (b) Yamanaka S. Okumura M, Nakano M, Yamaguchi K. J Mol Struct: THEOCHEM 1994;310:205–218. Google ScholarGoogle Scholar
(a) Kolc J, Michl J. Photochemical synthesis of matrix-isolated pleiadene. J Am Chem Soc 1970;92:4147–8. (b) Kolc J, Michl J. π,π-Biradicaloid hydrocarbons. Pleiadene family. I. Photochemical preparation from cyclobutene precursors. J Am Chem Soc 1973;95:7391–401. CrossrefGoogle ScholarGoogle Scholar
Miyoshi H, Nobusue S, Shimizu A, Hisaki I, Miyatab M, Tobe Y. Benz[c]indeno[2,1-a]fluorene: a 2,3- naphthoquinodimethane incorporated into an indenofluorene frame. Chem Sci 2014;5:163. CrossrefGoogle Scholar
Inoue J. Fukui K, Kubo T, et al. The first detection of a Clar’s hydrocarbon, 2,6,10-tri-tert-butyltriangulene: a ground-state triplet of non-Kekulé polynuclear benzenoid hydrocarbon. J Am Chem Soc 2001;123:12702–03. PubMedCrossrefGoogle Scholar
Li Y, Huang KW, Sun Z, et al. A kinetically blocked 1,14:11,12-dibenzopentacene: a persistent triplet diradical of a non-Kekule polycyclic benzenoid hydrocarbon. Chem Sci 2014;5:1908–14. CrossrefGoogle Scholar
(a) Chase DT, Rose BD, McClintock SP, Zakharov LN, Haley MM. Indeno[1,2-b]fluorenes: fully conjugated antiaromatic analogues of acenes. Angew Chem Int Ed 2011;50:1127. (b) Chase DT, Fix AG, Rose BD et al. Electron-accepting 6,12-diethynylindeno[1,2-b]fluorenes: synthesis, crystal structures, and photophysical properties. Angew Chem Int Ed 2011;50:11103 (c) Chase DT, Fix AG, Kang SJ et al. 6,12-Diarylindeno[1,2-b]fluorenes: syntheses, photophysics, and ambipolar OFETs. J Am Chem Soc 2012;134:10349. (d) Nishida J, Tsukaguchi S, Yamashita Y. Synthesis, crystal structures, and properties of 6,12-diaryl-substituted indeno[1,2-b]fluorenes. Chem Eur J 2012;18:8964. CrossrefGoogle ScholarGoogle ScholarGoogle ScholarGoogle Scholar
(a) Hartzler HD. Synthesis and decomposition of 3-diazo-6-dicyanomethylene-1,4-cyclohexadiene. Arylmalononitriles. J Am Chem Soc 1964;86:2174–5. (b) Addison AW, Dalal NS, Hoyano Y, Huizinga S, Weiler L. The chemistry of anions derived from tetracyanodiphenoquinodimethane (TCNDQ). Can J Chem 1977;55:4191–9. CrossrefGoogle ScholarGoogle Scholar
West R, Jorgenson JA, Stearley KL, Calabrese JC. Synthesis, structure and semiconductivity of a p-terphenoquinone. J Chem Soc Chem Commun 1991:1234. Google Scholar
Rebmann A, Zhou J, Schuler P, Stegmann HB, Rieker A. Synthesis, EPR spectroscopy and voltammetry of a p-quaterphenyl biradical/Quinone. J Chem Res Synop 1996;318. Google Scholar
Rebmann A, Zhou J, Schuler P, Rieker A, Stegmann HB. Synthesis of two novel para-extended bisaroxyls and characterization of their triplet spin states. J Chem Soc Perkin Trans 1997;2:1615. Google Scholar
Zhu X, Tsuji H, Nakabayashi K, Ohkoshi S, Nakamura E. Air- and heat-stable planar tri-p-quinodimethane with distinct biradical characteristics. J Am Chem Soc 2011;133:16342–5. CrossrefPubMedGoogle Scholar
Sbargoud K, Mamada M, Marrot J, Tokito S, Yassar A, Frigoli M. Diindeno[1,2-b:20,10-n]perylene: a closed shell related Chichibabin’s hydrocarbon, the synthesis, molecular packing, electronic and charge transport properties. Chem Sci 2015;6:3402. CrossrefGoogle Scholar
Zeng Z, Ishida M, Zafra, JL, et al. Pushing extended p-quinodimethanes to the limit: stable tetracyano-oligo(N-annulated perylene)quinodimethanes with tunable ground states. J Am Chem Soc 2013;135:6363–71. CrossrefPubMedGoogle Scholar
Zeng Z, Lee S, Zafra JL, et al. Tetracyanoquaterrylene and tetracyanohexarylenequinodimethanes with tunable ground states and strong near-infrared absorption. Angew Chem Int Ed 2013;52:8561–5. CrossrefGoogle Scholar
Zeng, Z, Lee S, Zafra JL, et al. Turning on the biradical state of tetracyano-perylene and quaterrylenequinodimethanes by incorporation of additional thiophene rings. Chem Sci 2014;5:3072–80. CrossrefGoogle Scholar
Zeng, Z, Lee S, Son M, et al. Push–pull type oligo(N-annulated perylene)quinodimethanes: chain length and solvent-dependent ground states and physical properties. J Am Chem Soc 2015;137:8572–83. CrossrefPubMedGoogle Scholar
Zeng Z, Sung YM, Bao N, et al. Stable tetrabenzo-chichibabin’s hydrocarbons: tunable ground state and unusual transition between their closed-shell and open-shell resonance forms. J Am Chem Soc 2012;134:14513–25. CrossrefPubMedGoogle Scholar
(a) Yao JH, Chi C, Wu J, Loh KP. Bisanthracene bis(dicarboxylic imide)s as soluble and stable NIR dyes. Chem Eur J 2009;15:9299–302. (b) Li J, Zhang K, Zhang X, Chi C, Wu J. meso-Substituted bisanthenes as soluble and stable near-infrared dyes. J Org Chem 2010;75:856–63. (c) Zhang K, Huang K, Li J, Chi C, Wu J. A soluble and stable quinoidal bisanthene with NIR absorption and amphoteric redox behavior. Org Lett 2009;11:4854–7. (d) Hirao Y, Konishi A, Matsumoto K, Kurata H, Kubo T. Synthesis and electronic structure of bisanthene: a small molecular-sized graphene with zigzag edges. AIP Conf Proc 2012;1504:863–6. CrossrefGoogle ScholarGoogle ScholarGoogle ScholarGoogle Scholar
Konishi A, Hirao Y, Nakano M, et al. Synthesis and characterization of teranthene: A singlet biradical polycyclic aromatic hydrocarbon having kekule structures. J Am Chem Soc 2010;132:11021–3. CrossrefPubMedGoogle Scholar
Konishi A, Hirao Y, Matsumoto K, et al. Synthesis and characterization of quarteranthene: elucidating the characteristics of the edge state of graphene nanoribbons at the molecular level. J Am Chem Soc 2013;135:1430–7. CrossrefPubMedGoogle Scholar
Liu J, Ravat P, Wagner M, Baumgarten M, Feng X, Müllen K. Tetrabenzo[a,f,j,o]perylene: a polycyclic aromatic hydrocarbon with an open-shell singlet biradical ground state. Angew Chem Int Ed 2015. DOI: . CrossrefGoogle Scholar
Matsumoto A, Suzuki M, Kuzuhara D, Hayashi H, Aratani N, Yamada H. Tetrabenzoperipentacene: stable five-electron donating ability and a discrete triple-layered β-graphite form in the solid state. Angew Chem Int Ed 2015;127:8293–6. CrossrefGoogle Scholar
Matsumoto A, Suzuki M, Kuzuhara D, et al. A kinetically protected pyrene: molecular design, bright blue emission in the crystalline state and aromaticity relocation in its dicationic species. Chem Commun 2014;50:10956–8. CrossrefGoogle Scholar
Goto K, Kubo T, Yamamoto K, et al. A stable neutral hydrocarbon radical: synthesis, crystal structure, and physical properties of 2,5,8-tri-tert-butylphenalenyl. J Am Chem Soc 1999;121:1619–20. CrossrefGoogle Scholar
Mota F, Miller JS, Novoa JJ. Comparative analysis of the multicenter, long bond in [TCNE]- and phenalenyl radical dimers: a unified description of multicenter, long bonds. J Am Chem Soc 2009;131:7699–707. PubMedCrossrefGoogle Scholar
Suzuki S, Morita Y, Fukui K, et al. Aromaticity on the pancake-bonded dimer of neutral phenalenyl radical as studied by MS and NMR spectroscopies and NICS Analysis. J Am Chem Soc 2006;128:2530–1. PubMedCrossrefGoogle Scholar
(a) Kubo T, Yamamoto K, Nakasuji K, Takui T, Murata I. Hexa-tert-butyltribenzodecacyclenyl: a six-stage amphoteric redox system. Angew Chem Int Ed 1996;35:439. (b) Kubo T, Yamamoto K, Nakasuji K, Takui T, Murata I. 4,7,11,14,18,21-hexa-t-butyltribenzodecacyclenyl radical: a six-stage amphoteric redox system. Bull Chem Soc Jpn 2001;74:1999. CrossrefGoogle ScholarGoogle Scholar
Beer L, Mandal SK, Reed RW, et al. The first electronically stabilized phenalenyl radical: effect of substituents on solution chemistry and solid-state structure. Cryst Growth Des 2007;7:802–9. CrossrefGoogle Scholar
Morita Y, Aoki T, Fukui K, et al. A new trend in phenalenyl chemistry: a persistent neutral radical, 2,5,8-tri-tert-butyl-1,3-diazaphenalenyl, and the excited triplet state of the gable syn-dimer in the crystal of column motif. Angew Chem Int Ed 2002;41:1973–6. Google Scholar
Ueda A, Wasa H, Suzuki S, et al. Chiral stable phenalenyl radical: synthesis, electronic-spin structure, and optical properties of helicene-structured diazaphenalenyl. Angew Chem Int Ed 2012;51:6691–5. CrossrefGoogle Scholar
Nakasuji K, Yoshida K, Murata I. Design and synthesis of a highly amphoteric condensed hydrocarbon with the highest reduction potential. Pentaleno[1,2,3-cd:4,5,6-c’d’]diphenalene. J Am Chem Soc 1983;105:5136–7. CrossrefGoogle Scholar
Kubo T, Shimizu A, Sakamoto M, et al. Synthesis, intermolecular interaction, and semiconductive behavior of a delocalized singlet biradical hydrocarbon. Angew Chem Int Ed 2005;44:6564–8. CrossrefGoogle Scholar
Shimizu A, Hirao Y, Matsumoto K et al. Aromaticity and π-bond covalency: prominent intermolecular covalent bonding interaction of a Kekule hydrocarbon with very significant singlet biradical character. Chem Commun 2012;48:5629. CrossrefGoogle Scholar
Kubo T, Sakamoto M, Akabane M, et al. Four-stage amphoteric redox properties and biradicaloid character of tetra-tert-butyldicyclopenta[b;d]thieno[1,2,3-cd;5,6,7-c′d′]diphenalene. Angew Chem Int Ed 2004;43:6474–9. CrossrefGoogle Scholar
Umeda R, Hibi D, Miki K, Tobe Y. Tetradehydrodinaphthoannulene: a hitherto unknown dehydroannulene and a viable precursor to stable zethrene derivatives. Org Lett 2009;11:4104–6. CrossrefGoogle Scholar
Das S, Lee S, Son M, et al. para-Quinodimethane-bridged perylene dimers and pericondensed quaterrylenes: the effect of the fusion mode on the ground states and physical properties. Chem -Eur J. 2014;20:11410–20. CrossrefGoogle Scholar
Sun Z, Lee S, Park K, et al. Dibenzoheptazethrene isomers with different biradical characters: an exercise of Clar’s aromatic sextet rule in singlet biradicaloids. J Am Chem Soc 2013;135:18229–36. PubMedCrossrefGoogle Scholar
(a) Smith MB, Michl J. Singlet Fission. Chem Rev 2010, 110, 6891–6936. (b) Minami T, Nakano M. Diradical character view of singlet fission. J Phys Chem Lett 2012;3:145–50. PubMedCrossrefGoogle ScholarGoogle Scholar
(a) Chikamatsu M, Mikami T, Chisaka J, Yoshida Y, Azumi R, Yase K. Ambipolar organic field-effect transistors based on a low bandgap semiconductor with balanced hole and electron mobilities. Appl Phys Lett 2007;91:043506/1–/3. (b) Koike H, Chikamatsu M, Azumi R et al. Stable Delocalized Singlet Biradical Hydrocarbon for Organic Field-Effect Transistors. Adv Funct Mater 2016;26:277–83. Google ScholarGoogle Scholar
Koike H, Kubo T, Uchida K et al. Direct observation of energy band development in a one-dimensional biradical molecular chain by ultraviolet photoemission spectroscopy. Appl Phys Lett 2013;102:134103/1–/4. CrossrefGoogle Scholar