Singlet biradicaloids are certainly one of the most frequently discussed topics at ISNA-15. In this review our own work on the synthesis, molecular structures, and physical properties relevant to biradical character of indenofluorene isomers are described. These include indeno[2,1-a]fluorene with an o-quinodimethane substructure, benz[c]indeno[2,1-a]fluorene which is the first 2,3-naphthoquinodimethane derivative isolated, and indeno[2,1-b]fluorene with an m-quinodimethane (m-xylylene) subunit. The observed physical properties are explained in terms of the theoretically derived biradical factors (y), HOMO-LUMO energy gaps, and singlet-triplet energy gaps in the ground state electronic configurations. In addition, we discuss here two perspectives in the biradicaloid chemistry, (i) two- and three-dimensional indenofluorene congeners arranged in a macrocyclic form and (ii) macrocyclic indenofluorenes having multiple radical characters.
The chemistry of polycyclic aromatic hydrocarbons (PAHs) has long history since the late 19th century when artificial dyes were synthesized and manufactured. It has once a climax in the 1950s through 70s in conjunction with the development of theoretical aspects of aromaticity. Numerous aromatic compounds including benzenoid PAHs and annulenes were synthesized during this period. Once again, it has been attracting tremendous interest during the last few decades because aromatic compounds have been recognized to have potential applications to organic electronic materials such as field effect transistors (FETs), organic light emitting diodes (OLEDs), and organic photo voltaics (OPVs) . This resurgence is supported by the concurrent advancement in synthetic methods, analytical tools, and theoretical understanding. Among the numerous polycyclic structures that emerged in recent years, singlet biradialoids constitute a unique class of compounds due to their potentially open-shell characters which endow them with characteristic physical properties such as small HOMO-LUMO gaps and nonlinear optical responses. In every ISNA symposium, there are focused themes of the time, and the chemistry of biradicaloids was apparently the timely theme at ISNA-15 as indicated by at least six oral presentations related to this topic delivered in the symposium.
Most of the biradicaloid molecules are characterized by the presence of quinodimethane substructures of three types, p-quinodimethane (p-QDM), o-quinodimethane (o-QDM), or m-quinodimethane (m-QDM, or better described as m-xylylene), of which the non-Kekulé open-shell canonical resonance structure indicates the presence of biradical character in the ground state electronic configuration as shown in Scheme 1. Some prototypical p-QDM type biradicaloid compounds such as Thiele’s hydrocarbon  and Chichibabin’s hydrocarbon  have been known since the early 20th century. Moreover, highly reactive o-QDM derivative such as pleiadene (Fig. 1)  was already shown to have a singlet ground state with a low-lying partly doubly excited state more than four decades ago. Nevertheless recent studies on the synthesis of stabilized QDM derivatives and investigations on their physical properties widen remarkably the view of biradicaloid chemistry. More specifically, by extending the conjugation length or embedding the QDM structure to PAH frameworks biradical characters were modified or amplified with purpose. Another structural motif of biradicaloids is the zig-zag edge structure found in polyacenes. In 2004, Bendikov and co-workers reported, based on theoretical study, the increase of biradical characters with increasing number of six-membered ring in acenes . This work was followed by synthetic and theoretical investigations of biradicaloids possessing various molecular structures, such as diphenalenoindacene  and zethrene , including their higher congeners, and anthenes  to name a few (Fig. 1), leading to the today’s intense research activity in biradicaloid chemistry .
Indenofluorenes belong to a class of biradicaloid compounds comprising of fully conjugated array of 6-5-6-5-6-membered rings, similar to pentacene which has linearly fused five six-membered rings . However, because of the presence of the five-membered rings, indenofluorenes have the following characteristics: (i) Five structural isomers are possible depending on the fusion pattern at the central six-membered ring and at the five-membered ring as shown in Fig. 2. These are indeno[1,2-a]fluorene (1), indeno[1,2-b]fluorene (2a), indeno[2,1-a]fluorene (3a), indeno[2,1-b]fluorene (4a), and indeno[1,2-c]fluorene (5a). (ii) Because of the presence of five-membered rings, they belong to non-alternant hydrocarbons and therefore may exhibit unique optical properties arising from the unsymmetrical distribution between each HOMO and LUMO.
Since 1 and 4a have an m-QDM substructure, 2a and 5a a p-QDM substructure, and 3a an o-QDM substructure, the electronic and optical properties of the indenofluorene isomers should be different from each other. Though none of the parent compounds are known, derivatives of 2a, 3a, 4a, and 5a are known. Only 1 is unknown even in a form of a derivative most probably because it is expected to have triplet ground state unlike others which are singlet in the ground states. For the p-QDM congeners, an air-sensitive tetraiodo derivative of indeno[1,2-b]fluorene (2a) was reported by Swager for the first time . Recently, stable derivatives such as 2b and 2c were synthesized and their properties were intensively studied by Haley  and Yamashita  independently with respect to their charge carrier mobility due to the relatively low bad gap. Similarly, derivatives such as 5b, which is expected to serve as electron accepting materials, of p-QDM congener 5a were reported by the group led by Haley . For the o-QDM congener 3a, while diphenyl derivative 3c was reported by Le Berre in 1957, its structure and physical properties were not investigated at that time when the modern analytical instruments were not available . Recently, we prepared stable dimesityl derivative 3b and investigated its molecularar structure and optical and electrochemical properties . In addition, highly air sensitive benzo homolog, benz[c]indeno[2,1-a]fluorene 6b with a half-life of only 77 min under air at room temperature, was isolated and its structure and unusual reactivity owing to the biradical character elucidated . Moreover, dimesityl derivative 4b of m-QDM congener 4a was synthesized and its structure and extraordinary optical property were unveiled . In this article, we review the results from our laboratories regarding indenofluorenes 3b and 6b both having an o-QDM substructure and 4b with an m-QDM unit and then discuss about some personal prospects in this field.
Compared to p-QDM congeners such as those listed in Figs. 1 and 2, synthesis and physical organic studies of o-QDMs have been much less done owing to their inherent high reactivity and the s-cis geometry of the exocyclic diene moiety which renders steric protection difficult. The scarce examples of o-QDMs include tetraphenyl derivative 7  and pleiadene , which have been detected in rigid glass matrices at low temperature, and a series of tetraaryl o-QDMs incorporated into a phenanthrene framework such as 8 , which were successfully isolated (Fig. 3). Though Le Berre reported the synthesis of 11,12-diphenylindenofluorene 3c, its molecular structure and detailed electronic structure have not been investigated . We initiated our research in the indenofluorene field inspired by an accidental finding of a dimeric product 14, which is most likely formed via an intermediate 13 having an indenofluorene backbone, obtained by treatment of octadehydrotribenz  annulene (12) with n-butyllithium (Scheme 2) . This finding prompted us to investigate molecular and electronic structure of stabilized dimesityl derivative of indeno[2,1-a]fluorene 3b as described below .
We noticed that 6a having additional benzene ring fused to 3a contained a 2,3-naphthoquinodimethane (NQDM) substructure. NQDM was known to be even more reactive than o-QDM and has never been isolated previously despite many attempts. The parent NQDM 9 and its bridged derivative 10 were only spectroscopically characterized in glass matrices at low temperatures (Fig. 3) . Sterically protected NQDM derivatives such as 11 were reported by Jones and co-workers to be persistent at room temperature for UV-vis measurement and were trapped by a dienophile . However, they were not isolated due to facile air oxidation. Given the stabilization effect observed in 3b, which was due to electronic and steric effects exerted by the indenofluorene framework and the mesityl groups, respectively, we thought it might be possible to isolate a 2,3-naphthoquinodimethane derivative such as 6b having an indenofluorene framework. This turned out indeed the case .
Though it has been well known that the triplet ground state of m-QDM (m-xylylene) itself lies well below the singlet ,the stabilization of the singlet state of indeno[2,1-b]fluorene (4a) relative to the triplet by full conjugation into the indenofluorene framework is expected. Indeed theoretical calculations suggest that the singlet state of 4a is more stable than the triplet by 10.3 kJ mol−1 as described below. Not only the small singlet-triplet (S-T) energy gap but also a large biradical character, a small HOMO-LUMO energy gap, and a small overlap between the HOMO-LUMO distributions suggest that 4a would be the most unique compound in the indenofluorene series. These considerations prompted us to synthesize and investigate mesityl derivative 4b as an intriguing object.
Compound 3b was synthesized as a purple solid through a modified method reported previously  as shown in Scheme 3. In contrast to 3c, it was found to be very stable in solid state and even in solution under ambient conditions.
X-ray crystallographic analysis showed that there are two crystallographically independent molecules (Molecule A and Molecule B). Except for the torsion angles of the s-cis diene moiety (1.7 ° for Molecule A, and 15.2 ° for Molecule B), there is little difference between the two molecules. The indenofluorene framework of 3b is almost planar and the two mesityl groups have a large dihedral angle of ca. 70 ° to the backbone. The mean bond lengths of the indenofluorene core are listed in Table 1 together with those of the known o-QDM 8  and 6b discussed in the next section. The structure of 3b shows a significant bond length alternation in the o-QDM unit: bonds a and c (1.391(2) and 1.359(3) Å, respectively) are short and thus have substantial double bond characters, whereas bonds b, d, and e (1.480(2), 1.431(3), and 1.454(2) Å, respectively) are longer than bonds a and c. However, bond a in 3b is significantly longer than a regular C(sp2)−C(sp2) double bond (1.349 Å) and that of the previously isolated o-QDM 8 (1.346(6) Å) , indicating the existence of biradical character in 3b (Scheme 4). Singlet biradical character (y) of 3a and o-QDM was calculated by the natural orbital occupation number (NOON) of LUMO with spin-unrestricted calculation . The broken-symmetry UHF/6-31G(d) calculations of 3a and o-QDM gave LUMO occupation numbers of 0.61 and 0.50, respectively. Using the Yamaguchi scheme , the indices for singlet biradical character of 3a and o-QDM were estimated to be 0.33 and 0.21, respectively. The spin density of 3a exhibits the largest distribution at the five-membered ring carbons as shown in Scheme 4, consistent with the resonance structures.
aBond positions are shown in Fig. 2. bMean value. cReference .
Theoretical calculations of 3a indicate a relatively small HOMO-LUMO gap of 2.25 eV. In accord with this, 3b showed low-energy absorption bands at 730 and 537 nm, from which the optical HOMO-LUMO energy gap of 3b was estimated to be ca. 1.70 eV. Form the cyclic voltammogram of 3b, which exhibited two reversible redox waves (Eox = +0.59 V, Ered = −1.51 V (V vs Fc/Fc+); Eredox = 2.10 V), the electrochemical HOMO-LUMO gap was estimated to be 2.10 eV. Calculations also indicate weak anti-aromaticity of 3a: the NICS(1) values at the central benzene and the five membered rings are +2.12 and +4.28, respectively. In the 1H NMR spectrum of 3b, the chemical shifts of the indenofluorene core appeared at higher magnetic field than those of dihydroindenofluorene derivatives such as the precursor diol of 3b (Scheme 3), consistent with the NICS calculations. The S-T energy gap of 3b was estimated to be 56.7 kJ mol–1 at the B3LYP/6-31G(d) level. The NMR spectra did not exhibit line broadening when heated up to 75 °C, a phenomena due to occupation of thermally excited triplet state as observed for compounds with large biradical characters [6, 7j, 8, 18], indicating that this system is best described as a closed-shell singlet species.
Compound 6b was synthesized in 8% yield as dark blue crystals by a method similar to that of the preparation of 3b as shown in Scheme 5. In contrast to 3b, however, 6b was found to be very sensitive to air. Its half-life in the dark, which was determined from the pseudo-first order decrease of the UV-vis absorption in CH2Cl2, was only 77 min. The product of the air oxidation was determined to be endoperoxide 16 whose structure was confirmed by X-ray crystallography (Fig. 4). Despite such sensitivity, pure samples of 6b were obtained by recrystallization under an inert atmosphere. This represents the first example of a NQDM derivative isolated and fully characterized.
Theoretical calculations (geometry optimized by the UB3LYP/6-31G(d) level of theory) for 6a indicate that it has larger singlet biradical character (y = 0.63) and smaller HOMO-LUMO energy gap (1.66 eV) and S-T energy gap (31.2 kJ mol–1) compared to 3a. X-ray crystallographic analysis of 6b show that though the s-cis diene moiety of 6b is slightly distorted similar to Molecule B of 3b, the indenofluorene framework of 6b is almost planar. The bond lengths of the benzindenofluorene core indicate larger biradical character of 6b compared to that of 3b (Table 1). Namely, the bond distance of the exo-methylene bond a (1.403(2) Å) of 6b is longer than that of 3b (1.391(2) Å) as is for bond c (1.398(2) vs. 1.359(3) Å). On the other hand, bond b is shorter than that of 3b (1.468(2) vs. 1.480(2) Å). Another notable feature is the bond length alternation in the outer naphthalene ring of 6b in which bonds f (1.441(2) Å) and h (1.419(2) Å) are relatively long whereas bond g is short (1.363(3) Å). The observed bond length alternation is comparable to that of the bicyclo [2.1.1] pentene-fused naphthalene derivative which exhibits a remarkable bond alternation .
In accord with the theoretical calculations, 6b exhibited longer wavelength absorption compared to 3b with a maximum at 697 nm which extends to NIR region (ca. 1050 nm) in CH2Cl2. Similarly, in cyclic voltammetry, 6b showed Eredox of 1.60 V which was smaller than that of 3b (2.10 V), with reduction waves at –1.22 and –1.61 V and oxidation waves at +0.38, +0.77, and ca. +1.1 V (irreversible). Moreover, in the 1H NMR spectra, 6b exhibited reversible line broadening at high temperature (100 °C) due to occupation of thermally excited triplet state, being consistent with the calculated small S-T gap. All these features indicate that 6a is regarded as an open-shell singlet species.
One of the most intriguing observations for 6b was its unusual reactivity toward cycloaddition. As described above, a dioxygen molecule added to the inner naphthalene positions to give endoperoxide 16, despite the fact that the largest spin density and HOMO distribution are located at the exo-methylene carbons as shown in Scheme 6. This is due to effective steric protection of the exo-methylene carbons by the mesityl groups and the next largest location of spin density and HOMO distribution at the inner naphthalene carbons. Similarly, addition of dichlorodicyano-p-benzoquinone took place at the inner naphthalene carbons to give adduct 17 (Fig. 4). These results are different from those of indenofluorene 3c which was reported to react with dioxygen and maleic anhydride at the exo-methylene carbons, though the structures of the products were not concretely established . Moreover, heating 6b in toluene-d8 in a sealed tube at 80 °C resulted in the formation of [4+2] dimer 18 in quantitative yield (Fig. 4). X-ray crystallographic analysis showed that in 18 the new bonds were formed at the inner naphthalene (a 4π component) and the outer naphthalene carbons (a 2π component), as a consequence of the strong bond length alternation in the outer naphthalene ring of 6b. These results indicate that the resonance hybrid of 6a should include a canonical structure with radical centres located at the inner naphthalene carbons as described in Scheme 6.
Indeno[2,1-b]fluorene (4a) is expected to have a larger singlet biradical character than its isomers due to the m-QDM subunit. Indeed, the biradical character of 4a (y = 0.68) estimated by the Yamaguchi scheme is larger than that of 3a (y = 0.33).The spin density distribution for 4a shows that the five-membered ring carbons have the largest amplitudes (Scheme 7). These results indicate that 4a should be described as a resonance hybrid of the Kekulé and non-Kekulé biradical structures (Scheme 7).
We synthesized 4b which was obtained as a green solid in two steps as shown in Scheme 8. X-ray crystal structural analysis of 4b showed that the lengths for bonds a (1.437 Å) and b (1.431 Å) 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). This observation indicates that 4b has a substantial contribution of the singlet biradical canonical structure to the ground-state electronic configuration.
Theoretical calculations (geometry optimized by the UB3LYP/6-31G(d) level of theory) for 4a indicate that it has not only large singlet biradical character but also a HOMO-LUMO energy gap (1.23 eV) which is smaller than those of typical closed-shell hydrocarbons and a small S-T energy gap (10.3 kJ mol–1). In accord with these estimates, 4b showed in cyclic voltammetry Eredox of 1.26 V which was smaller than those of 3b (2.10 V) and 6b (1.60 V), with reduction waves at –1.13 and –2.03 V and oxidation waves at +0.13 and +0.90 V. Moreover, in the 1H NMR spectrum, 4b did not show signal at 30 °C because of occupation of the thermally excited triplet state. By cooling down to –93 °C, broad signals due to the aromatic protons appeared at 5.6–6.9 ppm. Moreover, a triplet species for 4b was observed by ESR spectroscopy, and the intensity of the ESR signal decreased with decreasing the temperature, indicating a singlet ground state in 4b. The singlet−triplet energy gap was experimentally estimated to be −17.6 kJ mol−1 using temperature-dependent magnetic susceptibility measurements, which is reasonable for the S-T energy gap theoretically estimated for 4a. The stabilization of the singlet state of 4b relative to the triplet by the indenofluorene framework should be contrasted to m-xylylene whose triplet ground state lies well below the singlet .
The most striking physical property of 4b was the existence of an unexpectedly low-energy light absorption despite its small conjugation space consisting of only 20 π electrons. The absorption spectrum for 4b in CH2Cl2 showed a strong absorption band at 638 nm and a weak absorption band at 850−2000 nm (Fig. 5). TD-DFT calculations [TD-UB3LYP/6-31G(d)] predict S0−S1 absorption at 1232 nm for 4a with a low oscillator strength (f = 0.018), being consistent with the experimental results. These results strongly suggest that the near-infrared band with a lowest-energy maximum at 1700 nm is from S0−S1 absorption in 4b. Theoretical investigations revealed that moderate amplitude of biradical character of 4b is critical for the extraordinary low-energy light absorption [M. Nakano, R. Kishi. private communication]. To demonstrate this theoretically, we compared the lowest-energy transitions of 4a with that of a hypothetical indenofluorene congener 19 having larger biradical characters (y = 0.79) and larger π conjugation spaces (Fig. 5) by TD-DFT calculations. As a result, the theoretical transition for 19 occurs at 985 nm, ca. 250 nm shorter than that of 4a. These results led us to conclude that a molecule with a smaller π conjugation space exhibits a lower-energy light absorption if it has a moderate biradical character.
As extension of the indenofluorene chemistry, we discuss here the following two systems as prospective objects: (i) indenofluorene congeners and their isomers arranged in a macrocyclic form with two five-membered rings. In this type of molecules, the two constituting biradicaloid componenets would either coordinate or conflict; (ii) indenofluorene congeners arranged in a macrocyclic form with more than two five-membered rings. This type of molecules have multiple radical characters.
Insertion of a fused benzene or a naphthalene ring to indeno[2,1-c]fluorene (5a) generates circulene-like two-dimensional macrocyclic structures 20 and 22 with a six- or a seven-membered ring in the center, respectively (Scheme 9). Additionally, their constitutional isomers 21 and 23 are generated by swapping the positions of one of five- and six-membered rings in 20 and 22, respectively.
First, we analyzed the spin distributions and electronic properties by drawing canonical structures of the hypothetical fragments constituting 20–23 on paper (Scheme 9). For example, we regard 20 as a hybrid of p-QDM and 3,6-dimethylenephenanthrene (24) sharing the methane carbons in the five-membered ring. For both componenets closed-shell Kekulé structures can be drawn, indicating both substructures have comparable stability. Consequently, the spin density may delocalize throughout the macrocyclic backbone. On the other hand, circulene analogs 22 is regarded as a hybrid of p-QDM and 2,11-dimethylenebenzo[c]phenanthrene (25). For the latter fragment only non-Kekulé structure can be drawn like m-QDM (m-xylylene). In such case, we expect the spin density will be localized on the p-QDM substructure to avoid an open-shell structure and therefore the electronic property may not be significantly different from that of p-QDM. Similarly, since another  circulene analog 23 can be regarded as a hybrid of open-shell 2,7-dimethylenenaphthalene (26) and closed-shell 24, the spin density must be localized on the latter part. Interestingly, since the last macrocycle 21 is constituted by two open-shell fragments 26, the spin density should be delocalized to the entire framework.
Theoretical calculations (geometries optimized by the B3LYP/6-31G(d) level of theory) predict the biradical characters, HOMO-LUMO energy gaps, and S-T energy gaps are different from each other as shown in Table 2. All parameters suggest 22 is most stable followed by 20 as predicted by the fragment analysis described above. The large biradical character and small S-T gap of 21 are attributed to the open-shell character of its fragment 26, whereas similar characteristics of 23 may be due to the open-shell character inherent in closed-shell 24. Spin density distributions shown in Fig. 6 are also different from each other. However, they qualitatively agree the predictions based on the fragment analysis. Namely, for 20 and 21 in which either two closed-shell structure or two open-shell structures coordinate, the spin distribute to the entire macrocyclic framework. Conversely, for 22 and 23 in which open- and closed-shell structures conflict, the spin distribution is localized to the closed-shell fragment.
|Compound||Biradical character (y)||HOMO-LUMO gap, eV||S-T gap,b kJ mol−1|
aGeometries optimized by the B3LYP/6-31G(d) level of theory. bCalculated by the UB3LYP/6-31G(d) level.
Moreover, the geometry optimization revealed that  circulene analogs 20 and 21 adopt non-planar geometries whereas  circulene analogs 22 and 23 are planar. Since bowl-shaped compounds such as corannulene  and sumanene  are known to exhibit interesting properties due to the three-dimensional molecular shape , bowl-shaped biradicaloids 20 and 21 may well be expected to show properties due to biradical character which is in conjunction with the three-dimensional geometry and the relevant molecular motions.
Naturally chemists extend the indenofluorene building block 2a to more elaborated structures such as linear quaterradicaloid 27 and sexiradicaloid 28 (Fig. 7). Another way of extension of π conjugation is to make a cycle to form tetracyclopentatetraphenylene (29a). Though Hellwinckel and Reiff reported in 1970 the generation of dicationic species of 29a from its tetrahydro derivative 30 in a mass spectral chamber , neither parent nor its derivative has been isolated. Theoretical calculations predict that it adopts a D4hsymmetric structure and will exhibit quaterradical character [M. Nakano, R. Kishi. private communication]. Because of the inner 8π- and outer 20π-electron circuits, it should exhibit strong anti-aromaticity. Recently we succeeded in the synthesis of tetramesityl derivative 29b and revealed its molecular structure and physical properties as reported at ISNA-15. We believe these results would advance the chemistry of biradicaloid aromatic hydrocarbons to the next step.
The authors are grateful to Professors Masayoshi Nakano and Dr. Ryohei Kishi (Osaka University) for the theoretical work, Professors Takeji Takui, Kazunobu Sato, and Daisuke Shiomi (Osaka City University) for the magnetic measurements, Professor Mikiji Miyata and Dr. Ichiro Hisaki (Osaka University) for their assistance in X-ray crystallography, Professors Takashi Kubo and Shinobu Ito (Osaka University) for electronic absorption spectroscopy, and Professor Benoît Champagne (Facultés Universitaires Notre-Dame de la Paix (FUNDP)) for the use of computers and the program for the theoretical calculations. This work was supported by Grant-in-Aid for scientific research which is gratefully acknowledged.
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