Investigating the electronic property of edges of graphene has been an important study in terms of understanding the relationship between the electronic structure and the carbon lattice topology . An essential material relevant to this concern is nanographenes, because nanographenes have a high ratio of edges to surface area compared to graphene, and consequently, because its effect on the electronic structure is intrinsically significant. Tanaka et al. demonstrated that zigzag-edged graphene nanoribbons (ZGNRs), but not armchair-edged GNRs, possess edge-localized non-bonding crystal orbitals, by using a tight-binding theoretical calculation , and Fujita et al. clarified a magnetic moment on the zigzag edges by applying the Hubbard model to the edge-localized orbitals . This peculiar electron localization in ZGNRs is referred to as “edge state” [3, 4], and scientists have attempted to observe the edge state by various experimental measurements [5–14]. Especially, scanning tunnelling microscopy and spectroscopy (STM/S) have been purported to provide the good evidence of the edge state around the zigzag edges in GNRs [5, 13, 14].
Recent advances in the preparation of GNRs, including chemical [15–18] and lithographic methods [19, 20], as well as unzipping of carbon nanotubes [21–24], enable investigation of the physical and chemical properties of the edges of GNRs experimentally. On the other hand, the synthesis of perfectly terminated and reliable size-controlled GNRs has been still in high demand, and therefore, the elucidation of the edge state at the molecular level is growing in importance.
Actually, some large polycyclic aromatic hydrocarbons (PAHs) are predicted to have similar edge-localization of frontier orbitals. Stein et al. demonstrated that the HOMO of a zigzag-edged PAH possesses the largest populations in the zigzag edge region . The distribution pattern at the zigzag edge resembles that of long acenes and ZGNRs, which bear non-bonding character.
This paper summarizes our recent studies on the origin of the edge state through the observation of magnetic, optical, and chemical behaviors of anthenes, which are good model systems for investigating the edge state, because they have well-defined two-edge structures; zigzag and armchair edges. Considering spin density distribution (see below), the terminology of the edge state can be translated into singlet biradical character for anthenes. Our interests are to reveal a structure–property relationship of anthenes in terms of singlet biradical character .
All anthenes can be drawn as a resonance hybrid of Kekulé and biradical forms (Scheme 1). In the resonance formula, anthenes are subjected to loss of one double bond when the structure is drawn with a maximum number of Clar sextets . In the biradical form, Clar sextets, the isolated double bonds, and the unpaired electrons have fixed positions, that is, the influence of sextet migration or spin delocalization is limited. Therefore, the discussion of the biradical character can be focused on the energy balance between the formal loss of the double bond and the aromatic sextet formation.
The amplitudes of biradical character (y0) of anthenes were theoretically estimated by using the index defined by Yamaguchi  coupled to the symmetry-broken UBHandHLYP/6-31G* calculation. The y0 is determined from the following equations: y0 = 1 - 2T/(1 + T2), T = (nHOMO – nLUMO)/2, where nHOMO and nLUMO represent natural orbital occupation numbers of HOMO and LUMO, respectively. The calculation shows that the biradical character drastically increases with increasing inner anthracene moieties (n); small (y0 = 12 %, 1), intermediate (59 %, 2), and large (84 %, 3). This is because the difference in the number of the sextet between the Kekulé and biradical forms increases with increasing molecular size; two for 1, three for 2, and four for 3. More sextets in the biradical form results in more dominant contribution of biradical electron configuration to the ground state. Spin density map shown in Fig. 1 indicates that unpaired electrons are more localized on the meso-carbons in larger anthenes.
Syntheses of anthenes
Straightforward stepwise syntheses
Unsubstituted bisanthene 1 was isolated as an air-sensitive crystalline powder [29, 30], and its crystal structure was recently determined by us . Wu  and Scott  prepared meso-substituted derivatives and investigated their physical properties and chemical reactivity. We decided to introduce four tert-butyl groups in order to increase solubility and stability of 1 (Fig. 2). The tert-butyl derivative (1a) was prepared basically according to the reported procedure  and was found to be moderately stable in air under room light (t1/2 = 19 days in a toluene solution at room temperature).
Teranthene 2 and quateranthene 3 were unknown compounds before our isolation. The key steps for the preparations are a partial cyclization with KOH/quinoline and a full cyclization with DDQ/Sc(OTf)3. Scheme 2 shows the synthetic route to the derivatives of 3. The compound 2a was obtained as dark green plates by recrystallization from a CH2Cl2–hexane solution under argon flow . A toluene solution of 2a showed gradual decomposition with a half-life period of 3 days open to air under room light at room temperature. We also succeeded in the isolation of 3a and 3b by careful recrystallization from an o-dichlorobenzene/mesitylene solution in a sealed degassed tube . The half-life of 3a at room temperature was only 15 h when exposed to air under room light.
Direct cyclization of anthracene oligomers
Recently we have established a new method (Scheme 3) that yields anthenes directly from the corresponding anthracene oligomers by improving the Scholl reaction . As opposed to the conventional Scholl reaction, our new approach produced acceptable yields of 1b and 2a through the simultaneous combination of all three components [DDQ, Sc(OTf)3, and Brønsted acids]. Although the mechanistic details of the reaction have not been clarified yet, strong Brønsted acids may promote protonation of the anthracene ring and electron transfer to DDQ, and arenium-type cations may be generated as intermediate species .
Quateranthene 3a can also be generated directly from quateranthryl using this synthetic method. The matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) mass spectra of the reaction mixture confirmed the formation of 3a. However, 3a could not be isolated in pure form, because the decomposition of 3a proceeded rapidly during quenching and purifying operations.
The length of the C–C bond, indicated by a in Scheme 1, is well correlated to the biradical character. The bond length should decrease with increasing the biradical character because the bond a has single and double bond character in the Kekulé and biradical forms, respectively. The bond lengths of anthenes were determined from the X-ray crystal structure of 1a, 2a, and 3a (Fig. 3). The bond length of bisanthene 1a is 1.451(2) Å, which is the same as the ordinary C(sp2)–C(sp2) single bond length (1.45 Å). Thus, 1a has negligible biradical character in the ground state. On the other hand, teranthene 2a and quateranthene 3a show quite short bond lengths, indicating appreciable biradical character.
The resonance formula in Scheme 1 also suggests that the peripheral six-membered rings bear larger benzenoid character in larger anthenes. The harmonic oscillator model of aromaticity (HOMA) [39, 40] value is known to be a good aromaticity index based on a ring geometry. The HOMA values of the corner rings of 2a (0.854) and 3a (0.823) are quite large compared to 1a (0.704), supporting the significant biradical character for 2a and 3a.
The aromatic stabilization energy of benzene based on the homodesmic stabilization energy is ca. 90 kJ/mol [41, 42], whereas the destabilization energy due to C–C π-bond cleavage is ca. 270 kJ/mol . For bisanthene 1, the destabilization energy of the π-bond cleavage is not fully compensated by the formation of aromatic sextets because the additional sextets in the biradical form are only two, thus the Kekulé form has dominant contribution to the ground state. Teranthene 2 has three more sextets in the biradical form, and therefore, the destabilization energy (270 kJ/mol) is canceled with the aromatic stabilization energy (90 × 3 = 270 kJ/mol). The aromatic stabilization energy of quateranthene 3 (90 × 4 = 360 kJ/mol) exceeds the destabilization energy, indicating the dominant contribution of the biradical form to the ground state.
Considering these geometrical findings, the edge state would come from that the formation of aromatic sextets overwhelms the penalty for breaking one π-bond and that the resulting unpaired electrons are pushed out to the zigzag edges, especially to the meso-positions, as shown in Scheme 1.
Kekulé singlet biradical molecules always encounter the difficulty in how their spin structures can be elucidated, because all π-electrons in the molecules are covalently paired to form the singlet ground state. Intrinsically, they are inactive for an ESR measurement that is the most powerful method for elucidating the spin structure of radical species. Instead, the presence of thermally accessible triplet species would be a good criterion for the singlet biradical ground state.
Bisanthene 1a gave sharp 1H NMR signals even at +110 °C, indicating a negligible influence of the triplet species due to a large singlet–triplet energy gap (ΔES–T). The ΔES–T of 1 was estimated to be 6300 K at the B3LYP/6-31G* level of calculation. The CD2Cl2 solution of teranthene 2a showed no 1H NMR signals from the teranthene core at room temperature, whereas upon cooling, progressive line sharpening was observed (Fig. 4). This behavior can be explained by the presence of thermally excited triplet species at elevated temperatures. The influence of the thermally excited triplet species is more distinct in the 1H NMR spectra of quateranthene. Even at -92 °C, 3b gave no 1H NMR signals in the aromatic region, which suggests that 3b possesses the large population of the thermally excited triplet species even at low temperatures, due to a smaller ΔES–T.
The small ΔES–T of 2a and 3b were confirmed by SQUID measurements. The measurements showed ΔES–T of 1920 K and 347 K for 2a and 3b, respectively. Generally, the ΔES–T of closed-shell compounds exceeds 10 000 K. These substantially small ΔES–T, that is, very weak coupling of electrons, strongly support the edge localization of unpaired electrons in 2a and 3b.
Singlet biradicals feature the presence of a low-lying excited singlet state dominated by the doubly excited configuration . As shown in Fig. 5, teranthene 2a and quateranthene 3b afford a weak low-energy band centered at 1054 and 1147 nm, respectively, whereas non-magnetic 1a gives an intense band at 686 nm whose profile is quite similar to that of non-magnetic rylenes . The weak bands observed in 2a and 3b are assignable to a HOMO → LUMO double excitation by a strongly contracted second-order n-electron valence state perturbation theory (NEVPT2) calculation that allows multielectron excitation . The NEVPT2(8,8)/6-31G* calculation revealed that the first excited singlet states (S1) of 2 and 3 is a 2Ag state dominated by the double excitation with a transition energy of 1.35 (916 nm) and 1.32 eV (940 nm), respectively. The transition to the 2Ag state is intrinsically a one-photon-forbidden process due to the parity (g–g transition), whereas a two-photon-allowed process. We measured a two-photon absorption spectrum of 3b in CS2 and could observe a broad band at around 2300 nm, which is the same excitation energy as that of the one-photon band at 1147 nm. The appearance of the forbidden bands in the one-photon absorption spectra is due to the intensity borrowing from intense HOMO → LUMO single-electron transitions at 878 nm (2a, ε = 97 800) and 917 nm (3b, ε = ~15 000). Thus, the weak bands observed in 2a and 3b are associated with the simultaneous excitation of the edge-localized electrons.
Most singlet biradicals show high reactivity to oxygen, and as described above, 2a and 3a,b are also the case. MALDI-TOF mass measurements of 2a and 3a,b accompany molecular ion peaks of oxidized species in addition to the parent ion peak. Fortunately, we could determine the structure of an oxidized species of 3a, whose single crystals were obtained by allowing the toluene solution of 3a to stand in air under a dark condition at 3 °C for several days. X-ray crystallographic analysis of the single crystal revealed that oxygen molecules bridge neighboring 3a molecules to form a one-dimensional peroxide chain (Fig. 6). The oxygen molecule attacks a less-protected carbon atom with a large spin density around the zigzag edge, presumably via a radical mechanism. After the oxygen attack, zigzag-edges of 3a disappear, and instead, a more stable PAH skeleton that is completely surrounded by armchair edges is generated.
2a and 3a,b are kinetically stabilized by the protection of the meso-positions with bulky aryl substituent groups. It is notable that a non-mesityl derivative of 2a shows instant decomposition even in a sealed degassed tube. The MALDI-TOF mass spectrum of the decomposed products suggests the generation of polymeric compounds, which would be derived from the σ-bond formations at the meso-positions.
We demonstrate that peri-condensations of anthracene lead to the appearance of magnetic spins on zigzag edges, which is closely related to the edge state of ZGNRs. The studies on bisanthene 1 and teranthene 2 revealed that bisanthene 1 can be categorized as a non-magnetic species, whereas teranthene 2 lies at the onset of the magnetic state. More distinct behaviors are observed in quateranthene 3, whose physical and chemical properties are well explained by the edge localization of the unpaired electrons. Aromatic sextet formation is a key mechanism of the magnetic state, and this classical and simple mechanism would indeed determine the electronic structure of nanographenes.
This work was supported in part by the Grant-in-Aid for Scientific Research on Innovative Areas “Reaction Integration” (No. 2105) from the Ministry of Education, Culture, Sports, Science and Technology of Japan and by the ALCA Program of the Japan Science and Technology Agency (JST).
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