Supporting Information

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1 Supporting Information Synthesis and Characterization of Quarteranthene: Elucidating the Characteristics of the Edge State of Graphene Nanoribbons at the Molecular Level Akihito Konishi, Yasukazu Hirao, Kouzou Matsumoto, Hiroyuki Kurata, Ryohei, Kishi, Yasuteru Shigeta, Masayoshi Nakano, Kazuya Tokunaga,, Kenji Kamada,, and Takashi Kubo, * Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka, Osaka , Japan Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka , Japan Research Institute for Ubiquitous Energy Devices, National Institute of Advanced Industrial Science and Technology (AIST), AIST Kansai Center, Ikeda, Osaka , Japan Department of Chemistry, Graduate School of Science and Technology, Kwansei Gakuin University, Sanda, Hyogo , Japan Figure S1. Electronic absorption spectrum of 3a in 1,2,4-trichlorobenzene at room temperature. / nm (ε /10 4 M 1 cm 1 ) 1147 (0.087), 917 (1.53), 814 (0.16), 611 (4.44), 591 (2.20), 565 (1.17), 535 (2.49), 508 (3.40), 384 (5.31), 361 (9.08). S 1

2 Figure S2. Packing diagram of 3a. H atoms and lattice solvents are omitted for clarity. Molecule A and B are depicted in green and dark blue, respectively. Figure S3. Cyclic voltammogram of 3a (V vs. Fc/Fc +, in 0.1M nbu 4 NClO 4 /o-dichlorobenzene, scan rate = 100 mv/s, room temperature). The cyclic voltammogram shows four reversible redox waves; E 2 ox = 0.17, E 1 ox = 0.41, E 1 red = 1.47, E 2 red = 1.59 (V vs. Fc/Fc + ). S 2

3 Figure S4. ESR spectra of 3b ( M, g = 2.002) (a) in a fluid toluene solution at room temperature and (b) in a glassy toluene matrix at 140 K. The inset indicates the M s = 2 halffield region. Although broad shoulder beaks indicated by arrows might be derived from triplet species, the intense M s = 1 peak produces ambiguity in peak analysis. (c) Temperature dependency of the signal intensity in the fluid toluene solution. S 3

4 Figure S5. Variable temperature 1 H-NMR spectra of 3b in CD 2 Cl 2. Figure S6. Odd electron density D odd y0 (r) for y 0. Yellow mesh represents the isosurface with the contour value of au. S 4

5 a b Figure S7. Spin density maps of 3 drawn at the contour level of / Å 3. a, Singlet state and b, triplet state are calculated at the UB3LYP/6-31G* level (light blue: up-spin, pink: down-spin). Figure S8. 1 H-NMR spectrum of 10,10'-((Z)-1,1',5,5'-tetrachlorobianthrone-10,10'-diylidene)- bis(2,7-di-tert-butylanthracen-9(10h)-one) (5) S 5

6 Figure S9. 1 H-NMR spectrum of 3,7,16,20-tetra-tert-butyldianthra[9,1-fgv;9,1-qr]bisanthene- 5,18-dione (6) S 6

7 CASSCF and NEVPT2 calculations: The ground and excited state wavefunctions are obtained at the state averaged (SA-)CASSCF(8,8)/6-31G* level of approximation, where three A g (involving the ground 1A g state) and two B 3u states are averaged. The transition dipole moments between the states are evaluated from the CASSCF wavefunctions, while the excitation energies are calculated at the strongly-contracted (SC-)NEVPT2 method. S1 Throughout these calculations, the inner core electrons are taken to be the frozen core. Oscillator strength f is defined from the excitation energy E m and transition dipole moment gm between the ground (g) and mth excited states (in the atomic unit) as f gm = 2 3 E m m gm 2. (s1) Here, we employ the NEVPT2 excitation energy and the CASSCF transition dipole moment to calculate the oscillator strength. All these calculations are performed using the Molpro Version program package. Figure 7 shows the highest occupied natural orbital (HONO) and the lowest unoccupied natural orbital (LUNO) obtained from the ground state density calculated at the SA- CASSCF(8,8)/6-31G* level of approximation. The non-bonding contributions in these natural orbitals appear in the edge regions. The odd electron density associated with the natural orbital f k (r) of occupation number n k is defined as D k odd (r) = min(2 - n k,n k )f k * (r)f k (r), (s2) where min(2 - n k,n k ) = Tr[D k odd (r)]º n k odd can be regarded as the probability for the electron of being unpaired in f k (r) S2,S3. Total odd electron density and odd electron number are calculated from the summation of the contributions from each natural orbital: D odd (r) = å D odd k (r), (s3) k odd n k N odd = å. (s4) k The odd electron density represents the spatial distributions of unpaired electrons. Detailed discussion on the relationship between the diradical character and odd electron density is presented in ref. S3. From the definition, natural orbitals with n k = 0 (unoccupied NOs) or 2 (closed-shell occupied NOs) do not contribute to the odd electron density. In the present CASSCF(8,8) calculations, we obtained eight NOs with the occupation numbers n k 0, 2, as shown in Table S1. We here employ the occupation number ( n LUNO+i ) of the LUNO+i (i = 0, 1,.), which is approximately equal to 2 - n HONO-i [ n HONO-i : occupation number of the HONO-i], as the definition of the diradical character y i, S3 which takes a value ranging from 0 (closed-shell) to 1 (pure diradical). As seen from Table S1, the HONO-LUNO pair (related to diradical character y 0 ) dominantly contributes to the total odd electron density. In case of n HONO-i +n LUNO+i = 2 S 7

8 (which is well satisfied in the present case), the odd electron density D yi expressed as D i odd y odd odd ( r) D ( r) D ( r), (s5) HONO i LUNO i odd (r) for y i can be where y i = ò é ëd odd yi (r) / 2ù û d3 r. S3 Figure S6 shows the distribution of odd electron density [ D odd y0 (r)] for y 0. The topological feature of D odd y0 (r) is similar to that of spin density amplitude, i.e., localized on the both edge regions, at the UB3LYP/6-31G* level of approximation (Figure S7). This indicates that the odd electron density distributions substantiate our experimental results, and that the spin density distributions obtained by the broken symmetry approach is useful for predicting the spatial correlations of unpaired electrons in open-shell singlet states. Table S1. Occupation numbers of HONO-i and LUNO+i (i = 0 3) of quarteranthene obtained from the ground state electron density calculated at the SA-CASSCF(8,8)/6-31G* level of approximation. i n HONO-i n LUNO+i References and Notes: S1. Angeli, C.; Cimiraglia, R.; Evangelisti, S.; Leininger, T.; Malrieu, J.-P. J. Chem. Phys. 2001, 114, S2. Staroverov, V. N.; Davidson, E. R. Chem. Phys. Lett. 2000, 330, S3. Nakano, M.; Fukui, H.; Minami, T.; Yoneda, K.; Shigeta, Y.; Kishi, R.; Champagne, B.; Botek, E.; Kubo, T.; Ohta, K.; Kamada, K. Theor. Chem. Acc. 2011, 130, ; erratum 130, 725. S 8