Supporting Information for

Transcription

1 Supporting Information for Carbon-Bridged Phenylene-Vinylenes: On the Common Diradicaloid Origin of Their Photonic and Chemical Properties Rafael C. González-Cano, a Simone di Motta, b Xiaozhang Zhu, c, Juan. T. López Navarrete, a Hayato Tsui, c,d Eiichi Nakamura, c, Fabrizia Negri, b Juan Casado a a Department of Physical Chemistry, University of Málaga, Campus de Teatinos s/n, Málaga 29071, Spain. b Università di Bologna, Dipartimento di Chimica G. Ciamician, Via F. Selmi, 2, Bologna, Italy and INSTM, UdR Bologna, Italy. c Department of Chemistry, School of Science, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo , Japan. d Department of Chemistry, Faculty of Science, Kanagawa University, 2946 Tsuchiya, Hiratsuka ; Japan. S1

2 Computational details DFT and TDDFT. DFT calculations were carried out by means of the Gaussian 09 program[1]. Simulations of the monomers were performed in the gas-phase to obtain the equilibrium structures and the electronic properties of the ground electronic state (S 0 ), and first excited triplet states (T 1 ). The B3LYP[2,3] functional and the 6-31G**[4,5] basis set were used in all calculations. To simulate the open-shell ground-state structures by DFT we used the broken-symmetry option with the key guess = mix keyword and the unrestricted wavefunctions at the (U)B3LYP level. The unrestricted methodologies were also used for the triplet states. The time-dependent DFT (TD-DFT) approach[6,7] was used to obtain the relevant excited states transitions (i.e., energies and oscillator strengths) and for the optimization of the lowest excited singlet states. All the calculations were carried out in vacuo. For the dimer calculations, the UM05-2X functional[8] and the standard 6-31G** basis set were used. The unrestricted M05-2X functional was chosen on account of its ability to describe π π interactions and estimate the energies of weak intermolecular interactions.[9] Vertical electronic excitation energies of the dimers were calculated by using the time-dependent DFT approach at the UM05-2X/6-31G** level. CASSCF and CASPT2 calculations: Equilibrium structures of ground and double exciton states (see Figures S2-S7) were obtained from quantum-chemical calculations carried out at state average (SA)- CASSCF/6-31G** level of theory[10] on models of QM1CN and QM2CN featuring hydrogens instead of the Ar and Ph substituents shown in Scheme 2. CAS energies were corrected with single state - single reference (SS-SR)-CASPT2 second-order perturbation calculations.[11] State-averaged calculations were carried out using the same weight for the lowest three singlet states in geometry optimization calculations of ground and double exciton states. The active space comprised generally 12 electrons in 12 π orbitals (12,12). For QM1CN geometries were obtained also with a CAS restricted to 8 electrons in 8 π orbitals (CAS(8,8)). CASPT2 energy corrections were evaluated for the full space of configurations, and level shifts, required to avoid intruder state problems, of 0.2 were applied to correct CAS(8,8) and CAS(12,12) energies. The biradical character of the ground state wavefunction of QM1CN and QM2CN was determined as twice the weight of the doubly excited configuration.[12] All the CASSCF and CASPT2 calculations were run with the MolPro suite of programs in vacuo.[13] Additional details on the simulation of Franck-Condon (FC) structure associated with the electronic transition to the doubleexciton state can be found in the following section. S2

3 Details on the simulated spectra at DFT and CASSCF level. The vibronic structure associated with the absorption and emission spectra of the excitation to the double exciton state were obtained by employing the S 0 -S 1 geometry change computed at CASSCF level while the set of normal coordinates and frequencies corresponded to those computed at B3LYP/6-31G** level. The use of DFT normal coordinates instead of CASSCF was dictated by the generally better quality of the former modes. Similarly the absorption to the single exciton state were obtained by employing the S 0 -S 1 geometry change computed at B3LYP/TD-B3LYP/6-31G** level. The Franck Condon (FC) vibronic structure[14,15] associated with electronic transitions was evaluated along the lines described in previous work[16]. The B i displacement parameters representing the proection of the geometry change upon excitation on vibrational normal coordinates were determined. Assuming the harmonic approximation, negligible Duschinsky effect and identical frequencies in the K and J states, the FC intensity of a band corresponding to the n=[n 1,n 2,n 3,...n N ] vibrational quantum in the excited state is given by I K S ( S ) 0, Jn 0 n = e (1) n! where ( ) S i = B i are the Huang-Rhys factors. 2 n The vibrational coordinates and frequencies of the ground state displaying the largest S values in the S 0 double exciton and S 0 single exciton transition are collected in Figures S2-S3. In plotting computed electronic spectra, a Lorentzian linewidth of the order of 0.1 ev was superimposed to each computed intensity to facilitate the comparison with experimental spectra. References [1] M. J. Frisch, G. W. Trucks, H. B. Schlegel et al., GAUSSIAN 09, Revision C.01, Gaussian, Inc., Wallingford, CT, [2]C. T. Lee, W. T. Yang, and R. G. Parr, Phys. Rev. B 37, 785 (1988). [3]A. D. Becke, J. Chem. Phys. 98, 5648 (1993). [4] W. J. Hehre, R. Ditchfie, and J. A. Pople, J. Chem. Phys. 56, 2257 (1972). [5] M. M. Francl, W. J. Pietro, W. J. Hehre, J. S. Binkley, M. S. Gordon, D. J. Defrees, and J. A. Pople, J. Chem. Phys. 77, 3654 (1982). [6] E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984). [7] H. H. Heinze, A. Gorling, and N. Rosch, J. Chem. Phys. 113, 2088 (2000). [8] Y. Zhao, N.E. Schultz, and D.G. Truhlar, J. Chem. Phys. 123, (2005). S3

4 [9] Y. Zhao, and D.G. Truhlar, J. Chem. Theory Comp. 3, 289 (2006). [10] Werner, H.-J.; Knowles, P. J. J. Chem. Phys. 1985, 82, [11] Celani, P.; Werner, H.-J. J. Chem. Phys. 2000, 112, [12] Kamada, K.; Ohta, K.; Shimizu, A.; Kubo, T.; Kishi, R.; Takahashi, H.; Botek, E.; Champagne, B.; Nakano, M. J. Phys. Chem. Lett. 2010, 1, [13] MOLPRO, version , a package of ab initio programs, H.-J.Werner, P. J. Knowles, R. Lindh, F. R. Manby, M. Schutz, P. Celani, T. Korona, A. Mitrushenkov, G. Rauhut, T. B. Adler, R. D. Amos, A. Bernhardsson, A. Berning, D. L. Cooper, M. J. O. Deegan, A. J. Dobbyn, F. Eckert, E. Goll, C. Hampel, G. Hetzer, T. Hrenar, G. Knizia, C. Koeppl, Y. Liu, A. W. Lloyd, R. A. Mata, A. J. May, S. J. McNicholas, W. Meyer, M. E. Mura, A. Nicklass, P. Palmieri, K. Pfluger, R. Pitzer, M. Reiher, U. Schumann, H. Stoll, A. J. Stone, R. Tarroni, T. Thorsteinsson, M.Wang, and A. Wolf,, see [14] Santoro, F.; Improta, R.; Lami, A.; Bloino, J.; Barone, V J. Chem. Phys. 2007, 126, [15] Dierksen, M.; Grimme, S. J. Chem. Phys. 2004, 120, [16] Di Donato, E.; Vanzo, D.; Semeraro, M.; Credi, A.; Negri, F. J. Phys. Chem. A 2009, 113, S4

5 Table S1. Comparison between CASPT2 corrected S 0 S 1 excitation energies (ev) and observed weak features in the absorption spectra. Computed Exp (dichloromethane) QM1CN 1.59 a 1.63 QM2CN 1.17 b 1.13 a Obtained with CASSCF(8,8)/6-31G** optimized geometries. b Obtained with CASSCF(12,12)//CASPT2/6-31G** corrected geometries. The (12,12) CAS space for QM2CN is comparable with the (8,8) CAS space of the smaller QM1CN molecule. Table S2. QM2CN: Computed CASSCF(12,12)/6-31G** and CASPT2 corrected energies for the S 0 and S 1 states as a function of the displacement along the S 0 -S 1 geometry difference, a displacement which closely matches the normal mode displacement dominated by the out of phase CC stretching. The biradicaloid character of the ground state wavefunction is also indicated. Displacement a S 0 -CAS S 1 -CAS % Biradicaloid S 0 CASPT2 S 1 CASPT2 character of S a 0.0 corresponds to the equilibrium geometry of S 0 at CASSCF level, while 1.0 corresponds to the equilibrium structure of S 1 at CASSCF level. S5

6 wavenumber / cm -1 Figure S1. Comparison of the B3LYP/6-31G** theoretical Raman spectrum of QM1CN with the experimental one of Figure 2. S6

7 Figure S2. B3LYP/6-31G** normal coordinates and frequencies (unscaled) associated with the largest computed FC activity (S parameter) in the S 0 S 1 (black) and S 0 S 2 (red) absorption spectrum of QM1CN. The vibrational frequency and the associated S i value are indicated for each normal mode. S7

8 Figure S3. B3LYP/6-31G** normal coordinates and frequencies (unscaled) associated with the largest computed FC activity (S parameter) in the S 0 S 1 (black) and S 0 S 2 (red) absorption spectrum of QM2CN. The vibrational frequency and the associated S i value are indicated for each normal mode. S8

9 Figure S4. Comparison between the ground state equilibrium structures of QM1CN computed at (black) CASSCF(12,12)/6-31G**, (red) CASSCF(8,8)/6-31G**, (blue) B3LYP/6-31G** levels. Bond numbering is shown at the bottom. S9

10 Figure S5. Comparison between the ground state equilibrium structures of TPQ computed at (black) CASSCF(12,12)/6-31G**, (green) B3LYP/6-31G** and (blue) UB3LYP-BS/6-31G** levels. S10

11 Figure S6. QM2CN: bond length changes upon excitation to the double exciton S 1 state from CASSCF(12,12)/6-31G** calculations (black); upon moving from the ground-state quinoid Closed Shell to the biradicaloid Open Shell structure, B3LYP/6-31G** level (red). The bond length changes overlap closely with the displacements (green) of the Raman active out-of-phase CC stretching mode (B3LYP/6-31G** level, computed frequency 1337 cm -1 ). S11

12 Figure S7. Linear fitting of the equilibrium constant from the monomer to the σ-dimer with the temperature according to Van t Hoff equation. S12

13 Figure S8. 1 H NMR spectrum within the aromatic 1 H area (6 9 ppm) of a saturated solution of QM1CN in deuterated methylcyclohexane at 300 K (top left) and 190 K (top right) in comparison with the theoretical prediction of 1 H chemical shifts at B3LYP/6-311+G** level. The structures used were the quinoid monomer (bottom left) and the aromatic σ-dimer (bottom right). The calculated signals are marked with their corresponding hydrogen, while the hydrogen of the lateral groups (Ph and Ar) are coloured in grey. S13