Nanosecond Photochromic Molecular Switching of a. Biphenyl-Bridged Imidazole Dimer Revealed by Wide. Range Transient Absorption Spectroscopy

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1 Electronic Supplementary Material (ESI) for ChemComm. This journal is The Royal Society of Chemistry 2014 Supporting Information for: Nanosecond Photochromic Molecular Switching of a Biphenyl-Bridged Imidazole Dimer Revealed by Wide Range Transient Absorption Spectroscopy Tetsuo Yamaguchi, a Michiel F. Hilbers, b Paul P. Reinders, b Yoichi Kobayashi, a Albert M. Brouwer, b and Jiro Abe *a,c a Department of Chemistry, School of Science and Engineering, Aoyama Gakuin University, Fuchinobe, Chuo-ku, Sagamihara, Kanagawa , Japan b University of Amsterdam, van t Hoff Institute for Molecular Sciences, P. O. Box 94157, 1090 GD Amsterdam, The Netherlands c CREST, Japan Science and Technology Agency, K s Gobancho, 7 Gobancho, Chiyoda-ku, Tokyo , Japan CONTENTS 1. UV-vis absorption spectrum S Durability S Nanosecond transient absorption spectra S Femtosecond transient absorption spectra S. 5 a) Two-state sequential model analysis S. 6 b) Three-state sequential model analysis S DFT calculations S Complete reference 25 S References S. 39 S. 1

2 1. UV-vis absorption spectrum The UV-vis absorption spectrum was measured with a Shimadzu UV3150 spectrometer after Ar bubbling over ten minutes. The 1,2 -isomer of imidazole dimers have a small and broad absorption band around nm due to the charge transfer from the 6π-imidazole to 4π-imidazole systems with excitation. On the other hand, because bisdmdpi-bp is the 2,2 -isomer and there is no charge transfer process, no absorption band is observed around 400 nm. Fig. S1 UV-vis absorption spectrum of bisdmdpi-bp in benzene at room temperature. S. 2

3 2. Durability The durability of bisdmdpi-bp was examined by repetitive exposures to ns laser pulses. A Continuum Minilite II Q-switched Nd:YAG laser was used for the excitation laser with the third harmonic at 355 nm (pulse duration, 5 ns; power, 8 mj) and the durability of the sample was analyzed by HPLC system and UV-vis absorption spectrometer. HPLC was carried out on a ODS reversed phase column (Mightysil RP-18 GP, Kanto Chemical Co., Inc.). The HPLC system consists of a pump unit (PU-2080 plus, JASCO), a photodiode array (PDA) detector (MD-2018 plus, JASCO), and a control unit (LC-NetII/ADC, JASCO). UV-vis absorption spectra were measured with a Shimadzu UV3150 spectrometer. Sample solutions were bubbled with argon or oxygen prior to the laser shots. a) b) Fig. S2 UV-vis absorption spectra of bisdmdpi-bp in benzene before and after laser shots (355 nm) under a) Ar ( M) and b) O 2 atmospheres ( M). The blue and red lines show the spectra before and after laser irradiation, respectively. a) b) Fig. S3 HPLC chromatograms of bisdmdpi-bp before 355 nm laser shot (blue line), after laser shots in Ar (red line) and O 2 atmospheres (green line) in benzene. The HPLC analysis was performed using a reverse phase column (eluent, H 2 O/acetonitrile = 1/4; flow rate, 1 ml/min; detected at a) 254 and b) 365 nm. S. 3

4 3. Nanosecond transient absorption spectra Nanosecond transient absorption spectra were measured using an in-house assembled setup. The excitation wavelength of 305 nm was generated using a tunable Nd:YAG-laser system (NT342B, Ekspla) comprising a pump laser (NL300), harmonics generators (SHG, THG) and optical parametric oscillator (OPO). The pulse length is 3-5 ns. The repetition rate of the laser system was 5 Hz. The laser beam homogeneously illuminates the front of a 1 cm quartz cuvette containing the sample solution in an area 1 cm wide and 1 mm high. A high-stability short arc xenon flash lamp (FX-1160, Excelitas Technologies) with a modified PS302 controller (EG&G) running at 10 Hz was used as the probe light. The probe light was split in a signal and a reference beam with a 50/50 beam splitter. The signal beam passed through the sample cell orthogonal to the excitation beam and probed the excited volume immediately behind the front window of the cell in a 1 mm 1 mm area along the 1 cm path length of the illuminated volume. The sample and reference beams were focused onto the entrance slit of a spectrograph (SpectraPro-150, Princeton Instruments) recorded with an intensified CCD camera (PI- MAX3, Princeton Instruments) using a ns gate depending on the time step of the measurements. The time delays of laser, flash lamp and camera were generated by a delay generator (Stanford Research System DG535). The whole set-up is controlled with an in-house written program (LabView) and the data were analyzed with macros implemented in Igor Pro 5.03J (WaveMetrics, Inc.). Fig. S4 Decay profiles of the colored species of bisdmdpi-bp in degassed benzene at room temperature ( M, excitation wavelength: 305 nm, pulse duration: 5 ns, excitation intensity: 1.8 mj). The dots and solid line are experimental data and fittings, respectively. S. 4

5 4. Femtosecond transient absorption spectra S1 Fig. S5 shows a time evolution of the transient absorption spectrum. Color represents ΔAbsorbance. As was seen in the Fig. 3a in the main text, the initial transient absorption spectra at ps are obviously broadened. Two possibilities are conceivable for the broadening: transient absorption from the precursor states of the colored species and/or the vibrational cooling from hot states. Fig. S5 Time-evolution of the chirp corrected transient absorption spectrum of bisdmpi-bp from 0 to 8 ps in benzene at room temperature ( M, excitation wavelength: 305 nm, pulse duration: 200 fs and laser intensity: 1.8 μj). As is described in the main text, the formation process of the colored species after the photoexcitation can be expected as follows: 1) the vibrational relaxation from the Franck-Condon state to the S 1 state, 2) the transition from the S 1 state to the hot state of the colored species, and 3) the vibrational cooling to the ground state of the colored species. In addition to the process 3), the higher excited states of the colored species may also contribute to the generation process of the radicals. All processes are completed within a ps. The time-resolved spectra were analyzed using the TIMP package with the graphical interface program Glotaran, version ( S2 The instrument response function (IRF) was set to 200 fs. We apply the global analyses to reveal the multi-wavelength kinetics of the transient absorption spectra at the ultrafast time scale. We propose two and three-state sequential models and found out that the three-state sequential model satisfactory explained the kinetics of bisdmpi-bp as shown follows: S. 5

6 Fig. S6 Plausible energy relaxation pathway of photochromic reaction of the HABI derivatives reported previously. S2,S3 a) Two-state sequential model analysis S Component 1 Colored species Firstly, the kinetics were fitted with the two-state sequential model with convolution by the IRF. Figs. S7a and b show evolution associated spectra (EAS) and decays of two components. The component 1 has a broad absorption band and it is quickly converted to the colored species. It is assigned to the transient absorption from the precursor state of the colored species, which is most probably the transient absorption from S 1 state and/or the vibrationally hot state of the colored species. The higher excited states of the colored species may also contribute to the component 1. Another component (denoted as blue) is assigned to the colored species of bisdmdpi-bp because of the strong similarity of the spectral shape to that observed in the ns experiments. The time constants of the decay of the component 1 (τ 1 ) and the colored species are estimated to be 760 fs and >50 ps, respectively. Fitted spectra at different delay times and fitted decays probed at different wavelengths are shown in Fig. S8. The gray dots and red solid lines indicate the raw data and fitted spectra, respectively. While the simulated transient absorption spectra obtained from the global analyses qualitatively fit with the data (except the spectrum at 0.3 ps), the simulated transient absorption dynamics obviously cannot reproduce the experimental data at 540, 580, and 590 nm (indicated as black arrows). These results suggest that another rise component is necessary to explain the kinetics of bisdmdpi-bp. S. 6

7 Fig. S7 (a) Evolution associated spectra (EAS) and time profiles of the concentration changes of two components obtained from the global analysis of the two-state sequential model. Fig. S8 (left) Transient absorption spectra and (right) dynamics of bisdmdpi-bp. The red curves represent the simulated spectra and decays obtained by global analysis with the two-state sequential model. S. 7

8 b) Three-state sequential model analysis Ground state Component 1 Component 2 Colored species The two-state sequential model assumes that the precursor of the colored species is described as a single component. However, the two-state sequential model does not reproduce the experimental data well. Next, we assume that the precursor state can be split into two states and we fit the kinetics with the three-state sequential model convoluted by the IRF. Figs. S9a and b show EAS and time profiles of each component. Component 1 has a broad absorption band and it is quickly converted to component 2. The spectrum of component 2 has sharp and broad peaks at ~390 and 550 nm and component 2 decays within 2 ps. By following to the relaxation energy diagram shown in Fig. S6, we assigned component 1 to the transient absorption from the S 1 state. Since the spectrum of component 2 is similar to that of the colored species and the spectrum is somewhat shifted and more broadened, component 2 can be assigned to the hot state of the colored species. The component which generates with decreasing the component 2 is assigned to the colored species of bisdmdpi-bp because of the similarity of the spectral shape. The time constants of the decay of the components 1, 2 (τ 1 and τ 2 ), and colored species are estimated to be 420 fs, 420 fs and >50 ps, respectively. Fitted transient absorption spectra at different delay times and fitted transient absorption dynamics probed at different wavelengths are shown in Fig. S10. The striking difference from the two-state sequential model is that the addition of component 2 satisfactorily reproduces the rise around nm. Fig. S9 (a) Evolution Associated Spectra and time profiles of the concentration changes of three components obtained from the global analysis of the three-state sequential model. The τ 1, τ 2, and colored species are 420 fs, 420 fs and >50 ps, respectively. S. 8

9 Fig. S10 (left) Transient absorption spectra and (right) dynamics of bisdmdpi-bp. The red curves represent the simulated spectra and decays obtained by global analysis with the three-state sequential model. S. 9

10 5. DFT calculations All DFT calculations were carried out using the Gaussian 09 program (revision D.01; reference 25 in the main text). The molecular geometries were fully optimized at the MPW1PW91/6-31G(d) level of the theory for the 2,2 -isomer (the colorless isomer) and the UMPW1PW91/6-31G(d) level for the biradical species (the colored isomer) of bisdmdpi-bp, and analytical second derivatives were computed using the vibrational analysis to confirm each stationary point to be a minimum. Zero-point energy (ZPE) corrections were adopted to compare the relative energies for the isomers. It has been reported that the B3LYP functional gives inaccurate results in the system where the medium-range correlation energy, such as van der Waals attraction, is important. S3), S4) In the DFT calculation for the biradical species of the bridged imidazole dimer systems, the van der Waals interaction between the radical units should be taken into consideration. Thus we applied the MPW1PW91 level of the theory. Table S1. Standard orientation of the optimized geometry for the 2,2 -isomer of bisdmdpi-bp. Center Atomic Atomic Coordinates (Angstroms) Number Number Type X Y Z S. 10

11 S. 11

12 SCF Done: E(RmPW+HF-PW91) = A.U. Zero-point correction = (Hartree/Particle) Thermal correction to Energy = Thermal correction to Enthalpy = Thermal correction to Gibbs Free Energy = Sum of electronic and zero-point Energies = Sum of electronic and thermal Energies = Sum of electronic and thermal Enthalpies = Sum of electronic and thermal Free Energies = Low frequencies Low frequencies Fig. S11 Optimized structure of the 2,2 -isomer of bisdmdpi-bp. The Result of the TDDFT calculation Excited State 1: Singlet-A ev nm f= > This state for optimization and/or second-order correction. Total Energy, E(RPA) = Excited State 2: Singlet-A ev nm f= S. 12

13 175 -> > > Excited State 3: Singlet-A ev nm f= > > > > Excited State 4: Singlet-A ev nm f= > > > Excited State 5: Singlet-A ev nm f= > > Excited State 6: Singlet-A ev nm f= > > > > Excited State 7: Singlet-A ev nm f= > > > > > Excited State 8: Singlet-A ev nm f= > > > S. 13

14 176 -> > > > > > Excited State 9: Singlet-A ev nm f= > > > > > > > > Excited State 10: Singlet-A ev nm f= > > Excited State 11: Singlet-A ev nm f= > Excited State 12: Singlet-A ev nm f= > > > > > > > Excited State 13: Singlet-A ev nm f= > S. 14

15 Excited State 14: Singlet-A ev nm f= > > > > > > Excited State 15: Singlet-A ev nm f= > > Excited State 16: Singlet-A ev nm f= > > > > > > Excited State 17: Singlet-A ev nm f= > > > > > > Excited State 18: Singlet-A ev nm f= > > > > > Excited State 19: Singlet-A ev nm f= S. 15

16 181 -> > > > > > > Excited State 20: Singlet-A ev nm f= > > > > > > > Excited State 21: Singlet-A ev nm f= > > > > > > > > > Excited State 22: Singlet-A ev nm f= > > > > Excited State 23: Singlet-A ev nm f= > S. 16

17 180 -> > Excited State 24: Singlet-A ev nm f= > > > > > > > Excited State 25: Singlet-A ev nm f= > > > Excited State 26: Singlet-A ev nm f= > > > > > > > Excited State 27: Singlet-A ev nm f= > > > > > Excited State 28: Singlet-A ev nm f= > > S. 17

18 171 -> > > > > > > > > Excited State 29: Singlet-A ev nm f= > > > > > > > > Excited State 30: Singlet-A ev nm f= > > > > > > > Excited State 31: Singlet-A ev nm f= > > > > > > S. 18

19 184 -> > > Excited State 32: Singlet-A ev nm f= > > > > > > > > Excited State 33: Singlet-A ev nm f= > > > > > > > > > > > > > > Excited State 34: Singlet-A ev nm f= > > > > > S. 19

20 180 -> > > > Excited State 35: Singlet-A ev nm f= > > > > > > > > Excited State 36: Singlet-A ev nm f= > > > > > > > > > > > Excited State 37: Singlet-A ev nm f= > > > > > > > S. 20

21 183 -> > > Excited State 38: Singlet-A ev nm f= > > > > > > > Excited State 39: Singlet-A ev nm f= > > > > > > > > > Excited State 40: Singlet-A ev nm f= > > > > > > > > > > > S. 21

22 186 -> Table S2. Standard orientation of the optimized geometry for the colored isomer of bisdmdpi-bp. Center Atomic Atomic Coordinates (Angstroms) Number Number Type X Y Z S. 22

23 S. 23

24 SCF Done: E(UmPW1PW91) = A.U. Zero-point correction = (Hartree/Particle) Thermal correction to Energy = Thermal correction to Enthalpy = Thermal correction to Gibbs Free Energy = Sum of electronic and zero-point Energies = Sum of electronic and thermal Energies = Sum of electronic and thermal Enthalpies = Sum of electronic and thermal Free Energies = Low frequencies Low frequencies Fig. S12 Optimized structure of the colored isomer of bisdmdpi-bp. The Result of the TDDFT calculation Excited State 1: A ev nm f= <S**2>= A ->187A B ->187B This state for optimization and/or second-order correction. Total Energy, E(TD-HF/TD-KS) = Excited State 2: A ev nm f= <S**2>= A ->187A B ->187B S. 24

25 Excited State 3: A ev nm f= <S**2>= A ->187A A ->187A A ->187A A ->188A B ->187B B ->187B B ->187B Excited State 4: A ev nm f= <S**2>= A ->187A A ->187A A ->187A B ->187B B ->188B Excited State 5: A ev nm f= <S**2>= A ->187A A ->187A A ->187A B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B Excited State 6: A ev nm f= <S**2>= A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A S. 25

26 182A ->187A A ->187A A ->187A B ->187B B ->187B B ->187B Excited State 7: A ev nm f= <S**2>= A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A B ->187B B ->187B B ->187B B ->189B Excited State 8: A ev nm f= <S**2>= A ->187A A ->187A A ->187A A ->189A B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B Excited State 9: A ev nm f= <S**2>= A ->187A A ->187A A ->187A S. 26

27 184A ->187A A ->187A Excited State 10: A 182B ->187B B ->187B B ->187B B ->187B ev nm f= <S**2>=1.064 Excited State 11: A 184A ->187A B ->187B B ->187B B ->187B B ->187B ev nm f= <S**2>=1.110 Excited State 12: A 178A ->187A A ->187A A ->187A A ->187A A ->187A B ->187B ev nm f= <S**2>=1.098 Excited State 13: A 169B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B ev nm f= <S**2>=1.081 S. 27

28 183B ->187B B ->187B Excited State 14: A 169A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A ev nm f= <S**2>=1.090 Excited State 15: A 172A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A ev nm f= <S**2>=1.077 Excited State 16: A 169B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B ev nm f= <S**2>=1.084 S. 28

29 Excited State 17: A 172B ->187B B ->187B B ->187B ev nm f= <S**2>=1.120 Excited State 18: A 172A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A ev nm f= <S**2>=1.135 Excited State 19: A 182A ->189A A ->189A A ->198A B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->191B B ->187B ev nm f= <S**2>=1.258 Excited State 20: A ev nm f= <S**2>= A ->187A A ->187A A ->187A A ->187A A ->187A S. 29

30 177A ->187A A ->187A A ->187A A ->197A A ->191A B ->189B B ->188B B ->189B B ->198B Excited State 21: A 182A ->189A A ->189A A ->198A B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B ev nm f= <S**2>=1.267 Excited State 22: A 172A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A ev nm f= <S**2>=1.133 Excited State 23: A ev nm f= <S**2>=1.166 S. 30

31 186A ->188A A ->189A B ->187B B ->187B B ->187B B ->187B B ->187B Excited State 24: A 172A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A B ->188B B ->189B ev nm f= <S**2>=1.171 Excited State 25: A 175A ->187A A ->190A A ->187A A ->199A A ->188A B ->187B B ->188B B ->190B B ->189B B ->198B B ->188B ev nm f= <S**2>=1.680 Excited State 26: A 182A ->188A A ->189A A ->198A A ->187A ev nm f= <S**2>=1.691 S. 31

32 186A ->188A B ->187B B ->187B B ->193B B ->190B B ->187B B ->199B B ->188B Excited State 27: A 171A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A A ->189A B ->187B B ->187B B ->187B B ->189B B ->190B ev nm f= <S**2>=1.264 Excited State 28: A 171A ->187A A ->187A A ->187A A ->187A A ->187A A ->189A B ->187B B ->187B B ->187B B ->188B ev nm f= <S**2>=1.204 S. 32

33 186B ->189B Excited State 29: A 169A ->187A A ->187A A ->192A A ->187A A ->187A A ->199A A ->188A A ->189A A ->190A A ->189A A ->190A A ->198A B ->187B B ->192B B ->193B B ->195B B ->187B B ->188B B ->189B B ->190B B ->189B B ->190B B ->198B ev nm f= <S**2>=2.195 Excited State 30: A ev nm f= <S**2>= A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A A ->188A A ->187A S. 33

34 186A ->189A B ->190B Excited State 31: A 169A ->187A A ->187A A ->192A A ->193A A ->187A A ->188A A ->189A A ->190A A ->189A A ->198A B ->187B B ->192B B ->193B B ->195B B ->187B B ->188B B ->189B B ->190B B ->189B B ->198B ev nm f= <S**2>=2.234 Excited State 32: A 186A ->189A B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B ev nm f= <S**2>=1.249 Excited State 33: A ev nm f= <S**2>=1.228 S. 34

35 169A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A A ->190A B ->188B B ->189B Excited State 34: A 174B ->187B B ->187B B ->187B B ->187B ev nm f= <S**2>=1.136 Excited State 35: A 173A ->187A A ->187A A ->187A A ->196A A ->189A A ->191A A ->188A A ->190A A ->189A A ->190A B ->187B B ->187B B ->187B B ->187B B ->197B B ->191B B ->190B B ->189B ev nm f= <S**2>=1.676 S. 35

36 Excited State 36: A 173A ->187A A ->187A A ->187A A ->187A A ->197A A ->191A A ->189A B ->187B B ->187B B ->187B B ->196B B ->197B B ->191B B ->189B B ->190B ev nm f= <S**2>=1.536 Excited State 37: A 171B ->187B B ->187B B ->187B B ->187B B ->187B B ->187B ev nm f= <S**2>=1.074 Excited State 38: A 171A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A A ->187A ev nm f= <S**2>=1.077 Excited State 39: A ev nm f= <S**2>=1.780 S. 36

37 178A ->193A A ->193A A ->191A A ->195A A ->192A B ->192B B ->189B B ->194B B ->188B B ->192B Excited State 40: A 182A ->192A A ->189A A ->194A A ->188A A ->192A B ->193B B ->193B B ->191B B ->195B B ->192B ev nm f= <S**2>=1.792 S. 37

38 MO187A (LUMO) MO187B (LUMO) MO183A MO183B Fig. S13 Relevant molecular orbitals of the colored isomer of bisdmdpi-bp obtained by the UMPW1PW91/6-31G(d) level of the theory. Fig. S14 Transient absorption spectrum (dotted line) and the oscillator strength (vertical lines) obtained by the TDDFT calculations (UMPW1PW91/6-31G(d) //UMPW1PW91/6-31G(d)). S. 38

39 6. Complete reference 25 Gaussian 09, Revision D.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, N. J.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian, Inc., Wallingford CT, References S1) A. Jacquart, R. M. Williams, A. M. Brouwer and E. Ishow, Chem. - Eur. J., 2012, 18, S2) J. J. Snellenburg, S. P. Laptenok, R. Seger, K. M. Mullen, and I. H. M. van Stokkum, J. Stat. Softw., 2012, 49, 1 22.s S3) Y. Zhao and D. G. Truhlar, J. Phys. Chem. A, 2008, 112, S4) Y. Zhao and D. G. Truhlar, Acc. Chem. Res., 2008, 41, S. 39