Ab Initio Trajectory Surface-Hopping Study on Ultrafast Deactivation

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Ab Initio Trajectory Surface-Hopping Study on Ultrafast Deactivation Process of Thiophene Ganglong Cui† and Weihai Fang* Chemistry College, Beijing Normal University, Beijing 100875, People's Republic of China ABSTRACT: The ultrafast S1(1ππ*) f S0 deactivation process of thiophene in the gas phase has been simulated with the complete active space self-consistent field (CASSCF) based fewest switch surface hopping method. It was found that most of the calculated trajectories (∼80%) decay to the ground state (S0) with an averaged time constant of 65 ( 5 fs. This is in good agreement with the experimental value of about 80 fs. Two conical intersections were determined to be responsible for the ultrafast S1(1ππ*) f S0 internal conversion process. After thiophene is excited to the S1(1ππ*) state in the Franck Condon region, it quickly relaxes to the minimum of the S1(1ππ*) state, then overcomes a small barrier near the conical intersection (CI(1ππ*/1πσ*)), and eventually arrives at the minimum of one C S bond fission (S1(1πσ*)). In the vicinity of this minimum, the conical intersection (CI(1πσ*/S0)) funnels the electron population to the ground state (S0), completing the ultrafast S1(1ππ*) f S0 internal conversion process. This decay mechanism matches well with previous experimental and theoretical studies.

I. INTRODUCTION Thiophene (C4H4S), also known as thiofuran, is a fivemembered heterocyclic molecule that contains four carbon atoms and one sulfur atom in the ring, as shown in Figure 1. It is considered to be aromatic because the electron pairs on sulfur are significantly delocalized in the conjugated π system.1,2 This electron delocalization has thiophene and thiophene-based materials and polymers exhibiting peculiar electronic and optical properties.3 9 The ultraviolet photochemistry of thiophene has been the subject of many previous studies, experimentally including the ultraviolet absorption spectrum in the gas phase,10 13 the magnetic circular dichroism spectrum in solution,14,15 the electron-energy loss spectrum,16 18 excited-state dynamics,13,19 and the resonance Raman spectrum,20 and theoretically including the absorption spectrum prediction in the Franck Condon region with complete active space self-consistent field with second order perturbation (CASPT2) and density functional theory/multireference configuration interaction (DFT/MRCI) methods,13,21 25 ultrafast internal conversion, and photodissociation dynamics.19,25,26 The photodissociation dynamics of thiophene in the S1(1ππ*) state was recently examined by Marian and co-workers using femtosecond pump probe photoelectron spectroscopy, followed by the DFT/MRCI calculations.19,25 Two radiationless deactivation mechanisms were detected, involving transient singlet and triplet states, which were used to explain the ultrafast decay of the initially populated first excited singlet state of thiophene. The first mechanism involves the ring opening of thiophene. It proceeds from the S1(1ππ*) minimum in the Franck Condon region over a shallow saddle near one conical intersection (CI(1ππ*/1πσ*)) to another S1(1πσ*) minimum with one r 2011 American Chemical Society

broken C S bond. Near this minimum, one conical intersection (CI(1πσ*/S0)) funnels the electronic population from the S1(1πσ*) to S0 states, completing the radiationless decay of the S1 thiophene. A similar nonradiative pathway to the S0 state also exists, which involves the first electronic triplet state as a consequence of the intersystem crossing of S1(1ππ*) f T1(3ππ*). Very recently, Wu et al. reported a combined resonance Raman spectroscopy and CASSCF computation on the excited state dynamics of thiophene. On the basis of the CASSCF-calculated structures, relative energies, and vibrational frequencies, they suggested a favorable decay path via one conical intersection (CI(1ππ*/1πσ*)).20 The previous electronic structure calculations provide a lot of information for understanding the photophysical processes of thiophene.19,20,25 However, such static calculations alone are inefficient to a certain extent because the dynamic information is totally lost. Dynamics simulations are the appropriate tool to resolve such mechanistic decay pathways.27 34 In recent years, nonadiabatic dynamics based on ab initio methods have become available and have been applied to simulations of carbonyl compounds, nucleobases, and related compounds.27,28,30,32 49 Importantly, until now, there have been no nonadiabatic dynamics simulations focusing on thiophene. In the present study, ab initio based surface-hopping simulations are performed on thiophene in order to gain better insight into the deactivation mechanism and the S1 decay times. The paper is divided into several sections: section II briefly presents the simulation details; Received: July 19, 2011 Revised: September 17, 2011 Published: September 19, 2011 11544

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Figure 1. Thiophene molecule studied in this work.

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bond is broken in the decay process, which will be discussed below. Therefore, the active space of the present CASSCF calculation is composed of eight electrons in seven orbitals, denoted as CASSCF(8,7) hereafter. The molecular orbitals in the active space are schematically shown in Figure 2. The cc-pVDZ and 6-31G* basis sets are employed for all calculations in this work. The equally average state weights over the involved two states are used in the state-averaged CASSCF(8,7) calculations. Furthermore, the multistate-multireference CASSCF (MS-MR-CASPT2) method is also employed when needed. The CASSCF and MSMR-CASPT2 calculations are performed with the Gaussian 03 and MOLPRO 2006 packages, respectively.50,51 Molecular dynamics simulations have been performed on the basis of the CASSCF(8,7)/cc-pVDZ calculated energies, gradients, and nonadiabatic coupling vectors. The maximum simulation time is 200 fs for each trajectory with the integration step size of 0.5 fs, since the nonadiabatic transition is an ultrafast process. Trajectories that hop to the S0 state from the S1(1ππ* or 1πσ*) state and stay in the S0 state for more than 5 fs are terminated because here we only focus on the exploration of the ultrafast internal conversion. Some trajectories stop at the initial stages of dynamics simulations as a consequence of convergent problems of the CASSCF(8,7)/cc-pVDZ calculations and are not included in the subsequent analysis. Initial conditions were selected from a distribution of the quantum harmonic oscillator in the specified vibrational state at the S0 state. Coordinates and momenta are sampled according to their probability distributions in a given state of harmonic vibration. Harmonic frequencies and normal modes are imported from electronic structure calculations. The sampling is uncorrelated by using the independent random events for coordinates and momenta, respectively. The details for the method and algorithm can be found in the recent literature.39,49,52,53 A total of 300 trajectories were calculated and they are divided into six groups in accordance with the initial conditions.

III. RESULTS AND DISCUSSION

Figure 2. Molecular orbitals (bottom, three occupied π orbitals; middle, two unoccupied π* orbitals; top, bonding and antibonding σ and σ* orbitals) used in the CASSCF(8,7) active space in this work.

section III is the results and discussion; section IV contains our conclusions.

II. SIMULATION DETAILS The state-averaged CASSCF (SA-CASSCF) method is used to calculate the required energies, gradients, and nonadiabatic coupling vectors of the S0 and S1(1ππ* or 1πσ*) states. Selection of the active space in the CASSCF calculations is crucial. First, two pairs of π electrons (π and π* orbitals) and the lone-pair electrons (n orbital) of the S atom should be included in the active space for describing thiophene in low-lying electronic states. In addition, one pair of σ electrons (σ and σ* orbitals) of one C S bond is also included in the active space, since the C S

Equilibrium Structures and Vertical Excitation Energies. Minimum-energy structures in the S0 and S1 states, referred to as MIN(S0), MIN(S1(1ππ*)), and MIN(S1(1πσ*)), are optimized at the CASSCF(8,7)/6-31G* level.20 The obtained results are shown in Figure 3, along with key bond lengths and atom numbering. The S1 state is of 1ππ* character in the Franck Condon region, and MIN(S1(1ππ*)) has a nonplanar structure (see Table 1). The linear-response TDDFT method with the B3LYP functional was used to optimize MIN(S1(1ππ*)) with C2 symmetry constraint.25 In the present calculations, the S1 stationary structures were optimized without any symmetry constraints, in order to be consistent with the subsequent nonadiabatic dynamics simulations. Since MIN(S1(1ππ*)) originates from the π f π* transition, the C C and C S bonds are significantly elongated in MIN(S1(1ππ*)), compared with those in MIN(S0). It should be pointed out the S1 C5 bond is 0.043 Å longer than the S1 C2 bond in MIN(S1(1ππ*)).20 The CASSCF(8,7)/6-31G* calculation reveals that the σ* orbital has a little contribution to the MIN(S1(1ππ*)) wave function. Actually, MIN(S1(1ππ*)) shows a tendency to MIN(S1(1πσ*)) where the S1 C5 bond is broken. On the basis of the CASSCF(8,7)/6-31G* optimized MIN(S0), the S0 f S1 vertical transition energy is predicted to be 5.74 eV at the MS-MR-CASPT2/cc-pVDZ level. In comparison 11545

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Figure 3. Important structures [from left to right: MIN(S0) (Cs), MIN(S1(1ππ*)) (C1), CI(1ππ*/1πσ*)(Cs), and MIN(S1(1πσ*))(Cs)] optimized by the CASSCF(8,7)/6-31*G method with key bond parameters (Å) (see ref 20 and Table 1 for more details).

Table 1. Some Key Angles and Dihedral Angles for the Optimized Structures with the CASSCF(8,7)/6-31G* Method20 C5 S1 C2 (deg)

S1 C2 C3 (deg)

C3 C4 C5 (deg)

91.4 94.3

111.5 108.2

112.7 113.3

0.0 12.0

0.0 8.4

CI(1ππ*/1πσ*)

90.4

106.5

115.6

0.0

0.0

MIN(S1(1πσ*))

72.0

82.8

130.3

0.0

0.0

MIN(S0) MIN(S1(1ππ*))

Figure 4. Used harmonically vibrational modes in the sampling of the initial conditions of trajectories.

with the experimental value of 5.35.4 eV, the MS-MR-CASPT2// CASSCF calculation provides a reasonable description on the vertical transition. Based on the B3LYP optimized structure, the DFT/MRCI calculation predicts the S0 f S1 vertical transition to be 5.4 eV, which is in excellent agreement with the experimental value.25 In comparison, the CASSCF(8,7)/6-31G* calculation overestimates the excitation energy due to the limited inclusion of the electronic correlation effect. However, the stateaveraged CASSCF(8,7)/6-31G* method can provide a balanced description on topological structures of S0 and S1 potential energy surfaces. Conventional time-dependent density functional theory (TDDFT) usually fails at predicting intersections correctly,54 while multireference methods (such as MS-MR-CASPT2) remain unaffordable for ab initio nonadiabatic dynamics simulations of such medium systems. Considering its acceptable accuracy and efficiency, the CASSCF(8,7) method is selected for exploring the nonadiabatic decay dynamics of the S1(1ππ*) state. Conical Intersection. Near the Franck Condon region, there is an important conical intersection (CI(1ππ*/1πσ*)) that is responsible for the electronic structure change from 1ππ* to 1 πσ* with respect to one C S bond elongation. At the CASSCF(8,7)/6-31G* level, this conical intersection (Cs symmetry) is optimized, as shown in Figure 3. It is predicted to be 0.02 eV

S1 C2 C3 C4 (deg)

S1 C5 C4 C3 (deg)

lower than MIN(S1(1ππ*)) at the CASSCF(8,7)/6-31G* level.20 Because our purpose in this work is studying the nonadiabatic decay dynamics of the S1(1ππ*) state, we thereby recommend interested readers to the recent literature.20,25 Initial Condition Distributions. There are a total of 21 vibrational modes for the C4H4S molecule, and six of them play an important role in the S1(1ππ*) f S0 internal conversion. The other modes have relatively small contributions for the displacements of the heavy atoms and can be considered as spectator modes for the internal conversion. As shown in Figure 4, the six modes are related to the motion of the five heavy atoms and are chosen for generating the initial conditions. The similar setup of the initial condition has been used in recent work.49 In the present work, six groups of trajectories are set up and each group uses one vibrational mode to sample the initial velocities and coordinates. In the setup of the initial conditions, the harmonically vibrational quantum number is used to sample the initial conditions of the system. The distributions corresponding to these six vibrational modes are shown in Figure 5, from which we can observe that the averaged initial kinetic energy (standard error) is around 1.0 eV in each vibrational mode, as shown in Table 2: for example, 0.846 (0.043) eV with VIB3; 0.887 (0.047) eV with VIB6; 0.902 (0.048) eV with VIB7; 0.942 (0.056) eV with VIB8; 0.992 (0.058) eV with VIB16; 1.078 (0.051) eV with VIB17. The maximal kinetic energy approaches 1.8 eV with VIB3, 2.0 eV with VIB6, 2.2 eV with VIB7, 2.2 eV with VIB8, 2.4 eV with VIB16, and 2.2 eV with VIB17, whereas the minimal one is 0.2 eV with VIB3, 0.4 eV with VIB6, 0.2 eV with VIB7, 0.2 eV with VIB8, 0.2 eV with VIB16, and 0.4 eV with VIB17. However, the property of each normal-mode coordinate is different from the others. Finally, one should be reminded that the distribution pattern of initial kinetic energy for each sampling is different even though their mean kinetic energies approach each other. This indicates that the initial velocities and positions of nuclei in a system are well sampled and the sampling is to a certain extent statistical. Nonadiabatic Dynamics Trajectories. As listed in Table 3, for each set of trajectories selected here, trajectory surfacehopping dynamics simulations of 50 trajectories are performed. The numbers of trajectories that eventually survive on the S1(1πσ*) state within 200 fs and decay to the S0 state within 200 fs are summarized in Table 3. It can be found that the percentage of 11546

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Figure 5. Distribution of the initial kinetic energy sampled from the six key harmonically vibrational modes.

Table 2. Mean Initial Kinetic Energy and Standard Error (eV) Corresponding to Different Initial Conditions Sampled from the Six Key Vibrational Modes VIB3

VIB6

VIB7

VIB8

VIB16

VIB17

Ækinetic energyæ

0.846

0.887

0.902

0.942

0.992

1.078

standard error

0.043

0.047

0.048

0.056

0.058

0.051

trajectories that eventually decay to the S0 state is 76% for VIB3, 84% for VIB6, 68% for VIB7, 72% for VIB8, 80% for VIB16, and 72% for VIB17. It is reasonable to expect that more trajectories will funnel to the S0 state if the overall simulation time is beyond 200 fs. Obviously, there is high probability that the ultrafast S1(1ππ*) f S0 internal conversion takes place upon photoexcitation of thiophene to the S1(1ππ*) state. More importantly, the initial conditions sampled from different vibrational modes were observed to have little influence on the percentages of trajectories decaying to the S0 state and their distribution patterns.

Table 3. Number of Total Trajectories Surviving on the S1 State and Decaying to the S0 State within 200 fs VIB3

VIB6

VIB7

VIB8

VIB16

VIB17

trajectories

50

50

50

50

50

50

S1 trajectories S0 trajectories

10 38

4 42

15 34

14 35

7 40

13 36

This could be ascribed to the fact that there is only one pathway deactivating the S1(1ππ*) electron population to the S0 state, which will be discussed below in detail. Estimated Internal Conversion Time. On the basis of the present trajectory surface-hopping dynamics, we calculate the averaged internal conversion time corresponding to the different initial conditions sampled from the six key vibrational modes. The internal conversion time is calculated only using the trajectories decayed to the ground electronic state within 200 fs, as shown in Table 3. It is clear that the initial conditions sampled 11547

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from the vibrational modes have not shown remarkable impacts on the internal conversion time, as illustrated in Table 4. Their internal conversion times are around 65 fs with a standard error of 5 fs. This gives further evidence that there exists only one decay channel for the S1(1ππ) thiophene, as discussed above. The present predicted internal conversion time is also in good agreement with the experimentally measured value of 80 fs.19 Furthermore, we also plot the frequency distribution of the S1(1πσ*) lifetime of trajectories for each sampled initial condition, as shown in Figure 6. For VIB3, the majority of trajectories, about 27 trajectories, decay to the S0 state in the range of 40 80 fs;

about 10 trajectories are still on the S1(1πσ*) state within 200 fs. For VIB6, half of the trajectories decay to the S0 state between

Table 4. Estimated Internal Conversion (IC) Times (fs) Corresponding to Initial Conditions Sampled from Different Harmonically Vibrational Modes VIB3

VIB6

VIB7

VIB8

VIB16

VIB17

samples

38

42

34

36

40

IC time

67.2

69.7

62.6

64.8

62.8

64.1

standard error

6.6

5.5

4.9

4.8

4.2

4.1

36

Figure 7. Illustrative trajectory selected from the simulations that shows the nonadiabatic transition near 55 fs.

Figure 6. S1 lifetime distributions of trajectories for each sampled initial condition simulated within 200 fs. The trajectories in the range 200 220 fs represent those surviving in the S1 state. 11548

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transfers to the S2(1ππ*) state via vibronic coupling; then, the S2(1ππ*) state decays to the T2(3ππ*) via intersystem crossing, which eventually transitions to the T1(3ππ*) state by internal conversion. As intersystem crossing is usually less efficient than internal conversion, this pathway is suggested to be a minor pathway.25 Wu et al. have also proposed another minor decay mechanism that is heavily related to the S2(1ππ*) state in the Franck Condon region, which is out of the scope of this paper: focusing on the S1(1ππ*) deactivation processes.20 Finally, one should note that such a ring-opening deactivation mechanism seems to be a common motif in five-membered heterocycles, e.g., furan, pyrrole, and imidazole.26,55 61

Figure 8. Illustrative internal conversion mechanism suggested by our nonadiabatic dynamics simulations.

40 and 80 fs; few approach 200 fs. For VIB7, more than half the trajectories decay to the S0 state in the range of 40 80 fs; nearly one-third of the trajectories stay on the S1(1πσ*) state after 200 fs. For VIB8, VIB16, and VIB17, the same feature is also observed that more than half the trajectories decay to the ground state in less than 100 fs. Decay Mechanism. Upon inspecting the time evolution of nuclear coordinates for these nonadiabatic trajectories, one common dynamic feature exists. Potential energies of the populated states are plotted in Figure 7 as a function of time for a typical trajectory randomly selected from the simulated trajectories, where structures are also given for a few snapshots. Once the system is excited to the S1(1ππ*) state in the Franck Condon region, it quickly relaxes to the minimum of the S1(1ππ*) state and overcomes a tiny barrier near the conical intersection (CI(1ππ*/1πσ*)). Then, the C S bond fission occurs, leading to a minimum-energy structure (S1(1πσ*)) where the system exhibits a biradical character. Near this minimum, one conical intersection (CI(1πσ*/S0)) exists and funnels the electron population to the S0(1ππ) state, completing the internal conversion process. Photoexcitation of thiophene to the S1 state and the subsequent internal conversion process are summarized in Figure 8 and the overall S1 f S0 internal conversion takes place on a time scale of about 60 fs. The nonadiabatic dynamics simulation reveals that the S1(1ππ*) f S0 internal conversion is an ultrafast process for thiophene. This decay mechanism predicted here is in good agreement with the previous experimental and theoretical studies.19,20,25 A short-time photodissociation dynamics was observed for thiophene in a resonance Raman spectroscopic experiment, which was assigned as the photoinduced C S bond cleavage.20 The two conical intersections (CI(1ππ*/1πσ*) and CI(1πσ*/S0)) have also been determined in previous studies at the CASSCF(8,7)/6-31G* and DFT/MRCI levels.20,25 In addition, other decay pathways could probably be responsible for the ultrafast S1(1ππ*) deactivation.20,25 For example, besides the ring-opening mechanism studied in this work, Marian et al. also suggested the another pathway that the S1(1ππ*) state

IV. CONCLUSIONS By combining the complete active space self-consistent field (CASSCF) method and the fewest switch surface hopping (FSSH) method, hundreds of trajectories are prepared to simulate the ultrafast S1(1ππ*) f S0 internal conversion process of thiophene in the gas phase, based on which the involved decay mechanism is uncovered. This decay mechanism matches well with previous experimental and theoretical studies.19,20,25 In terms of the obtained trajectories decayed to the ground state, we have estimated the decay time of the S1(1ππ*) thiophene: around 65 fs with a standard error of 5 fs, which is consistent with the experimental measured value of 80 fs. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Present Addresses †

Max-Planck-Institut fuer Kohlenforschung, Kaiser-Wilhelm-Platz 1 45470, Muelheim an der Ruhr, Germany.

’ ACKNOWLEDGMENT This work is supported by grants from the NSFC (Grants 20720102038 and 21033002) and from the Major State Basic Research Development Programs (Grant 2011CB808503). W.F. and G.C. also thank Prof. Xuming Zheng at Zhejiang Sci-Tech University for providing the optimized structures. ’ REFERENCES (1) Hartough, H. D. The Chemistry of Heterocyclic Compounds; Wiley-Interscience: New York, 1952; Vol. 3. (2) Gronowitz, S. The Chemistry of Heterocyclic Compounds; WileyInterscience: New York, 1992; Vol. 44. (3) Murphy, A. R.; Frechet, J. M. J. Chem. Rev. 2007, 107, 1066. (4) Chen, J. W.; Cao, Y. Acc. Chem. Res. 2009, 42, 1709. (5) Shuttle, C. G.; Hamilton, R.; O’Regan, B. C.; Nelson, J.; Durrant, J. R. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 16448. (6) Liang, Y. Y.; Yu, L. P. Polym. Rev. 2010, 50, 454. (7) Kim, J. B.; Allen, K.; Oh, S. J.; Lee, S.; Toney, M. F.; Kim, Y. S.; Kagan, C. R.; Nuckolls, C.; Loo, Y. L. Chem. Mater. 2010, 22, 5762. (8) Liang, Y. Y.; Yu, L. P. A Acc. Chem. Res. 2010, 43, 1227. (9) Brusso, J. L.; Lilliedal, M. R.; Holdcroft, S. Polym. Chem. 2011, 2, 175. (10) Lonardo, G. D.; Galloni, G.; Trombetti, A.; Zauli, C. J. Chem. Soc., Faraday Trans. 2 1972, 68, 2009. (11) Bendazzoli, G. L.; Bertinelli, F.; Palmieri, P.; Brillante, A.; Taliani, C. J. Chem. Phys. 1978, 69, 5077. (12) Nyulaszi, L.; Veszpremi, T. J. Mol. Struct. 1986, 140, 253. 11549

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The Journal of Physical Chemistry A (13) Palmer, M. H.; Walker, I. C.; Guest, M. F. Chem. Phys. 1999, 241, 275. (14) Norden, B.; Hakansson, R.; Pedersen, P. B.; Thulstrup, E. W. Chem. Phys. 1978, 33, 355. (15) Igarashi, N.; Tajiri, A.; Hatano, M. Bull. Chem. Soc. Jpn. 1981, 54, 1511. (16) Flicker, W. M.; Mosher, O. A.; Kuppermann, A. J. Chem. Phys. 1976, 64, 1315. (17) Flicker, W. M.; Mosher, O. A.; Kuppermann, A. Chem. Phys. Lett. 1976, 38, 489. (18) Van Veen, E. H. Chem. Phys. Lett. 1976, 41, 535. (19) Weinkauf, R.; Lehr, L.; Schlag, E. W.; Salzmann, S.; Marian, C. M. Phys. Chem. Chem. Phys. 2008, 10, 393. (20) Wu, X. F.; Zheng, X. M.; Wang, H. G.; Zhao, Y. Y.; Guan, X. G.; Phillips, D. L.; Chen, X. B.; Fang, W. H. J. Chem. Phys. 2010, 133, 134507. (21) Serrano-Andres, L.; Merchan, M.; Fulscher, M.; Roos, B. O. Chem. Phys. Lett. 1993, 211, 125. (22) Rubio, M.; Merchan, M.; Orti, E.; Roos, B. O. J. Chem. Phys. 1995, 102, 3580. (23) Rentsch, S.; Yang, J. P.; Paa, W.; Birckner, E.; Schiedt, J.; Weinkauf, R. Phys. Chem. Chem. Phys. 1999, 1, 1707. (24) Haberkern, H.; Asmis, K. R.; Swiderek, P. Phys. Chem. Chem. Phys. 2003, 5, 827. (25) Salzmann, S.; Kleinschmidt, M.; Tatchen, J.; Weinkauf, R.; Marian, C. M. Phys. Chem. Chem. Phys. 2008, 10, 380. (26) Koppel, H.; Gromov, E. V.; Trofimov, A. B. Chem. Phys. 2004, 304, 35. (27) Carloni, P.; Rothlisberger, U.; Parrinello, M. Acc. Chem. Res. 2002, 35, 455. (28) Martinez, T. J. Acc. Chem. Res. 2006, 39, 119. (29) Lan, Z. G.; Frutos, L. M.; Sobolewski, A. L.; Domcke, W. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 12707. (30) Olivucci, M.; Santoro, F. Angew. Chem., Int. Ed. 2008, 47, 6322. (31) Prezhdo, O. V.; Duncant, W. R.; Prezhdo, V. V. Acc. Chem. Res. 2008, 41, 339. (32) Virshup, A. M.; Punwong, C.; Pogorelov, T. V.; Lindquist, B. A.; Ko, C.; Martinez, T. J. J. Phys. Chem. B 2009, 113, 3280. (33) Lan, Z. G.; Fabiano, E.; Thiel, W. Chem. Phys. Chem. 2009, 10, 1225. (34) Groenhof, G.; Boggio-Pasqua, M.; Schafer, L. V.; Robb, M. A. Adv. Quantum Chem. 2010, 59, 181. (35) Barbatti, M.; Aquino, A. J. A.; Szymczak, J. J.; Nachtigallova, D.; Hobza, P.; Lischka, H. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 21453. (36) Sellner, B.; Barbatti, M.; Lischka, H. J. Chem. Phys. 2009, 131, 024312. (37) Sellner, B.; Ruckenbauer, M.; Stambolic, I.; Barbatti, M.; Aquino, A. J. A.; Lischka, H. J. Phys. Chem. A 2010, 114, 8778. (38) Barbatti, M.; Lischka, H. J. Am. Chem. Soc. 2008, 130, 6831. (39) Doltsinis, N. L.; Marx, D. Phys. Rev. Lett. 2002, 88, 166402. (40) Bockmann, M.; Doltsinis, N. L.; Marx, D. Angew. Chem., Int. Ed. 2010, 49, 3382. (41) Nieber, H.; Hellweg, A.; Doltsinis, N. L. J. Am. Chem. Soc. 2010, 132, 1778. (42) Lan, Z. G.; Fabiano, E.; Thiel, W. J. Phys. Chem. B 2009, 113, 3548. (43) Ong, M. T.; Leiding, J.; Tao, H. L.; Virshup, A. M.; Martinez, T. J. J. Am. Chem. Soc. 2009, 131, 6377. (44) Tapavicza, E.; Tavernelli, I.; Rothlisberger, U. Phys. Rev. Lett. 2007, 98, 023001. (45) Tapavicza, E.; Tavernelli, I.; Rothlisberger, U.; Filippi, C.; Casida, M. E. J. Chem. Phys. 2008, 129, 124108. (46) Olivucci, M.; Lami, A.; Santoro, F. Angew. Chem., Int. Ed. 2005, 44, 5118. (47) Fang, Q.; Zhang, F.; Shen, L.; Fang, W. H.; Luo, Y. J. Chem. Phys. 2009, 131, 164306. (48) Cui, G. L.; Ai, Y. J.; Fang, W. H. J. Phys. Chem. A 2010, 114, 730. (49) Cui, G. L.; Fang, W. H. J. Phys. Chem. A 2011, 115, 1547.

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(50) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (51) Werner, H. J.; et al. MOLPRO, version 2006.6, a package of ab initio programs; 2006; see http://www.molpro.net. (52) Barbatti, M.; Granucci, G.; Persico, M.; Ruckenbauer, M.; Vazdar, M.; Eckert-Maksic, M.; Lischka, H. J. Photochem. Photobiol., A 2007, 190, 228. (53) Fabiano, E.; Keal, T. W.; Thiel, W. Chem. Phys. 2008, 349, 334. (54) Levine, B.; Ko, C.; Quenneville, J.; MartInez, T. Mol. Phys. 2006, 104, 1039. (55) Gromov, E.; Trofimov, A.; Vitkovskaya, N.; Schirmer, J.; Koppel, H. J. Chem. Phys. 2003, 119, 737. (56) Vallet, V.; Lan, Z.; Mahapatra, S.; Sobolewski, A.; Domcke, W. Faraday Discuss. 2004, 127, 283. (57) Barbatti, M.; Vazdar, M.; Aquino, A.; Eckert-Maksic, M.; Lischka, H. J. Chem. Phys. 2006, 125, 164323. (58) Gavrilov, N.; Salzmann, S.; Marian, C. Chem. Phys. 2008, 349, 269. (59) Barbatti, M.; Lischka, H.; Salzmann, S.; Marian, C. J. Chem. Phys. 2009, 130, 034305. (60) Fuji, T.; Suzuki, Y.; Horio, T.; Suzuki, T.; Mitric, R.; Werner, U.; Bonacic-Koutecky, V. J. Chem. Phys. 2010, 133, 4303. (61) Gromov, E.; Trofimov, A.; Gatti, F.; Koppel, H. J. Chem. Phys. 2010, 133, 164309.

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