Ab Initio Molecular Dynamics Study of the Photoreaction of 1,1

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Ab Initio Molecular Dynamics Study on Photoreaction of 1,1'-Dimethylstilbene Upon S # S Excitation 0

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Yu Harabuchi, Rina Yamamoto, Satoshi Maeda, Satoshi Takeuchi, Tahei Tahara, and Tetsuya Taketsugu J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b07548 • Publication Date (Web): 21 Oct 2016 Downloaded from http://pubs.acs.org on October 21, 2016

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The Journal of Physical Chemistry

Ab Initio Molecular Dynamics Study on Photoreaction of 1,1'-Dimethylstilbene upon S0 → S1 Excitation Yu Harabuchi1, Rina Yamamoto1, Satoshi Maeda1, Satoshi Takeuchi2,3, Tahei Tahara2,3, and Tetsuya Taketsugu1,* 1) Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan 2) Molecular Spectroscopy Laboratory, RIKEN, 2-1 Hirosawa, Wako 351-0198, Japan. 3) Ultrafast Spectroscopy Research Team, RIKEN Center for Advanced Photonics (RAP), RIKEN, 2-1 Hirosawa, Wako 351-0198, Japan.

ABSTRACT Ab initio molecular dynamics (AIMD) simulations were carried out for *-excited 1,1'-dimethylstilbene (dmSB) at the spin-flip time-dependent density functional theory (SF-TDDFT) level with the TSF-index technique, to get insights into the substitution effects on the photoisomerization dynamics of stilbene (SB). It is found that the reaction path from the Franck-Condon structure of cis-dmSB is oriented toward the 4,4-dihydrophenanthrene (DHP) side from the beginning, which is in contrast to the case of SB where the pathway is oriented toward the twist-side in the initial stage. The optimized geometries of minima and minimum energy conical intersection (MECI) suggested that molecules in the DHP region could easily decay to the ground state. On the other hand, S1/S0-MECI and S1-minimum in the twist region have a relatively different geometry from each other, which is consistent with the experimental observation of the long lifetime of the perpendicular structure. AIMD simulations showed that more trajectories enter the well of the DHP side than the well of the twist side, and that all of the trajectories going to the DHP-side reached the S1/S0-CI region with ~0.2 ps on average, while very few trajectories reached S1/S0-CI even after 1 ps in the twist region. Decrease in the S1-population in the cis and twist regions qualitatively reproduced the temporal profiles of the transient absorption bands of dmSB observed in the visible and ultraviolet regions, respectively. AUTHOR INFORMATION Corresponding Author: E-mail: [email protected] (T. Taketsugu) Tel: 81-11-706-3535 Notes: The authors declare no competing financial interest.

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I. INTRODUCTION Stilbene is one of typical molecules that exhibit cis-trans photoisomerization. It is known that a photoreaction from cis-stilbene accompanies a sub-product, 4,4-dihydrophenanthrene (DHP),1 and the photocyclization from cis-stilbene to DHP is an important model for diarylethene derivatives which are popular optical switching molecules.2 Experimental studies showed that ππ*-excited cis-stilbene exhibits ultrafast decay to the ground state with a lifetime of ca. 1.0 ps,3-9 and the branching ratio for cis : trans : DHP was reported as 55 : 35 : 10.10-12 Recent steady-state13 and femtosecond time-resolved14 fluorescence study revealed that the decay of ππ*-excited cis-stilbene shows a bi-exponential nature with the lifetimes of 0.23 ps and 1.2 ps, suggesting that an ultrafast process is involved within the excited-state lifetime. The initial dynamics of ππ*-excited cis-stilbene was investigated also from the structural viewpoint by femtosecond Raman spectroscopy.15,16 It showed a temporal change of the vibrational spectrum, which was assigned to the twisting motion of the central C=C bond through quantum chemical calculations.15 Further elaborate experiments on isotope labeled17 and geometrically constrained18 cis-stilbene were also carried out to get insight into the vibrational structure of ππ*-excited cis-stilbene. Theoretical studies elucidated that ππ*-excited cis-stilbene evolves on the S1(*) potential energy surface (PES) with the twisting motion of the central C=C bond.19-23 An accessible minimum energy conical intersection (MECI) point between S0 and S1 states (denoted S1/S0-MECI) was located near the minimum on the S1-PES, which corresponds to the C=C bond twisting structure (denoted as twist).20-21 The molecular motion of C=C bond twisting with keeping the orientation of two phenyl rings was named "hula-twist".22 Dou et al.24-26 performed semi-classical electron-radiation-ion dynamics simulations on the relaxation process of S1 cis-stilbene, and examined three dominant processes, i.e. cis-trans isomerization,25 cis-cis (no isomerization),24 and cis-DHP photocyclization.23 Recently, Minezawa and Gordon examined the reaction pathways in the relaxation process of ππ*-excited cis-stilbene by the spin-flip time-dependent density functional theory (SF-TDDFT),27-29 and found that the photocyclization is in competition with the photoisomerization.30 They located geometries of minima and S1/S0-MECIs for twist ((S1)twist-min and (S1/S0)twist) and DHP ((S1)DHP-min and (S1/S0)DHP-MECI) regions on the S1-PES by the SF-TDDFT method, which was later confirmed by the more sophisticated method, i.e., extended multi-configuration quasi-degenerate second order perturbation theory (XMCQDPT2).31 Very recently we also employed the SF-TDDFT method to examine the 3


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reaction pathway and reaction dynamics of *-excited cis-stilbene.32 First the steepest descent pathway was calculated starting from the Franck-Condon (FC) structure on the S1-PES, which is oriented towards (S1)twist-min initially, but changes its direction at the very flat region of the PES, and reaches (S1)DHP-min. Then, ab initio molecular dynamics (AIMD) simulation was performed for *-excited cis-stilbene at the SF-TDDFT level (AIMD/SF-TDDFT),32 in which the experimental branching ratio10-12 was well reproduced (twist : DHP = 35 : 13). This result indicates the significance of dynamical effects to understand the branching mechanism of photoreaction of excited cis-stilbene. The experimentally observed two components of the lifetime14 were also discussed based on results from AIMD simulations. In 2012, Berndt et al. measured transient absorption spectra of 1,1'-dimethylstilbene (dmSB) in solution.33 The lifetime of a transient band observed around 600 nm (CIS* band) was 0.2 ps, which is shorter than the corresponding CIS* band of cis-stilbene (0.92 ps). Another transient band, which they associated with the perpendicular conformation (denoted as P*), was also observed around 330 nm (P* band). It was found that the lifetime of the P* band of cis-dmSB is 19 ps in hexane and 2.9 ps in acetonitrile, and it is much longer than the lifetime of the corresponding P* band of cis-stilbene.34 They suggested that the longer lifetime of dmSB is attributable to the structural difference between the minimum and the conical intersection around P*. As far as we know, there has been no theoretical study on the relaxation process of S1 dmSB, and the mechanism of changes in the decay time, as well as the structure of P*, have never been revealed. In the present study, the static reaction pathways and dynamical trajectories are calculated for the *-excited cis-dmSB by the SF-TDDFT method (1) to understand the reaction mechanism and reaction dynamics including branching into trans-dmSB (photoisomerization) and 1,1'-dimethyl-DHP (dmDHP) (photocyclization), (2) to clarify the origin of the S1 dynamics, which exhibits the CIS* and P* bands in time-resolved absorption experiments, and (3) to reveal the structure corresponding to P*. The results will be also compared with the previously reported mechanism and dynamics for cis-stilbene to examine substitution effects on dynamics of the photoreaction. In addition, a new treatment to follow the target electronic state along the trajectory in AIMD/SF-TDDFT simulations is introduced.

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II. COMPUTATIONAL DETAILS To investigate the decay process of cis-dmSB excited to the S1(ππ*) state, the steepest descent path in the S1 state was calculated from the FC structure in mass-weighted coordinates that is referred to as the meta-IRC path. Geometries corresponding to minima of cis, DHP, and twist (in the intermediate region between cis-dmSB and trans-dmSB) and the transition states (TS) in the S1 state were located, and the IRC paths were calculated from the TSs. The S1/S0-MECI geometries were optimized by using the branching plane update method.35 The SF-TDDFT method was employed with BHHLYP functional and 6-31G(d) basis sets, using the GAMESS program.36-37 The TS geometries in the excited state were optimized by the developmental version of GRRM.38 It is well known that a conventional TDDFT method cannot be employed for a crossing region of S0 and S1 states because the reference state in TDDFT is a closed-shell singlet configuration.39 To overcome this limitation, the SF-TDDFT method has been developed so that an open-shell triplet configuration is employed as the reference state and the ground and excited states are described as the response state.27,29 In the SF-TDDFT method, five types of electronic states are obtained as solutions,40 i.e., the ground state, the open-shell singlet and triplet states of HOMO-LUMO single excitation, the singlet excited state of HOMO-LUMO double excitation, and spin-mixed states of singlet, triplet and quintet. In the recent AIMD simulation with SF-TDDFT,32 the target state was followed by monitoring orbital coefficients and configuration interaction (CI) coefficients along the trajectory, but such approach sometimes did not work in the region where the singlet and triplet states approach each other.32 Very recently, a new approach, TSF-index method,41 was proposed to trace the target state in S1/S0-MECI-search calculations with SF-TDDFT. In this approach, the open-shell triplet state of HOMO-LUMO single excitation is identified from the solution of SF-TDDFT, based on TSF-index defined as TSF = VHOMO-LUMO + ,

(1)

where VHOMO-LUMO is a squared sum of the CI coefficients for the four configurations of two-electrons over HOMO and LUMO, and is the expectation value for the S2 operator. The two lowest states other than triplet states are regarded as S0 and S1. In the case of dmSB, the three lowest states are verified to correspond to S0, S1(ππ*), and T1, and thus, the target ππ* state can be traced based on TSF-index. Then, AIMD simulations were performed for *-excited cis-dmSB at the SF-TDDFT level with the TSF-index method, to investigate dynamical effects on the photo-isomerization 5


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process. The initial conditions were determined by the normal mode sampling in the ground state equilibrium geometry of cis-dmSB. The atomic coordinates and momenta were generated randomly by adding an energy of kT to each normal mode under the Boltzmann distribution at 300 K. The time step was set to 0.2 fs, and 33 trajectories were calculated until the energy difference between S0 and S1 states becomes less than 4.6 kcal/mol, or the simulation time reaches 1 ps. AIMD simulations were performed by the SPPR program.42

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III. RESULTS AND DISCUSSION A. Geometries of minima and MECI in S0 and S1 states For dmSB, we located four minima in the ground state, corresponding to cis (denoted (S0)cis-min), DHP (denoted (S0)DHP-min), and two trans (denoted (S0)trans-min1 and (S0)trans-min2), as shown in Fig. 1a. The numbering for carbon atoms are partly indicated for (S0)cis-min. The interatomic distance of C5 and C6 (denoted as rC5C6) characterizes the cyclization from cis-dmSB to dmDHP, while the dihedral angle of C3-C1-C2-C4 (denoted as dC3C1C2C4) characterizes the isomerization from cis-dmSB to trans-dmSB (or twist-dmSB). The dihedral angle of C7-C1-C2-C8 (denoted as dC7C1C2C8) characterizes the planarity of the central ethylenic part of dmSB. The relative energy, three internal coordinates (rC5C6, dC3C1C2C4, and dC7C1C2C8), and the dipole moment are shown under each geometry in Fig. 1. As to trans-forms, the phenyl groups are deviated from the planar configuration due to a steric effect with methyl groups. The difference of (S0)trans-min1 and (S0)trans-min2 is in the orientation of two phenyl groups. The energies of cis and trans-forms are very similar (trans-dmSBs are ca. 1 kcal/mol lower in energy than cis-dmSB), while dmDHP is energetically high (39.2 kcal/mol). In geometry optimizations for dmSB in the S1 state, three minima, (S1)cis-min, (S1)DHP-min, and (S1)twist-min, were located as shown in Fig. 1b. Their energies are close to each other. The central C=C part of (S0)cis-min has almost a planar structure (dC3C1C2C4 = 8.0°; dC7C1C2C8 = 2.5°), while (S1)cis-min has a non-planar structure (dC3C1C2C4 = 49.6°; dC7C1C2C8 = 47.0°). In (S0)DHP-min and (S1)DHP-min, the dihedral angles show similar values but the C5-C6 interatomic distance is relatively different: rC5C6 = 1.53 Å for S0 and rC5C6 = 2.05 Å for S1. We also located three S1/S0-MECI structures, as shown in Fig. 1c. There is one MECI in a region of DHP (denoted as (S1/S0)DHP), while there are two in a twist region (denoted as (S1/S0)twist-1 and (S1/S0)twist-2) where (S1/S0)twist-1 is located nearby cis, while (S1/S0)twist-2 is located nearby trans. The geometries of (S1)twist-min, (S1/S0)twist-1, and (S1/S0)twist-2 are all characterized by a twisted pyramidal structure of the central CC bond, but the geometry of (S1)twist-min is significantly different from those of (S1/S0)twist-1 and (S1/S0)twist-2. The dihedral angle dC3C1C2C7 that characterizes a pyramidalization is 153.3° for (S1)twist-min, while dC3C1C2C7 is 114.0° and 116.3° for (S1/S0)twist-1 and (S1/S0)twist-2, respectively, indicating that the pyramidalization at (S1)twist-min is relatively weak. The larger dC3C1C2C7 for (S1)twist-min can be understood as the result of the steric hindrance between phenyl group and methyl group. The energy of (S1/S0)twist relative to (S1)twist-min is also relatively large, ~ 9 kcal/mol. Such a significant difference in geometry and energy between minimum and MECI was not reported for other molecules such as 7


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ethylene, stylene, stilbene, and stiff-stilbene,30,31,39,43-46 and it is expected that the lifetime of the S1 molecule in the twist region of dmSB should be longer than that of SB. This finding is consistent with the longer lifetime of the P* state of dmSB.33,34 It is interesting to note that (S1)twist-min has a large dipole moment (9.07 D), which is also consistent with the experimental suggestion.33

Figure 1. Geometries of dmSB and dmDHP as well as significant internal coordinates, dipole moments, and relative energies: (a) minima in the ground state; (b) minima in the S1(ππ*) state; (c) S1/S0-MECI. Atomic coordinates are provided in the supporting information. 8



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B. Reaction pathways in the S1 state Once cis-dmSB is excited to the S1(*) state, the molecule starts to change its geometry according to atomic forces determined by energy gradients on the S1-PES. The structural changes can be discussed based on the steepest descent paths from the FC structure (meta-IRC), as well as the IRCs connecting minima on the S1-PES. As shown in Fig. 2, two TSs in the S1 state, (S1)TS1 and (S1)TS2, were located. Through IRC calculations, it was confirmed that (S1)TS1 connects (S1)cis-min and (S1)DHP-min, while (S1)TS2 connects (S1)cis-min and (S1)twist-min. The energy variations along the IRC paths are shown in Fig. 3. The relative energies for the three minima and two TSs in the S1 state are in a range of 84.5 ~ 87.7 kcal/mol, indicating that the S1-PES is very flat.

Figure 2. TS geometries for (a) (S1)DHP-min → (S1)TS1 → (S1)cis-min and (b) (S1)cis-min → (S1)TS2 → (S1)twist-min in the S1 state of dmSB. Significant internal coordinates, dipole moments and relative energies are also shown. Atomic coordinates are provided in the supporting information.

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Figure 3. The energy variations of the S1 (in red) and S0 (in black) states along the IRC pathways for (a) (S1)DHP-min → (S1)TS1 → (S1)cis-min and (b) (S1)cis-min → (S1)TS2 → (S1)twist-min-1. To discuss photo-reaction processes of cis-dmSB after the * excitation, positions of stationary points and MECIs and traces of reactions pathways (meta-IRC and IRCs) projected into a two-dimensional configurational space of rC5C6 and dC3C1C2C4 are depicted in Fig. 4a. For comparison, the corresponding figure for SB32 is also shown in Fig. 4b. In these figures, minima in the ground state are denoted by a black circle, while minima, TS, and MECI in the S1(ππ*) state are depicted by a red circle, a red triangle, and a red cross mark, respectively. The meta-IRC path from the FC point is denoted by a red solid line, while the IRC paths are denoted by a blue dotted line. As 10



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shown in Fig. 4a (dmSB case), the meta-IRC paths from the FC regions of cis-form approaches (S1)TS1 that separates (S1)DHP-min and (S1)cis-min, and smoothly enters a side of (S1)DHP-min. On the other hand, in SB case, there is no (S1)cis-min and no (S1)TS1 (this region is a kind of shoulder and shows a very flat nature); the meta-IRC path is initially oriented toward a twist direction, and drastically changes its direction toward (S1)DHP-min. The difference in geometrical feature of the pathways suggests that, in cis-dmSB case, photo-cyclization is enhanced compared with the case of cis-SB. Since S1/S0-MECI ((S1/S0)DHP) point is located near (S1)DHP-min, the molecule entering the (S1)DHP-min side would reach the S1/S0-CI region easily, resulting in a nonradiative transition to the ground state. Since the energy barriers for pathways from cis-dmSB to dmDHP or twist-dmSB are very low, the molecule near (S1)cis-min region can easily enter DHP or twist regions.

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Figure 4. Plots of reaction pathways on the S1-PES, projected on a two-dimensional configurational space in terms of rC5C6 and dC3C1C2C4, for (a) dmSB and (b) SB.32 Minima in the ground state are denoted by a black circle, while minima, TS, and MECI in the S1(ππ*) state are denoted by a red circle, a red triangle, and a red cross mark, respectively. The meta-IRC path from the FC point is denoted by a red solid line, while the IRC paths are denoted by a blue dotted line. 12



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To illustrate geometrical difference of the meta-IRC pathways for cis-dmSB and cis-SB, variations of three internal coordinates, rC5C6, dC3C1C2C4 and dR7C1C2R8 (R = CH3, H), along the pathways are plotted in Fig. 5a and 5b, respectively. In both dmSB and SB, rC5C6 decreases gradually along the meta-IRC paths, and the dihedral angles, dC3C1C2C4 and dR7C1C2R8, first increase and then decrease almost simultaneously. The difference is the rate of increase in two dihedral angles: slow for dmSB and very fast for SB. This difference is caused by a difference in the weight of moving fragments, i.e., methyl group (dmSB) and hydrogen atoms (SB).

Figure 5. Variation of significant internal coordinates, rC5C6 (green), dC3C1C2C4 (red), and dR7C1C2R8 (blue) (R = CH3, H), along the meta-IRC pathways for (a) dmSB and (b) SB.

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C. AIMD simulations AIMD simulations were performed for photoexcited cis-dmSB in the S1(*) state by the SF-TDDFT method with the TSF-index technique, to investigate the mechanism of branching to DHP and twist sides. To verify the reliability of SF-TDDFT/TSF-index, we examined values for the respective states obtained from SF-TDDFT calculations along the AIMD trajectories. As the results, it was shown that the appropriate target S1 state was correctly picked up at all the points through the trajectories. In total 33 trajectories were run starting from the FC region of cis-dmSB on the S1-PES, and all trajectories were verified to enter the cis region initially, which corresponds to appearance of the transient absorption band observed in the 600-nm region (CIS* band).33 (For simplicity, we call the S1 molecules in the cis region that exhibit the CIS* band as “the CIS* state”, hereafter.) Then, 28 trajectories (85%) smoothly moved in the well of the DHP side, which is opposite to the results for SB that prefers initial movements toward the twist-side.32 This is owing to the difference in initial orientation of the meta-IRCs shown in Fig. 4. Figure 6 shows a classification of AIMD trajectories based on the destination and dynamical behavior: (a) trajectories entering the DHP-side and reaching the S1/S0-CI region (19/33); (b) trajectories entering the DHP-side and moving to the twist-side (9/33); (c) trajectories entering the twist-side (4/33); (d) trajectories entering the twist-side and moving to the DHP-side (1/33). According to the rate of the destinations of trajectories from our AIMD simulations (DHP : twist ~ 20 : 13), the photo-cyclization is favorable in the case of dmSB, and this feature is opposite to the case of SB (DHP : twist ~ 13 : 35).32 This difference in the branching ratio between cis-dmSB and cis-SB seems to accord with the experimental observation. The reported transient absorption spectrum of cis-dmSB shows a band at around 450 nm at late delays (> 16 ps),33 which is most likely assignable to dmDHP by analogy with the corresponding band observed for cis-SB.34 The comparison of the transient absorption data of cis-dmSB and cis-SB shows that the amplitude of the dmDHP band (relative to that of the CIS* band immediately after photoexcitation) is substantially larger than that of the DHP band observed with excitation of cis-SB. If the absorption cross sections of the corresponding transitions are comparable in cis-dmSB and cis-SB, it implies that dmDHP is formed more efficiently in cis-dmSB than DHP in cis-SB, which is consistent with the present AIMD simulation.

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Figure 6. A classification of AIMD trajectories that start from the FC region of cis-dmSB in the S1 state: (a) trajectories that enters the DHP region via the CIS* state and reach the S1/S0-CI region (19/33); (b) trajectories that first enters the DHP region via the CIS* state and then moves to the twist region (9/33); (c) trajectories that enters the twist region via the CIS* state (4/33); (d) a trajectory that first enters the twist region via the CIS* state and then moves to the DHP region (1/33). The trace of trajectories is shown by black solid lines, and the important points in the S1 state are indicated in the same way as Fig. 4a. The terminal point of each trajectory is indicated by a blue cross mark. The condition for terminating each trajectory calculation is whether the energy difference of S1 and S0 becomes less than 4.6 kcal/mol or the simulation time reaches 1 ps. Note that the terminal points of trajectories do not necessarily coincide with the S1/S0-MECIs, since the S1/S0-CI region is not a point but a space with some volume around the S1/S0-MECI point in the configurational space. In the transient absorption spectra of cis-dmSB,33 the lifetimes of the CIS* band at 600 nm and the P* band at 330 nm were reported to be 0.2 ps and 19 ps, respectively, in hexane. In AIMD simulations, 15


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all 20 trajectories entering the DHP-side reached the S1/S0-CI region, while only 2 of 13 trajectories reached the S1/S0-CI region in the twist side, within 1 ps. According to the flow of AIMD trajectories on the S1-PES, the population of the CIS* state should increase initially and gradually decrease through a movement to the DHP side or the twist-side which occurred during the initial 0.2 ps. Actually this time span is in very good agreement with the experimental lifetime of the CIS* band (τ = 0.2 ps).33 On the other hand, most trajectories entering the twist-side stay around (S1)twist-min for a long time (at least longer than 1 ps) without reaching the S1/S0-CI region. This feature can be attributed to the geometrical difference between (S1)twist-min and (S1/S0)twist already discussed in section A (shown in Fig. 1), and thus, the molecule staying at the twist-side should have a long lifetime in the S1 state, corresponding to the P* band observed in the experiment.33 Figure 7 shows the S1-population decay for (a) dmSB and (b) SB,32 calculated from AIMD simulations under the assumption that trajectories reaching the S1/S0-CI regions immediately decay to the ground state. The population decay for the trajectories finally staying in the DHP-side is indicated by a red line, while the decay for those in the twist-side is indicated by a blue line. The decay for all the trajectories is indicated by a black line. As indicated in Fig. 7a, the molecule at the DHP-side has a short lifetime while the molecule at the twist-side has a relatively long lifetime in the case of dmSB. However, in the case of SB shown in Fig. 7b, the molecule at the DHP-side has a relatively long lifetime while the molecule at the twist-side has a short lifetime,32 which is just opposite to the case of dmSB. The difference between dmSB and SB can be explained as follows: The species with the short lifetime is determined due to the initial direction of the meta-IRC pathway from the FC region (to DHP in dmSB, while to twist in SB). As to a component of the long lifetime, geometry of minimum and MECI in the twist side for dmSB is different from each other as discussed above, and thus, the lifetime of the twist-side becomes long due to the difficulty to reach the S1/S0 regions. For the case of SB, most molecules goes into the twist region due to the initial motion in the S1 state, and it takes a relatively long time to enter the DHP side.32

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Figure 7. The decay of S1-population as a function of time derived from AIMD simulations for (a) dmSB and (b) SB.32 The S1-population for all the trajectories is plotted in black, while the decays for the trajectories staying at the DHP region and for those at the twist region are plotted in red and in blue, respectively. In the transient absorption data of cis-dmSB (in acetonitrile), it was reported that the CIS* band around 600 nm immediately appears with photoexcitation, while the P* band around 330 nm shows up with a finite rise time of ca. 0.1 ps. In the reported 17


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time profile of the P* band (Fig. 8b), when normalized to the maximum amplitude of 1.0, the P* signal increases to ~ 0.8 in the first 0 – 0.2 ps, exhibits a shoulder feature at 0.2 – 0.3 ps, and increases again to 1.0 within 0.6 ps. Then, it gradually decreases, reflecting the lifetime of the P* state. It was also shown that the CIS* signal rapidly decays with a lifetime of 0.2 ps with a distinct shoulder feature observed at 0.2 – 0.3 ps.33 To understand these features seen in the time profiles of the CIS* and P* signals, the time variations of the S1-population for the cis/DHP- and twist-sides in AIMD trajectories are analyzed. To distinguish the cis/DHP- and twist-sides based on geometrical parameters, we employed the dihedral angle about the central CC bond, dC3C1C2C4. The structures with dC3C1C2C4 ≤ 68.7° (value at (S1)TS2) are regarded as those located in the cis/DHP-side, while the structures with dC3C1C2C4 > 68.7° are regarded as those located in the twist-side. Figure 8a shows the time variations of the S1-population for cis/DHP-side (in red) and for twist-side (in blue) where the plot for twist-side is normalized so that the maximum value is equal to 1. The S1-population of the cis/DHP-side decreases with a lifetime of ca. 0.3 ps since some trajectories move out to the twist-side or reach the S1/S0-CI regions within the DHP side (which is consistent with the experimental lifetime of the CIS* band, 0.2 ps). The S1-population of the twist-side increases during 0 ~ 0.6 ps due to moving-in of the trajectories from the cis/DHP-side (which is in good agreement with the finite rise time observed in the time profile of the P* band). It is very interesting to note that there is a shoulder feature in the plots of both cis/DHP- and twist-sides during 0.2 ~ 0.3 ps. Based on analyses of AIMD trajectories, these shoulders are related to the trajectories which once move in the twist-side and then go back to the cis/DHP-side. This feature is in good agreement with the shoulder observed in the experimental time profiles of the CIS* and P* bands (Fig. 8b).33

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Figure 8. (a) Variations of the S1-population as a function of time derived from AIMD simulations for dmSB. The rate of S1-population for trajectories located in the cis/DHP-side (dC3C1C2C4 ≤ 68.7 °) is plotted in red, while that in twist-side (dC3C1C2C4 > 68.7 °) is plotted in blue. (b) Decay of the CIS* band (a red line) and development of the P* band (a cyan line) for cis-dmSB (in acetonitrile). Reprinted from Ref. 33, Copyright (2016), with permission from Elsevier.

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In the present AIMD simulation, the energy relaxation to solvent molecules is not considered and the total energy is conserved. Under this limitation, two trajectories reached S1/S0-CI regions in the twist-side within 1 ps, indicating that dmSB can reach S1/S0-CI regions faster in gas-phase than in hexane. It is also noted that the accuracy of SF-TDDFT results is not quantitatively high, and there remains possibility that the relative energy of (S1/S0)twist to (S1)twist-min (~ 9 kcal/mol) is an overestimated value. However, we believe that the present explanation of the long lifetime of P* in dmSB is qualitatively correct, and possibly the P* structure of dmSB is a good target to be examined experimentally since it has a relatively long lifetime.

IV. CONCLUSION There have been a lot of experimental data on photoisomerization of stilbene and its derivatives, but a detailed reaction mechanism remains unknown. Nowadays the state-of-the-art theoretical and computational approach is expected to deepen the understanding of the reaction mechanism. In the present study, we examined the reaction pathways and dynamics for * excited cis-dmSB to get insights to the substitution effects on the photoisomerization of stilbene, by the reaction path calculations and AIMD simulations at the SF-TDDFT level. Through a comparison with the previous AIMD study for the * excited SB,33 we succeeded in understanding the branching mechanism of the products and the origin of the short and long lifetimes. In the SF-TDDFT method, a new treatment, TSF-index, was employed first time with AIMD simulations, which makes it possible to follow the target state along the trajectory. From static calculations of the reaction pathways, it is found that the meta-IRC path from the FC structure of cis-dmSB is oriented toward the DHP side from the beginning on the S1-PES. This feature is in contrast to the case of SB where the meta-IRC pathway is oriented toward the twist-side in the initial stage. Through analyses of geometrical changes along the pathways, this difference was verified to be caused by a difference in the weights of CH3 and H that move in the initial process after the vertical excitation. The optimized geometries of minima and MECI suggested that molecules in the DHP region could easily decay to the ground state because the geometries of the minimum and MECI are similar to each other. It is also found that, in the twist region, both MECI and minimum show the twisted pyramidal geometries of the C=C bond, but the pyramidalization of the minimum geometry is relatively weak 20



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due to the steric hindrance between phenyl group and methyl group. Then, molecules in the twist region are expected to have a long lifetime due to the difficulty to reach the S1/S0-CI. This feature is in contrast to the SB case. AIMD simulations indicated that, after entering and leaving the cis region, more trajectories enter the DHP region than the twist region for S1-excited cis-dmSB, which is opposite to the case of SB. This result is consistent with geometrical features of the reaction pathways, and also the lifetime of the molecules in the DHP region of dmSB is expected to be short compared with that of SB. It was also shown that all of the trajectories staying in the DHP region reached the S1/S0-CI region with ~0.2 ps on average, while among 13 trajectories staying in the twist region, only two trajectories reached the S1/S0-CI region within 1 ps. The calculated S1-population decay qualitatively reproduced the experimental lifetimes of the CIS* and P* bands, as well as the finite rise time in the growth of the P* band.

ACKNOWLEDGMENT This work is partly supported by a grant from Japan Science and Technology Agency with a Core Research for Evolutional Science and Technology (CREST) in the Area of “Establishment of Molecular Technology towards the Creation of New Functions” at Hokkaido University, and is partly supported by JSPS KAKENHI with Grant Number 26288001 (Taketsugu), 25104005 (Tahara), and 16H04102 (Takeuchi). A part of calculations was performed using the Research Center for Computational Science, Okazaki, Japan.

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