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Surface-Hopping Dynamics Simulations of Malachite Green: A Triphenylmethane Dye Bin-Bin Xie, Shu-Hua Xia, Li-Hong Liu,* and Ganglong Cui* Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China S Supporting Information *

ABSTRACT: Malachite green is a typical triphenylmethane dye widely used in fundamental and industrial research; however, its excited-state relaxation dynamics remains elusive. In this work we simulate its photodynamics from the S2 and S1 states using the fewest-switches surface-hopping scheme. In the S2 photodynamics, the system first relaxes to the S2 minimum, which immediately hops to the S1 state via an S2/S1 conical intersection. In the S1 state, 90% trajectories evolve into a structurally symmetric S1 minimum; the remaining ones proceed toward two propeller-like S1 minima. Two kinds of S1 minima then decay to the S0 state via the S1/S0 conical intersections. The S1 photodynamics is overall similar to the S1 excited-state dynamics as a result of the ultrafast S2 → S1 internal conversion in the S2 photodynamics, but the weights of the trajectories that decay to the S0 state via three different S1/S0 conical intersections are variational. Moreover, the S2 relaxation dynamics mainly happens in a concerted synchronous rotation of three phenyl rings. In comparison, in the S1 relaxation dynamics, the rotations of two aminophenyl rings can proceed in the same and opposite directions. In certain trajectories, only the rotation of an aminophenyl ring is active. On the basis of the results, the S2 and S1 excited-state lifetimes of malachite green in vacuo are calculated to be 424 fs and 1.2 ps, respectively. The present work provides important mechanistic insights for similar triphenylmethane dyes.

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INTRODUCTION

remains unclear. Yoshizawa et al. employed femtosecond fluorescence spectroscopy to study the S2 and S1 relaxation dynamics in solution.41 The S2 decay time and the subsequent S2 → S1 internal conversion time are estimated to be 0.27 and 1.2 ps in water solution, respectively. They also found that the S2 decay kinetics consists of fast and slow components in highviscosity solvents. Nagasawa et al. employed pump−probe spectroscopy to explore the solvent dependence of ultrafast ground-state recovery of several triphenylmethane dyes including malachite green and observed that the ground-state bleaching is highly nonexponential and depends on solvent

Triphenylmethane dyes have been long investigated in fundamental and industrial research.1−8 The earlier interest mainly focused on molecular structures and electronically excited states.9−24 Later, their complicated photophysical and photochemical processes have also been studied using various time-resolved spectroscopy.25−37 Malachite green is a typical member of triphenylmethane dyes and has been widely used as a molecular probe of microscopic viscosity and dynamics due to its dependence of solvent viscosity (Figure 1). Its optical properties, viscositydependent fluorescence, electron and energy transfer, and ultrafast internal conversion have attracted much attention.38−47 Many excellent experiments have been dedicated to studying the S2 and S1 relaxation dynamics, but the mechanism © XXXX American Chemical Society

Received: March 16, 2015 Revised: May 5, 2015

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DOI: 10.1021/acs.jpca.5b02549 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

so a barrierless relaxation is expected. Nakayama and Taketsugu50 also pointed out that large distortion of phenyl rings is required for the ultrafast nonradiative decay to the S0 state. Obviously, static electronic structure calculations cannot shed light on these dynamical details. Instead, full-dimensional nonadiabatic dynamics simulations must be carried out, which not only can verify the S1 and S2 deactivation paths proposed previously but also can provide many valuable dynamical insights, e.g., the interplay of various competitive decay channels, time-dependent excited-state properties, and detailed dynamics partterns. For these reasons, we have employed the semiempirical OM2/MRCI method to simulate the S2 and S1 photodynamics of malachite green in this work.

Figure 1. Malachite green system with the atomic numbering and three selected dihedral angles used for discussion in the text: C3C1C2C5 (ϕ1), C4C1C3C6 (ϕ2), C2C1C4C7 (ϕ3).

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SIMULATION DETAILS All semiempirical calculations were performed using the OM2/ MRCI method as implemented in the MNDO99 code.51−54 During geometry optimizations and dynamics simulations, all required energies, gradients, and nonadiabatic coupling elements were computed analytically. Minimum-energy conical intersections were optimized using the Lagrange−Newton approach.55,56 In the OM2/MRCI calculations, the restricted open-shell HF formalism was applied in the self-consistent field (SCF) treatment. The active space in the MRCI calculations included 12 electrons in 12 orbitals (Supporting Information, Figure S1). In terms of the SCF configuration it comprised five highest doubly occupied orbitals, two singly occupied orbitals, and five lowest unoccupied orbitals. For the MRCI treatment, three configuration state functions were chosen as references, namely, the SCF configuration and the two closed-shell configurations derived therefrom (i.e., all singlet configurations that can be generated from HOMO and LUMO of the closed-shell ground state). The MRCI wave function was built by allowing all single and double excitations from these three references. The S1 and S2 nonadiabatic dynamics simulations were studied by performing 1 ps OM2/MRCI trajectory surfacehopping simulations. The initial atomic coordinates and velocities for the S1 and S2 photodynamics simulations were randomly selected from a 5 ps ground-state trajectory. The numbers of excited-state dynamics runs were then chosen according to the computed S0−S1 and S0−S2 transition probabilities. A total of 100 and 150 surface-hopping trajectories were run for the S1 and S2 photodynamics, respectively, with all relevant energies, gradients, and nonadiabatic coupling vectors being computed on-the-fly as needed. For points with an energy gap of less than 10 kcal/ mol, the fewest-switches criterion was applied to decide whether to hop. The time step was chosen to be 0.1 fs for the nuclear motion and 0.0005 fs for the electronic propagation. The unitary propagator evaluated at midpoint was used to propagate the electronic motion. The translational and rotational motions were removed in each step. The empirical decoherence correction (0.1 au) proposed by Granucci et al. was employed.57 The final evaluations were done for the 96 and 132 trajectories that finished successfully in the S1 and S2 photodynamics, respectively, and that satisfied our energy continuity criterion (no change greater than 30 kcal/ mol between any two consecutive MD steps). Further technical details were given in previous publications.58−76 The DFT and TD-DFT methods in the GAUSSIAN09 program77 have been employed to calculate the vertical excitation energies to the lowest two excited singlet states.

viscosity.42 Later, they have studied the ultrafast excited-state deactivation of triphenylmethane dyes and concluded that the signal decays in a multiexponential manner and the slower components show stronger linear dependence on solvent viscosity than do the faster components.36 Bhasikuttan et al. suggested a cascade relaxation mechanism for the S2 state, which is almost independent of solvent viscosity.44 They also proposed that a conical intersection promoted by a torsional coordinate of the unsubstituted phenyl ring of the dye is related to the excited-state relaxation dynamics. Rafiq et al. employed femtosecond fluorescence up-conversion measurements to reveal a strong dependence of the S1 state relaxation dynamics on solvent viscosity and a very weak dependence for the S2 state relaxation.46 Recently, Li et al. adopted femtosecond timeresolved infrared spectroscopy to directly observe a local excited (LE) state and a twisted intramolecular charge-transfer (TICT) state.47 Solvent-controlled measurements in a series of linear alcohols indicate that the transition time from LE to TICT is strongly dependent on alcohol viscosity. Despite having numerous experimental data available for the S2 and S1 relaxation dynamics of malachite green, its relaxation processes remain unclear, for example, why does the S1 state relaxation dynamics strongly depend on solvent viscosity? etc. To shed light on the photophysical mechanism, electronic structure computations and dynamics simulations are very helpful. To our best knowledge, there are few ab initio electronic structure computations on malachite green. Guillaumont and Nakamura,48 and Preat et al.49 separately used the timedependent density functional theory (TD-DFT) method to calculate its absorption wavelengths and oscillator strengths in the Franck−Condon region. Rafiq et al. exploited the TD-DFT method to roughly scan the S2, S1, and S0 potential energy profiles along the torsional coordinates of phenyl rings.46 Nakayama and Taketsugu50 employed the high-level complete active space self-consistent field (CASSCF) and its secondorder perturbation (CASPT2) methods to investigate the nonradiative deactivation processes in the lowest S1 and S2 states. In their excited-state geometry optimizations, the central four carbon atoms are constrained to lie in a plane, as well as additional constraints in the path optimizations. However, these S1 and S2 deactivation paths are not validated up to now. In addition, the S1 and S2 dynamical details are elusive. It was believed that the S1 deactivation involves a rotation of phenyl groups, which leads to an S1/S0 conical intersection where the system efficiently decays from the S1 to S0 state. The S2 relaxation process involves the twisting motion of phenyl rings, but the initial relaxation is on a downhill ramp potential, B


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Figure 2. OM2/MRCI optimized S0, S1, and S2 minima, and S2/S1 and S1/S0 conical intersections. See Table 1 for selected geometric parameters and relative energies.

Table 1. Selected Bond Lengths (Å) and Dihedral Angles (deg) and Relative Energies [(kcal/mol)/eV] of All OM2/MRCI Optimized Structures in This Work S0 S1 S1-ISO1 S1-ISO2 S1S0 S1S0-ISO1 S1S0-ISO2 S2 S2S1 a

C1C2

C1C3

C1C4

ϕ1

ϕ2

ϕ3

energy

energya

1.472 1.422 1.477 1.474 1.450 1.485 1.484 1.418 1.427

1.422 1.463 1.428 1.464 1.470 1.452 1.477 1.464 1.463

1.422 1.466 1.457 1.424 1.482 1.479 1.451 1.465 1.459

45.1 0.0 50.2 70.6 16.9 53.4 93.8 3.4 16.2

26.9 87.8 7.8 99.9 73.9 20.2 110.2 85.1 48.5

25.0 92.0 101.5 20.8 67.1 106.6 19.4 98.0 51.5

0.0/0.00 51.8/2.25 54.5/2.36 54.4/2.36 53.5/2.32 58.6/2.54 58.6/2.54 57.9/2.51 62.7/2.72

0.0/0.00 49.4/2.14 55.1/2.39

CASPT2 Energies Taken from Ref

54.7/2.37 60.4/2.62

50

.

Figure 3. Three main resonance structures of Malachite Green in the S0 state. It is found that at least in a resonance structure, the C1C3 and C1C4 bonds are of double-bond character, whereas in all the three structures, the C1C2 bond is of single-bond character.

angles with respect to the rotations of the C1C3 and C1C4 bonds are numerically close to each other, 26.9° vs 25.0° (see ϕ2 and ϕ3); they are much smaller than the nearby dihedral angle around the C1C2 bond rotation (ϕ1, 45.1°). The C1C3 and C1C4 bond lengths are equilong in the S0 state, 1.422 Å; both are much shorter than their neighboring C1C2 bond length (1.472 Å). This can be understood in view of available resonance structures of malachite green in the S0 state. As shown in Figure 3, the C1C3 and C1C4 bonds are of doublebond character at least in a resonance structure, whereas in all

Ground-state geometry optimizations were done with the B3LYP functional78−80 and the 6-31G* basis set.81 Vertical excitation energies were calculated using the TD-DFT method with the B3LYP and CAM-B3LYP exchange-correlation functionals.82

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RESULTS S0 Equilibrium Structure. At the OM2/MRCI level, we optimized an S0 minimum, which is referred to as S0 in Figure 2. Its geometric parameters are listed in Table 1. The dihedral C


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S2 electronic state at the Franck−Condon point is of clear charge-transfer character from the phenyl to aminophenyl groups. Charge-transfer electronic transition is usually associated with remarkable change of electronic permanent dipole moments, either magnitudes or directions. In our OM2/ MRCI computations, electronic permanent dipole moments at the S0 minimum S0 are computed to be 2.1 D for the S0 state, 4.8 D for the S1 state, and 4.3 D for the S2 state; thus, both S1 and S2 are of charge-transfer character. This feature is consistent very well with previous analysis.50 S1 and S2 Geometric Structures. Two kinds of minima are optimized in the S1 state using the OM2/MRCI method. In the first one, referred to as S1 in Figure 2, the phenyl group is perpendicular to the two aminophenyl groups (ϕ1 = 0.0°). Its C1−C3 and C1−C4 bond lengths are nearly same, 1.463 and 1.466 Å at the OM2/MRCI level, but the corresponding ϕ2 and ϕ3 dihedral angles are a little different, ϕ2 = 87.8° and ϕ3 = 92.0° (Table 1). In addition, we have also optimized the other kind of S1 minima, which are referred to as S1-ISO1 and S1ISO2 in Figure 2. In both structures, one aminophenyl group is nearly perpendicular to the other aminophenyl and phenyl groups, for example, ϕ3 = 101.5° for S1-ISO1 and ϕ2 = 99.9° for S1-ISO2. Energetically, these three S1 minima are close to each other, which are 51.8 (49.4), 54.5 (55.1), and 54.4 kcal/ mol at the OM2/MRCI (CASPT2) level.50 However, their importance in the photodynamics of malachite green dye is different due to the ease of access to these structures. Without any geometric constraints we have also optimized an S2 minimum at the OM2/MRCI level, which is referred to as S2 in Figure 2. Its two dihedral angles related to the rotations of two aminophenyl groups are close to each other, ϕ2 = 85.1° and ϕ3 = 98.0° in Table 1. In addition, the S2 minimum S2 is structurally similar to the S1 minimum S1 but dissimilar to the other two S1 minima S1-ISO1 and S1-ISO2. The potential energy of the S2 minimum S2 relative to the S0 minimum S0 is calculated to be 57.9 kcal/mol at the OM2/MRCI level. S2/S1 and S1/S0 Conical Intersections. At OM2/MRCI level we optimized a minimum-energy S 2 /S 1 conical intersection, referred to as S2S1 in Figure 2. Its C1−C2 [C1−C3 and C1−C4] bond length decreases [increase] compared with those at the S0 minimum S0. Furthermore, the three main dihedral angles ϕ1, ϕ2, and ϕ3 change significantly from S0 to S2S1. Although S2S1 is 4.8 kcal/mol higher than the S2 minimum S2 at the OM2/MRCI level, this

the three structures the C1C2 bond is of single-bond character. Thus, the C1C3 and C1C4 bond lengths are in between those of typical C−C single and double bonds, whereas the C1C2 bond is a typical C−C single bond. Vertical Excitation Energies. Vertical excitation energies computed at the S0 minimum S0 are given in Table 2. Table 2. Vertical Excitation Energies (eV) to the Lowest Two Electronically Excited Singlet States (S1 and S2) Computed by Various Electronic Structure Methods and Experimental Values in Aqueous Solution41 S1 S2

OM2/MRCI

CASPT2

B3LYP

CAM-B3LYP

exp

2.5 3.4

2.0 2.8

2.5 3.1

2.7 3.5

2.0 3.0

Compared with experimental values measured in water solution41 TD-B3LYP and TD-CAM-B3LYP computations overestimate the S0 → S1 and S0 → S2 vertical excitation energies, but CASPT2 computations fortuitously give good agreement.50 Our current OM2/MRCI computations give reasonably accurate numbers, which are in between TD-CAMB3LYP and CASPT2 computed values. Analysis of molecular orbitals involved illustrates that the S0 → S1 vertical excitation mainly originates from the HOMO− LUMO electron transition, as shown in panel a of Figure 4. The

Figure 4. Primary molecular orbitals related to (a) S0 → S1 and (b) S0 → S2 electronic transitions at the S0 minimum.

Figure 5. Time-dependent S1 and S0 state populations (left) and distribution of the S1 → S0 hopping times (right). D


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Figure 6. Three typical trajectories in the S1 photodynamics. Left panels show three time-dependent geometric parameters and right ones show associated nonadiabatic coupling terms. The S1 → S0 hopping times are highlighted in vertical black lines.

On the basis of the results of static electronic structure computations, one can see that the chosen OM2/MRCI method gives similar S2 and S1 excited-state electronic and geometric structures in comparison to those computed by the CASSCF method.50 More important for the photodynamics is that the OM2/MRCI method can accurately describe the conical intersections among the lowest three singlet states, i.e., S0, S1, and S2. Therefore, the OM2/MRCI method is exploited to simulate the photodynamics of malachite green starting from the initial S2 and S1 excited states, respectively. S1 Nonadiabatic Dynamics. In our 96 trajectories of the S1 nonadiabatic dynamics simulations, 43% trajectories decay to

conical intersection is still able to be accessed readily taking into account that it is ca. 15 kcal/mol lower than the S2 energy at the Franck−Condon point (Table 1). In addition to the S2/S1 conical intersection, we have obtained three S1/S0 conical intersections, which are labeled as S1S0, S1S0-ISO1, and S1S0-ISO2 hereinafter. Structurally, S1S0 is closer to the S1 minimum S1 than S1S0-ISO1 and S1S0-ISO2 (see ϕ1, ϕ2, and ϕ3 in Table 1). Energetically, the former is 5.1 kcal/mol lower than the latter two at both OM2/ MRCI and CASPT2 levels.50 But, all these three conical intersections are accessible in view of the S2 energy at the Franck−Condon point. E


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Figure 7. Time-dependent S2, S1, and S0 state populations (left) and distribution of the S2 → S1 hopping times (right).

the S0 state at the end of 1 ps and 57% still survive in the S1 state. The left panel of Figure 5 shows the time-dependent S1 and S0 state populations. In the first 300 fs, the state populations do not change at all. This period of time corresponds to the initial relaxation time from the S1 Franck−Condon region via the S1 minima to the S1/S0 conical intersections. This process takes a relatively longer time because such process involves marked conformational change; e.g., ϕ1/ϕ2/ϕ3 changes from 45.1/26.9/25.0° of S0 to 16.9/ 73.9/67.1° of S1S0 (Table 1). After this relaxation, the S1 system starts to decay gradually to the S0 state until the end of 1 ps simulation. The S1 excited-state decay is treated as a firstorder reaction process. According to the fitting equation p = exp[−(t/τ)2], we have estimated the S1 excited-state lifetime τ to be 1.2 ps, for which the initial delay time t0 and the residual S1 state population p0 are assigned to 329.1 fs and 0.569, respectively. Furthermore, we have analyzed the S1 → S0 hopping-time distribution. As seen in the right panel of Figure 5, most of trajectories decay to the S0 state at around 750 fs. There are two groups of S1/S0 conical intersections responsible for the S1 excited-state deactivation, i.e., S1S0, and S1S0-ISO1 and S1S0-ISO2. To explore the importance of these two kinds of S1/S0 conical intersections, we further analyzed the S1 → S0 hopping regions responsible for the S1 excited-state deactivation in Figure SI-2, Supporting Information. It is found that 82% trajectories decay to the S0 state via S1S0 and only 18% via S1S0-ISO1 and S1S0-ISO2. How does one understand this biased distribution? On the energetic side, S1S0 is the lowest one among these three S1/S0 conical intersections. At the OM2/MRCI level, the former is computed to be 5.1 kcal/mol lower than the latter two. On the structural side, S1S0 is closer to the S1 Franck−Condon structure than S1S0-ISO1 and S1S0-ISO2 (see ϕ1, ϕ2, and ϕ3 in Table 1). Taken together, we can understand why S1S0 is preferred for the S1 excited-state deactivation. This point of view is consistent with previous CASPT2//CASSCF50 and present OM2/MRCI electronic structure computations (vide supra). Figure 6 shows three typical trajectories that decay to the S0 state via S1S0, S1S0-ISO1, and S1S0-ISO2, respectively. In panel a, the three dihedral angles only oscillate in the beginning around their initial values. Starting from about 400 fs, the C4C1C3C6 and C2C1C4C7 dihedral angles increase quickly in an almost concerted synchronous way, while the C3C1C2C5 dihedral angle decreases. At 714 fs, the system first encounters the S1/S0 conical intersection. There exists a large S1/S0

nonadiabatic coupling; as a result, the system hops to the S0 state. In panel b, the three dihedral angles change differently. At 300 fs, the C2C1C4C7 dihedral angle starts to increase. After ca. 300 fs, i.e., at 600 fs, the C3C1C2C5 dihedral angle starts to increase and, meanwhile, the C4C1C3C6 dihedral angle starts to decrease. At 647 fs, the S1 excited state is deactivated to the S0 state in the vicinity of S1S0-ISO1. In this run the system does not hop to the S0 state when it for the first time meets the S1/S0 conical intersection at ca. 100 fs where a large nonadiabatic coupling occurs (see the right subfigures of Figure 6). In panel c, the C3C1C2C5 dihedral angle varies mildly before the system jumps to the ground state at 658 fs. In comparison, the C4C1C3C6 dihedral angle increases rapidly starting from ca. 150 fs. However, the C2C1C4C7 dihedral angle merely oscillates within a small window of 30° in the whole process. S2 Nonadiabatic Dynamics. The S2 photodynamics processes are also simulated to explore the S2 excited-state lifetime and the S2 → S1 deactivation pathway. In our 132 trajectories, 109 trajectories decay to the S1 state, 19 trajectories decay to the S0 state, and 4 trajectories still survive in the S2 state at the end of 1 ps simulation. The left panel of Figure 7 shows the time-dependent S2, S1, and S0 state populations in the S2 photodynamics. The S2 state population almost does not change in the beginning; it starts to decrease after 200 fs. At the end of 1 ps simulation, the S1 population becomes close to 0.8. We have also fitted the timedependent S2 state population using the equation of p = exp(−(t − t0)/τ), in which the initial delay time t0 is assigned to 200 fs. The estimated S2 excited-state lifetime is 424 fs. The right panel shows the S2 → S1 hopping-time distribution in all trajectories that have already decayed to the S1 state. It can be found that most of trajectories hop to the S0 state around 400 fs, which numerically approaches the S2 excited-state lifetime. In addition, there is a peak for this distribution, which implies that the S2 → S1 hoppings mainly happen around an S2/S1 conical intersection. This dynamical feature is confirmed by our further analysis of the S2 → S1 hopping structures. This is also in line with previous and present static electronic structure computations:50 only an S2/S1 conical intersection is found at the OM2/ MRCI and CASSCF levels. What will happen upon arriving at the S1 state from the S2 state? Similar to the aforementioned S1 photodynamics, there exist again three main S1 → S0 hopping regions, which correspond to S1S0, S1S0-ISO1, and S1S0-ISO2, respectively. F


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Figure 8. Three typical trajectories starting from the S2 state. Left panels show three time-dependent geometric parameters and right ones show associated nonadiabatic coupling terms. The S2 → S1 and S1 → S0 hopping times are highlighted in vertical green and black lines, respectively.

Among them, S1S0 is still the major S1 → S0 hopping region (90% in Figure SI-3, Supporting Information); S1S0-ISO1 and S1S0-ISO2 contribute almost equally, but both are minor (5%). Why do the S1 → S0 hoppings prefer to S1S0 rather than S1S0ISO1 and S1S0-ISO2? This is due to the fact that S2S1 is structurally closer to S1S0 than S1S0-ISO1 and S1S0-ISO2. Therefore, when the system decays to the S1 state from the initial S2 state, S1S0 is first encountered dynamically. The S1 excited-state dynamics as a result of the S2 → S1 internal conversion in the S2 photodynamics is similar to the S1 photodynamics in which the S1 electronic state is directly

populated in the Franck−Condon region. In both cases, S1S0 is the major S 1 → S 0 hopping region, 82% in the S 1 photodynamics vs 90% in the S2 photodynamics. The only difference is that S1S0-ISO2 (13%) is slightly preferred over S1S0-ISO1 (5%) in the S1 photodynamics, whereas in the S2 photodynamics, both have almost equal weights. This could be due to the fact that in the S1 photodynamics, S1S0-ISO2 is a little closer to the initial Franck−Condon structure than S1S0ISO1, but in the S2 photodynamics, the S1 state is populated via the S2/S1 conical intersection S2S1. G


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The Journal of Physical Chemistry A Figure 8 shows the time-dependent evolution of three important dihedral angles and two nonadiabatic coupling terms in three typical trajectories in the S2 photodynamics. For the trajectory in panel a, the C4C1C3C6 and C2C1C4C7 dihedral angles increase monotonously and concertedly in the first 600 fs, while the C3C1C2C5 dihedral angle decreases. After ca. 300 fs, the system approaches the S2/S1 conical intersection S2S1; then, it decays to the S1 state at 923 fs. Only after 39 fs does the system decay again from the S1 to S0 state in the vicinity of the S1/S0 conical intersection S1S0. This small time interval of 39 fs between two sequential S2 → S1 and S1 → S0 internal conversion stems from the fact that both S2S1 and S1S0 conical intersections are structurally close to each other (see discussion above). For the trajectory in panel b, the C4C1C3C6 and C2C1C4C7 [C3C1C2C5] dihedral angles increase [decreases] monotonously in the first 500 fs. But, when the system decays to the S1 state from the S2 state at 551 fs, the C2C1C4C7 and C3C1C2C5 dihedral angles start to decrease and to increase, respectively, in contrast to those of the trajectory in panel a. This is due to the fact that the trajectory hops from the S1 to S0 state via a different S1/S0 conical intersection, S1S0-ISO1. The dynamical process of the trajectory in panel c is similar to that in panel b, except decaying to the S0 state via the other S1/S0 conical intersection, S1S0-ISO2. In addition, we have noted that the time interval between the sequential S2 → S1 and S1 → S0 internal conversions for the trajectories in panels b and c is much longer than that in panel a. This can be understood. Structurally, S2S1 and S1S0 are close to each other, so it is easy for the system to travel from S2S1 to S1S0; however, it takes time from S2S1 to S1S0-ISO1 or S1S0-ISO2. Thus, the system stays in the S1 state for a relatively longer time, up to several hundreds of femtoseconds, for the trajectories in panels b and c, whereas only tens of femtoseconds are seen for the trajectory in panel a.

Figure 9. Schematic excited-state deactivation channels starting from the initially populated S2 state. Also shown are the branch ratios of various competitive channels. See text for discussion.

mechanistic insights and time-dependent properties. First, they proposed that the S1 deactivation will occur almost exclusively through the S1/S0 conical intersection S1S0. Our results show that although the deactivation path via S1S0 is major, the other two paths via S1S0-ISO1 and S1S0-ISO2 cannot be fully excluded, in particular in the S1 photodynamics, which account for about 20% trajectories (Figure 9). In addition, it can be found that the weights of these three deactivation routes are variational and slightly state-dependent. Second, they expected a simultaneous rotation of three phenyl rings in the S2 relaxation process on the basis of the constrained potential energy surfaces. Our present dynamics simulations confirm the concerted rotation of these three phenyl rings. As shown in Figure 8, prior to decaying to the S1 state, the C2C1C4C7 and C4C1C3C6 dihedral angles increase in a nearly concerted way, while the C3C1C2C5 dihedral angle decreases. In contrast to the S2 relaxation dynamics, the S1 relaxation processes are complicated. Closer examination of the typical trajectories in Figure 6 reveals several different relaxation patterns. In the top and middle panels, the C2C1C4C7 and C4C1C3C6 dihedral angles (red and blue lines) are rotated in an almost concerted synchronous way. The difference is that the rotations of both dihedral angles proceed in the same direction in the former; in the latter, however, they do in the opposite directions. Surprisingly, for the trajectory in the bottom panel, the C3C1C2C5 and C2C1C4C7 dihedral angles are inactive in the relaxation process, in which only the C4C1C3C6 dihedral angle is active. These complicated S1 relaxation processes are again seen in the S1 excited-state dynamics as a result of the ultrafast S2 → S1 internal conversion in the S2 photodynamics. The complex S1 deactivation modes should originate from the fact that there exist multiple, accessible S1/S0 conical intersections available in malachite green.

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DISCUSSION On the results of the present static electronic structure computations and nonadiabatic dynamics simulations, we summarize the photophysical mechanism of malachite green in Figure 9. When the S2 state is populated upon irradiation at the Franck−Condon point, the system quickly relaxes to the S2 minimum; then, it speedily decays from the S2 to S1 state via a nearby efficient S2/S1 conical intersection. On the S1 state, 90% trajectories will be further de-excited to the S0 state via the S1/ S0 conical intersection S1S0 because it is structurally closer to the S2/S1 conical intersection. However, there remain 10% trajectories decayed to the S0 state via the other two S1/S0 conical intersections, S1S0-ISO1 and S1S0-ISO2. Once arriving at the ground state, the vibrationally “hot” trajectories will bifurcate two different S0 rotamers in forward and backward ways. Finally, we point out that if the S1 state is directly populated, the overall photodynamics is similar to that as a result of the S2 → S1 internal conversion from the S2 state. The only difference is that the weight of the trajectories that decay to the S0 state via the S1/S0 conical intersection S1S0 decreases a little. Nakayama and Taketsugu50 proposed a mechanism by optimizing the key stationary points in the S2, S1, and S0 states, such as minima and conical intersections, and by scanning the relevant potential energy surfaces, but they did not verify the proposed mechanism. More pivotally, the dynamical information is totally lacking. In addition to supporting their mechanism, our present dynamics simulations also provide new

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CONCLUSIONS By using the OM2/MRCI-based fewest-switches surfacehopping dynamics simulations, we have for the first time simulated the S2 and S1 relaxation dynamics of malachite green. H


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Our simulations not only verify the photophysical mechanism proposed previously on the basis of static electronic structure calculations50 but also provide many new valuable mechanistic insights, in particular time-dependent properties and the interplay of various deactivation channels. The present work again exemplifies that full-dimensional dynamics simulations are necessary for acquiring a correct mechanistic scenario for complicated polyatomic molecules that have multiple competitive deactivation channels and conical intersections. Our current work represents the first effort to simulate excited-state deactivation processes of triphenylmethane dyes and provides crucial mechanistic details for this kind of important dye.

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ASSOCIATED CONTENT

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AUTHOR INFORMATION

S Supporting Information *

Distributions of the S1 → S0 hoppings in the S1 and S2 photodynamics, active orbitals in the OM2/MRCI computations, and Cartesian coordinates of all optimized structures. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b02549.

Corresponding Authors

*L.-H. Liu. E-mail: [email protected]. *G. Cui. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (NSFC-21421003). G.C. is also grateful for the financial support from “The Recruitment Program of Global Youth Experts” and “Youth Scholars Program of Beijing Normal University”.

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REFERENCES

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