Ultrafast Nonradiative Decay of Electronically Excited States of

Jul 25, 2011 - Surface-Hopping Dynamics Simulations of Malachite Green: A Triphenylmethane Dye. Bin-Bin Xie , Shu-Hua ... Seth Olsen , Ross H. McKenzi...
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Ultrafast Nonradiative Decay of Electronically Excited States of Malachite Green: Ab Initio Calculations Akira Nakayama* and Tetsuya Taketsugu Division of Chemistry, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan

bS Supporting Information ABSTRACT: We have investigated the nonradiative deactivation process of malachite green in the singlet excited states, S1 and S2, by high-level ab initio quantum chemical calculations using the CASPT2//CASCF approach. The deactivation pathways connecting the Franck Condon region and conical intersection regions are identified. The initial population in the S1 state is on a flat surface and the relaxation involves a rotation of phenyl rings, which leads the molecule to reach the conical intersection between the S1 and S0 states, where it efficiently decays back to the ground state. There exists a small barrier connecting the Franck Condon and conical intersection regions on the S1 potential energy surface. The decay mechanism from the S2 state also involves the twisting motion of phenyl rings. In contrast to the excitation to the S1 state, the initial population is on a downhill ramp potential and the barrierless relaxation through the rotation of substituted phenyl rings is expected. During the course of relaxation, the molecule switches to the S1 state at the conical intersection between S2 and S1, and then it decays back to the ground state through the intersection between S1 and S0. In relaxation from both S1 and S2, large distortion of phenyl rings is required for the ultrafast nonradiative decay to the ground state.

I. INTRODUCTION Triphenyl methane (TPM) dyes have received considerable attention for long time both in the fundamental and industrial researches. In particular, the ultrafast relaxation dynamics of TPM dyes has been the subject of extensive investigations and various time-resolved spectroscopic experiments have been performed to elucidate the relaxation mechanism.1 6 Malachite green (MG; see Figure 1) belongs to a class of TPM dyes and the photodynamics from the singlet excited states (from both the S1 and S2 states) has been extensively investigated in various solvents by many research groups. It is known that the nonradiative relaxation process of MG exhibits strong solvent viscosity dependence2,3,6 10 and this feature has been widely used as a molecular probe for microscopic viscosity.11 14 It is now generally accepted that the diffusive rotation of two N,Ndimethyl-amino-substituted phenyl rings is responsible for the viscosity dependence. However, the detailed microscopic deactivation mechanism is not yet known. Several simplified deactivation models have been proposed to interpret experimental data on the TPM dyes obtained by timeresolved spectroscopic techniques. It has been considered that the excited-state potential energy surface is flat and barrierless with respect to the rotation of phenyl rings. The Bagchi, Fleming, and Oxtoby (BFO)15 model is one of the earliest models, which considers a sink at the bottom of the excited-state potential energy surface. They assumed that the initial population caused by photoexcitation spreads diffusively on the barrierless excited-state r 2011 American Chemical Society

potential energy surface and decays to the ground state through this sink. This model predicted the nonexponential population decay and viscosity effects observed in their experiments fairly well. Subsequently, Ben-Amotz and Harris4 6 generalized the idea proposed by Oster and Nishizawa2 that assumes a flat onedimensional potential energy curve along the torsional coordinate and “pinhole” sinks located at equally distant positions from the vertically excited wavepacket. They applied this model to their experimental results and concluded that their model is better than the BFO model. Currently, it is generally concluded that there exists an intermediate nonradiative state Sx, which has a distorted structure, and the vertically excited wavepacket passes through this state in the decay process. The existence of the intermediate state is inferred from the plateau region16 20 or a rise component observed in the pump probe measurement.8,10 Also Martin et al. predicted the existence of conical intersection between the S1 and ground states in their experiments on a julolidino analogue of crystal violet, which is one of the TPM dyes, and the decay pathway through this conical intersection was proposed.21 In this paper, we investigate the excited-state potential energy surfaces of MG using ab initio electronic structure calculations Received: April 12, 2011 Revised: July 1, 2011 Published: July 25, 2011 8808

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Figure 1. Structure of malachite green (MG).

and examine the ultrafast nonradiative decay processes from both the S1 and S2 states. Because it has been considered that the twisting motion of the phenyl rings dominates the kinetics of the TPM dyes, we focus on the nonradiative deactivation mechanism along these coordinates. There have been several calculations of vertical excitation energies by time-dependent density functional theory (TD-DFT),22,23 and very recently potential energy profiles were calculated along the torsional coordinate of phenyl rings by TD-DFT,14 but to the best of our knowledge, ab initio quantum chemical calculations including the optimization of conical intersection have not been performed for the investigation of the decay process. Section II describes the computational methods, and results and discussion are presented in section III. Conclusions are given in section IV, which also includes the future directions of research.

II. COMPUTATIONAL METHOD The geometry optimization in the electronic ground state is performed without any geometrical constraints using the MP2 method with the DZP basis set,24 where the polarization functions are omitted for hydrogen atoms to reduce the computational cost. After this optimization, potential energies of the ground and excited states are computed by the state-averaged complete active space self-consistent field (SA-CASSCF) method using the same basis set as above. The active space in the SACASSCF calculations consists of twelve π orbitals of phenyl rings and one unoccupied p orbital of the central carbon atom (12 electrons in 13 orbitals). The ground and two low-lying excited states are included with equal weights in the averaging procedure. The CASPT2 calculations25 are subsequently carried out to include dynamic electron correlation for quantitative description of the energetics and a level shift with a value of 0.2 is applied.26 The excited-state potential energy profiles are obtained by CASPT2 calculations at the geometries optimized by the SACASSCF method. Unless otherwise noted, on the geometry optimization in the excited states by SA-CASSCF calculations, the central four carbon atoms (C1, C2, C3, and C4) are constrained to lie in planar, and also the following each set of four carbon atoms are constrained to be in a plane as well to define the rotational angle of phenyl rings clearly: (C1, C2, C5, and C6), (C1, C3, C15, and C16), and (C1, C4, C20, and C21). Hereafter, we use the following three dihedral angles, j1(C5 C2 C1 C3), j2(C15 C3 C1 C4), and j3(C20 C4 C1 C2) to discuss the relaxation dynamics on the excited-state

Figure 2. Equilibrium structure of MG in the electronic ground state optimized by the MP2 method. The bond lengths are given in units of Å.

Figure 3. Natural orbitals involved in the excitations to the S1 and S2 states at the equilibrium structure in the electronic ground state.

potential energy surfaces (see Figures 1 or 2 for the numbering of atoms). The TD-DFT calculations are also performed with the B3LYP combination of exchange and correlation functionals and also Coulomb attenuated B3LYP (CAM-B3LYP) functionals27 for evaluating the vertical excitation energy at the equilibrium structure for comparison. The SA-CASSCF and CASPT2 calculations are carried out by the MOLPRO2008.1 package,28 while the TD-DFT calculations are performed using the GAMESS package.29

III. RESULTS AND DISCUSSION A. Equilibrium Structure and Vertical Excitation Energies. The equilibrium geometry in the ground state optimized by the MP2 calculation without any geometrical constraints is shown in Figure 2. The calculation predicts the minimum energy structure almost in the C2 symmetry, where j2(C15 C3 C1 C4) ≈ j(C21 C4 C1 C3). The dihedral angles j1(C5 C2 C1 C3) and j2(C15 C3 C1 C4) were calculated to be 41.5 and 28.8°, respectively. The twisted structure of phenyl rings is due to steric hindrance between the hydrogen atoms, H25 and H30. The bond lengths are also shown in Figure 2. The excitations to the S1 and S2 states are characterized by π f π* transition in both cases. Figure 3 shows the SA-CASSCF natural orbitals involved in these transitions. The excitations to the S1 and S2 states are viewed as HOMO f LUMO and 8809

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Table 1. Mulliken Partial Charges of Selected Atoms for the S0, S1, and S2 States at the Equilibrium Geometry in the Ground Statea S0

S1

C1

+0.36

+0.19

+0.18

C2

0.05

0.04

+0.04

C3 (C4)

0.06

+0.03

+0.00

C5 (C6)

0.18

0.21

0.15

C7 (C8) C9

0.11 0.12

0.11 0.15

0.10 0.06

Table II. Vertical Excitation Energies for the S1 and S2 States at the Equilibrium Structure in the Ground Statea

S2

C15 (C20)

0.13

0.14

0.18

C16 (C21)

0.12

0.14

0.15

C17 (C22)

0.27

0.25

0.27

C18 (C23)

0.26

0.22

0.20

C19 (C24)

+0.44

+0.44

+0.39

N33 (N34)

0.44

0.42

0.45

C35 (C36) C37 (C38)

0.33 0.34

0.33 0.33

0.33 0.34

S1 S2

TDDFT

TDDFT

SA-CASSCF

CASPT2

(B3LYP)

(CAM-B3LYP)

exp.

2.91 (1.12) 3.96 (0.38)

2.02 (0.78) 2.80 (0.27)

2.52 (0.85) 3.06 (0.34)

2.71 (0.97) 3.46 (0.46)

2.00 2.95

a

The energies are given in units of eV and the numbers in parentheses are oscillator strengths. Experimental results are taken from ref 30.

a

The density matrices obtained by SA-CASSCF calculations are used in obtaining the charges.

HOMO-1 f LUMO transitions, respectively. As seen in the figure, the S1 transition involves a charge transfer from the substituted phenyl rings to the central carbon atom (C1), while the S2 transition is associated with a charge transfer from both the substituted and unsubstituted phenyl rings to C1. Table 1 shows the Mulliken partial charges of selected atoms in the S0, S1, and S2 states, calculated from density matrices obtained by the SA-CASSCF wave functions. The decrease in charge of C1 indicates the charge-transfer character in both the S1 and S2 excitations. The increase in charge of the C3 (or C4) atom in the S1 excitation and the increase in charge of the C2 and C3 (or C4) atoms in the S2 excitation are consistent with the charge-transfer character inferred from the natural orbitals described above. The nitrogen atoms carry relatively large negative charge and the charge remains almost unchanged upon photoexcitation. The vertical excitation energies obtained by SA-CASSCF calculations are given in Table II. As is seen in the table, they are overestimated in both excitations in comparison to experimental values, which is usually attributed to insufficient treatment of dynamic electron correlation. The subsequent CASPT2 calculations reproduced the excitation energies quite well (see Table II). This agreement may be somewhat fortuitous because the experimental values are measured in water solution,30 while the calculated values correspond to the excitation energy in the gas phase. Usually, excitation energy in the gas phase would be higher than in solution. However, the CASPT2 method has tendency to underestimate the ππ* excitation energy. These factors might have brought this agreement, but at least the calculated results show quantitative accuracy. The excitation energies obtained by TD-DFT are also included in Table II, where in this case the ground-state geometry is optimized by the DFT(B3LYP) method. Because the excitations to both S1 and S2 have the charge-transfer character, the excitation energies obtained by B3LYP functionals would be slightly underestimated. The TD-DFT calculation with CAM-B3LYP functionals, which accounts for long-range electron electron exchange interactions, predicts higher excitation energies than those with

Figure 4. Optimized structure in the S1 state obtained by SA-CASSCF calculation.

B3LYP functionals. The CASSCF oscillator strengths are 1.12 and 0.38 for the S1 and S2 excitations, respectively, as shown in Table II. The CASPT2 oscillator strengths are obtained using the vertical excitation energies by CASPT2 and transition dipole moments taken from the SA-CASSCF calculations. B. Relaxation Pathway from the S1 State. The geometry optimization in the S1 state was performed with the SA-CASSCF calculations. We have found two minima, both of which involve large displacement of torsional angles of phenyl rings, as is shown in Figure 4. In both structures, two phenyl rings have torsional angle of about 90°, while the other ring has the one close to 0°. We refer to Structure-I (St-I) for the structure where two substituted phenyl rings have torsional angle of about 90° (close to C2v), and the other structure, where the unsubstituted and one of the substituted phenyl rings have torsional angle of about 90°, to Structure-II (St-II). Although St-II is slightly lower in energy than St-I by 0.18 eV at the SA-CASSCF level, this relation is reversed by inclusion of dynamic electron correlation through the CASPT2 calculations and in this case St-I is lower in energy than St-II by 0.24 eV. When we reoptimize the geometry without any geometrical constraints of planarity starting from both St-I and St-II, very small structural changes are observed. The energies are lowered by ∼0.02 eV for both St-I and St-II at the SACASSCF level, and the change of torsional angles are within 5°. Since it is generally recognized that the twisting of substituted phenyl rings is the primary deactivation pathway, we explored potential energy surfaces along this coordinate. First, we investigate the pathway of the synchronous rotation of substituted phenyl rings (j2 = j3) that leads to St-I. Figure 5a shows the CASPT2//CASSCF potential energy profiles as a function of torsional angles j2 (= j3), where all other internal coordinates were optimized at the SA-CASSCF level in the S1 state. It is seen that the S1 state exhibits a relatively flat potential energy curve along this torsional coordinate and a slight increase in energy is 8810

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Figure 5. (a) CASPT2 potential energy profiles for fixed torsional angles of substituted phenyl rings j2 = j3 at the geometries obtained by SA-CASSCF calculations. All other internal coordinates are optimized in the S1 state. Energies are relative to that at the equilibrium structure in the ground state. (b) Contour plots of two-dimensional potential energy surface in the S1 state for fixed torsional angles, j1 and j2 = j3, obtained by CASPT2//CASSCF calculations. The cross mark represents the position of the equilibrium structure in the electronic ground state.

Figure 6. Optimized structure of MECI point between the S1 and S0 states, with natural orbitals at the SA-CASSCF level.

observed with increasing the torsional angle. The barrier height relative to the value at j2 (= j3) = 30° is ∼0.3 eV. As seen from the shape of the potential energy curves of S1 and S2, the electronic characters of these states are interchanged around j2 (= j3) = 70 80°. Because it is seen that this twisting motion accompanies the rotation of unsubstituted phenyl ring, the two-dimensional potential energy surface for torsional angles, j1 and j2 (= j3), was also determined by CASPT2//CASSCF calculations, where all other internal coordinates were optimized in the S1 state at the SA-CASSCF level. The contour plots are given in Figure 5b and this result supports a picture of the simultaneous rotation of phenyl rings after the photoexcitation. However, it is found that the synchronous rotation of substituted phenyl rings (i.e., j2 = j3) does not correspond to the minimum energy pathway that reaches St-I. When we relax the constraint j2 = j3 in Figure 5a and explore the potential energy surface, it is found that the asynchronous pathway where one of the substituted phenyl rings rotates first until its torsional angle reaches about 90°, followed by the rotation of the other substituted phenyl ring, is slightly preferable in energy to the synchronous one. This is an apparently distinct pathway from the synchronous one, but the difference in barrier height for these

two pathways is very small (∼0.15 eV), and in reality, the molecule would not follow these ideal pathways and it may be hard to distinguish these pathways. Around the St-I structure, potential energies of the S1 and S0 states are very close, which implies the existence of conical intersection. The population in the S1 state would be transferred to the ground state through this conical intersection. We then optimized the minimal energy conical intersection (MECI) point at the SA-CASSCF level of theory without any geometrical constraints, staring from the St-I structure. The optimized structure (hereafter denoted as MECI-I) is given in Figure 6, where the torsional angles are j1 = 11.0°, j2 = 91.6°, and j3 = 105.4°. The natural orbitals are also shown in this figure. The dominant configurations for the ground and first excited state at this point are similar to those at the Franck Condon region, where the ground and first excited state have configurations of (jHOMO-1)2(jHOMO)2(jLUMO)0 and (jHOMO-1)2(jHOMO)1(jLUMO)1, respectively. The CASPT2 energies for the S0 and S1 states at MECI-I were calculated to be 2.24 and 2.54 eV, respectively, implying that the MECI geometry is different between the SA-CASSCF and CASPT2 levels. Due to the highly expensive cost of the CASPT2 calculations, we do not optimize the MECI points at the CASPT2 level, but at least, the average of 8811

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The Journal of Physical Chemistry A these energies 2.39 eV would be a good estimate, and in fact the CASPT2 energies for S1 and S0 at j2 = 90.0° in Figure 5a are very close to each other; therefore, the excited-state population will be transferred to the ground state around this structure. At this point it is interesting to note that the relaxation to the equilibrium structure in the ground state possesses the possibility of bifurcating pathways after passing through this conical intersection. One of them involves the twisting of the phenyl rings in the opposite direction from the motion on the S1 surface (backward pathway), while in the other pathway the molecule keeps the twisting motion of phenyl rings and accordingly the torsional angle is increased further (forward pathway), both of which go back to the equivalent equilibrium structure in the ground state. This bifurcating deactivation mechanism is schematically shown in Figure 7. The shape of the potential energy curve given in Figure 5a implies that a state-switch to the ground state may occur with a torsional angle slightly smaller than 90°. Therefore, in the course of relaxation on the excited-state potential energy surface, if phenyl rings have enough momentum to keep their direction, the molecule would decay through the forward pathway.

Figure 7. Schematic illustration of deactivation mechanisms via bifurcating pathways passing through conical intersection.

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The relaxation pathway which leads to St-II is also calculated under the restriction of j1 = j2, as in the same way explored in the previous pathway. The CASPT2//CASSCF potential energy curves are given in Figure 8a. As seen in the figure, the potential energy curve in the S1 state exhibits a flat surface with the existence of very low barrier connecting to St-II. The twodimensional potential energy surfaces for torsional angles, j1 (= j2) and j3, are also given in Figure 8b for CASPT2// CASSCF calculations and the barrier in this pathway leading to St-II is lower than the previous pathway which connects to St-I. Here it is noted that St-II is no longer a local minimum configuration when evaluated at the CASPT2 level. There is a very shallow well at j1 = j2 ≈ 70°, as seen in Figure 8b. In contrast to St-I, it is seen that the energy difference between S1 and S0 at St-II is large. The MECI search was also performed from St-II at the SA-CASSCF level without any geometrical constrains, and the MECI geometry was located with an almost planar structure for the central four carbon atoms (C1, C2, C3, and C4) as shown in Figure 9 (hereafter denoted as MECI-II). It is interesting to note that at MECI-II the dimethylamino group of substituted phenyl ring which lies in the same plane as the central four carbon atoms rotates almost 90°. This displacement destabilizes the ground state energy and makes it accessible to the conical intersections. The CASPT2 energies at this point were calculated to be 2.60 and 2.64 eV for S0 and S1, respectively, and the average value 2.62 eV is higher than energy at St-II by 0.32 eV. Because the vertical excitation energy at the Franck Condon region is 2.02 eV by CASPT2 calculations, the molecule would exhibit slow dynamics on the S1 potential energy surface. There is a small barrier connecting the Franck Condon region and St-I (St-II) with a barrier height of ∼0.2 eV (∼0.1 eV). When the molecule approaches either St-I or St-II, the nonradiative decay to the ground state through conical intersections would be observed. It is seen from the CASPT2 calculations that St-I is energetically stable than St-II and the energy at MECI-I is lower than that of MECI-II. Therefore, the transition to the ground state would occur preferentially through MECI-I. However, because the energy difference between these structures is relatively small, there would be a good chance that the molecule decays though MECI-II.

Figure 8. (a) CASPT2 potential energy profiles for fixed torsional angles of unsubstituted and one of substituted phenyl rings j1 = j2 at the geometries obtained by SA-CASSCF calculations. All other internal coordinates are optimized in the S1 state. Energies are relative to that at the equilibrium structure in the ground state. (b) Contour plots of two-dimensional potential energy surface in the S1 state for fixed torsional angles, j1 = j2 and j3, obtained by CASPT2//CASSCF calculations. 8812

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C. Relaxation Pathway from the S2 State. Several timeresolved spectroscopic experiments have been performed to provide insight into the relaxation dynamics of MG from the S2 state,30 32 and a relaxation mechanism through conical intersection between the S2 and S1 potential energy surfaces has been proposed.32 This conical intersection is thought to be promoted by the twisting of an unsubstituted phenyl ring.32 We have explored potential energy surface in the S2 state in the same way as in the S1 state. Figure 10a shows the CASPT2// CASSCF potential energy profiles along the synchronous torsional angle with j2 = j3, where all other internal coordinates were optimized in the S2 state. All states exhibit similar profiles to those optimized in the S1 state, but in contrast to the excitation to the S1 state, the initially excited population in the S2 state is on a downhill ramp potential and the torsional angles will increase much faster than in the S1 state. The two-dimensional potential energy surface is also calculated in the S2 state and the contour plot is given in Figure 10b. It is seen that the simultaneous rotation of three phenyl rings is expected in the relaxation process.

As seen in Figure 10a, it is anticipated that there exists intersection between the S2 and S1 potential energy surfaces at j2 = j3 = 70 80° in the course of relaxation. The MECI point between the S2 and S1 states is located using the SA-CASSCF calculation that is almost in the C2 symmetry (see Figure 11). After switching to the S1 state through this region, the decay to the ground state via the conical intersections between S1 and S0 is expected, which is similar to the relaxation dynamics from the S1 state. The potential energy profile along the synchronous rotation of substituted and unsubstituted phenyl rings with j1 = j2 fixed is also explored using the SA-CASSCF method as in the same way in the S1 state. In this case the potential energy increases as the torsional angle is increased (see the Supporting Information). Therefore, in the relaxation dynamics from the S2 state, the molecule moves toward St-I, and the decay to the ground state would occur almost exclusively through MECI-I. Finally, the oscillator strengths are calculated by the SACASSCF method along the geometries given in Figures 5a and 10a for the S1 and S2 transitions, respectively, and the result is given in the Supporting Information. It clearly shows that as the torsional angles are increased, the oscillator strength decreases, and it becomes almost zero around conical intersection.

Figure 9. Optimized structure of MECI point between the S1 and S0 states at the SA-CASSCF level.

Figure 11. Optimized structure of MECI point between the S2 and S1 states at the SA-CASSCF level.

Figure 10. (a) CASPT2 potential energy profiles for fixed torsional angles of substituted phenyl rings j2 = j3 at the geometries obtained by SACASSCF calculations. All other internal coordinates are optimized in the S2 state. Energies are relative to that at the equilibrium structure in the ground state. (b) Contour plots of two-dimensional potential energy surface in the S2 state for fixed torsional angles, j1 and j2 = j3, obtained by CASPT2// CASSCF calculations. The cross mark represents the position of the equilibrium structure in the electronic ground state. 8813

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IV. CONCLUSIONS AND FUTURE DIRECTIONS In this paper we have investigated the relaxation process of malachite green in the singlet excited states (S1 and S2) by highlevel ab initio calculations. The deactivation pathways connecting the Franck Condon region and conical intersection regions are identified and it is seen that the twisting motion of substituted phenyl rings is responsible for the deactivation process from both states. The initial population in the S1 state is on a flat surface, and the relaxation involves a rotation of phenyl rings. Two minima in the S1 state are found, both of which exhibit the structure where the torsional angle of two phenyl rings is about 90° and the other ring exhibits about 0°. Around these minima, there exist conical intersections and the molecule would decay back to the ground state through these points. The resulting highly distorted structure in the electronic ground state is related to the intermediate state Sx inferred in the experimental reports. The decay mechanism from the S2 state also involves a simultaneous rotation of the phenyl rings. In contrast to the excitation to the S1 state, the excited-state population is on a downhill ramp potential, and the fast barrierless relaxation would be expected. When the torsional angle of substituted phenyl ring is increased to 70°, the molecule reaches the conical intersections between the S2 and S1 states. After switching to the S1 state, the molecule would decay to the ground state through the conical intersection between S1 and S0, which is similar to the relaxation dynamics from the S1 state. The decay to the ground state would occur almost exclusively through MECI-I. We suggest that in both excitations there is the possibility of bifurcating pathways after passing through the conical intersections. In this work all calculations were carried out as a dye in vacuum. This is surely not sufficient to compare with experimental results, because most of the experiments were performed in the solution phase. One of the fascinating behaviors on the deactivation process of the TPM dyes is its strong solvent dependence, where one can observe microscopic interactions with solvent molecules and also macroscopic friction in different time scales. These solvent dependencies can be investigated in the hybrid treatment of quantum mechanics/molecular mechanics (QM/MM) approach, where a dye molecule is treated by ab initio calculations while surrounding solvent molecules are represented at the molecular level by empirical force fields. By combining with dynamical simulations, microscopic nature of solute and solvent dynamics of the TPM dyes can be investigated. Very recently, Tahara et al. measured the ground-state recovery of MG at air/water interface by femtosecond time-resolved electronic sum frequency generation spectroscopy13 and observed much slower dynamics than in solution. They argued that the slow dynamics observed at the interface may be due to both the high local viscosity and substantial change of the potential energy surface of MG at the interface. The above-mentioned QM/MM approach combined with dynamical calculations would also provide an explanation for observed slow dynamics in the viewpoint of local viscosity and different electronic interactions between MG and water molecules at the interface and in bulk water. While we have only studied the relaxation process of malachite green among various TPM dyes, it is also interesting to investigate the effects of substitution of a functional group connected to phenyl rings. For example, Maruyama et al. observed that the relaxation is faster in the aminophenyl groups compared with that in the dimethylaminophenyl groups.10 A more detailed

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investigation of the photophysical and photochemical processes of the TPM dyes is now currently in progress.

’ ASSOCIATED CONTENT

bS

Supporting Information. Potential energy surfaces, contour plots, and oscillator strength obtained by SA-CASSCF calculations. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT The authors thank Prof. Tahei Tahara at RIKEN for valuable discussions and comments on the manuscript. They are also grateful to Dr. Shohei Yamazaki for fruitful discussions. They gratefully acknowledge financial support by a Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology (MEXT, Japan) and a generous allocation of supercomputer time from the Research Center for Computational Science (RCCS), Okazaki, JAPAN. ’ REFERENCES (1) Duxbury, D. F. Chem. Rev. 1993, 93, 381–433. (2) Oster, G.; Nishijima, Y. J. Am. Chem. Soc. 1956, 78, 1581–1584. (3) F€orster, T.; Hoffman, G. Z. Phys. Chem. NF 1971, 75, 63. (4) Ben-Amotz, D.; Harris, C. B. J. Chem. Phys. 1987, 86, 4856–4870. (5) Ben-Amotz, D.; Harris, C. B. J. Chem. Phys. 1987, 86, 5433–5440. (6) Ben-Amotz, D.; Jeanloz, R.; Harris, C. B. J. Chem. Phys. 1987, 86, 6119–6127. (7) Sundstr€om, V.; Gillbro, T.; Bergstr€om, H. Chem. Phys. 1982, 73, 439–458. (8) Nagasawa, Y.; Ando, Y.; Okada, T. Chem. Phys. Lett. 1999, 312, 161–168. (9) Nagasawa, Y.; Ando, Y.; Kataoka, D.; Matsuda, H.; Miyasaka, H.; Okada, T. J. Phys. Chem. A 2002, 106, 2024–2035. (10) Maruyama, Y.; Magnin, O.; Satozono, H.; Ishikawa, M. J. Phys. Chem. A 1999, 103, 5629–5635. (11) Engh, R. A.; Petrich, J. W.; Fleming, G. R. J. Phys. Chem. 1985, 89, 618–621. (12) Nagasawa, Y.; Nakagawa, Y.; Nagafuji, A.; Okada, T.; Miyasaka, H. J. Mol. Struct. 2005, 735, 217–223. (13) Sen, P.; Yamaguchi, S.; Tahara, T. Faraday Discuss. 2010, 145, 411–428. (14) Rafiq, S.; Yadav, R.; Sen, P. J. Phys. Chem. B 2010, 114, 13988–13994. (15) Bagchi, B.; Fleming, G. R.; Oxtoby, D. W. J. Chem. Phys. 1983, 78, 7375–7385. (16) Mokhtari, A.; Fini, L.; Chesnoy, J. J. Chem. Phys. 1987, 87, 3429–3435. (17) Robl, T.; Seilmeier, A. Chem. Phys. Lett. 1988, 147, 544–550. (18) Martin, M. M.; Breheret, E.; Nesa, F.; Meyer, Y. H. Chem. Phys. 1989, 130, 279–287. (19) Martin, M. M.; Plaza, P.; Meyer, Y. H. J. Phys. Chem. 1991, 95, 9310–9314. (20) Martin, M. M.; Plaza, P.; Meyer, Y. H. Chem. Phys. 1991, 153, 297–303. (21) Jurczok, M.; Plaza, P.; Martin, M. M.; Rettig, W. J. Phys. Chem. A 1999, 103, 3372–3377. (22) Guillaumont, D.; Nakamura, S. Dyes Pigm. 2000, 46, 85–92. 8814

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dx.doi.org/10.1021/jp203415m |J. Phys. Chem. A 2011, 115, 8808–8815