Quantum Wave Packet Propagation Study of the Photochemistry of

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Quantum Wave Packet Propagation Study of the Photochemistry of Phenol: Isotope Effects (Ph-OD) and the Direct Excitation to the 1 πσ* State Heesun An and Kyoung Koo Baeck* Department of Chemistry, Gangneung-Wonju National University, Gangneung, Gangwondo, 210-702, Korea ABSTRACT: An earlier time-dependent quantum wave packet propagation study of the photochemistry of Ph
OH [J. Chem. Phys. 2005, 122, 224315] is extended to investigate isotope effects (for Ph-OD) and the dynamics initiated by direct (vibronically induced) excitation to the 1πσ* state. The isotope effect is significant only when the initially excited state is 1ππ*, that is, there are noticeable changes not only in the time scale but also in the branching ratio ~ /X ~ ) for the electronic states of the product Ph-O radical. In (A contrast, the isotope effect on the dynamics initiated by direct excitation to the 1πσ* state is very small. Our most important observation for the dynamics initiated by direct excitation to the 1πσ* state is that the initial excitation of the O
H stretch mode does not result in a noticeable enhancement of the product Ph-O radical ~ state, which corresponds to a dissociating H atom with low kinetic energy. The initial excitation of the CCOH torsion mode in the A ~ state that was observed in a vibrationally mediated twois the main reason for the enhancement of the product Ph-O radical in the A photon experiment [J. Chem. Phys. 2008, 128, 104307].

’ INTRODUCTION The photoinduced hydrogen elimination reaction of phenol has attracted significant interest in recent years as a prototype of the ultrafast photochemistry of aromatic biomolecules. One of the main dynamical aspects of this reaction is that there are conical intersections (CIs) between the dark dissociative S2(1πσ*) state and the initially excited bright S1(1ππ*) state and also with the electronic ground S0(1ππ) state.1 A mechanism based on tunneling through the S1/S2 conical intersection (CI) has been proposed to explain the excited-state hydrogen detachment and hydrogen transfer process.2 The coincidence of the two CIs, that is, the CI1 of 1ππ*
1πσ* and the CI2 of 1πσ*
S0, within the same coupling coordinates, namely, the stretching of the OH bond, r, and the torsion of the CCOH dihedral angle, θ, means that the main features of the potential energy surfaces (PESs) of the three states (S0, S1, and S2) can easily be described in a two-dimensional (2D) space.3 The relevance and importance of this 2D space in the photochemistry of phenol has subsequently been demonstrated by using elaborate ab initio characterization.4 The PESs in the 2D space have served as the main framework for the qualitative analysis of experimental studies.5
7 According to the time-dependent quantum wave packet description of the 2D diabatic PESs of the three states,3 the PES of the 1πσ* state is accessed through nonadiabatic coupling with the initially excited bright 1ππ* state. Lan et al. calculated the lifetime of the 1ππ* state as well as the branching ratio of the ~ (2σ) states of the ~ (2π) and A two dissociation channels to the X 3 Ph-O radical product. They showed that the nodal structure of the nuclear wave packet, which is determined not only by the r 2011 American Chemical Society

initial vibration level of the S0 state but also by the transition through the first CI1 of 1ππ*
1πσ*, has a profound effect on the nonadiabatic dynamics of the second CI2 of 1πσ*
S0. Based on these theoretical results, they proposed the possibility of the laser control of the overall time scale and the final branching ratio of the 1πσ* photochemistry of phenol via IR mode-specific excitation of the vibration levels in the S0 state, as has been demonstrated for ammonia.8 The results of a subsequent two-photon (IR + UV) experiment6 with phenol-d5 were analyzed with the theoretical results of Lan et al.3 A complementary indirect statistical understanding was suggested by Nix et al.,9 in which the νOH specific internal conversion (IC) from the initially excited S1 state to S0 is followed by predissociation along the S0 PES. This indirect mechanism was used to analyze their experimental observations.10,11 However, more recent studies of the time-scale of the H-atom detachment12 and of the dependence of the S1 state lifetime on the energy gap between the S1 and S2 states13 strongly support the nonadiabatic S1/S2 coupling mechanism2,3 rather than the indirect S1/S0 internal conversion scheme.9 A very recent study suggests the use of a higher symmetry point group (G4) for the nonadiabatic S1/S2 coupling scheme, and successfully explains the distributions of the vibration states observed in the UV photodissociation of phenol.14 In the new scheme, the ring-torsion mode (ν16a) enables the O
H bond fission. However, the consequences of this new S1/S2 coupling scheme for the branching ratio of the Received: August 23, 2011 Revised: October 7, 2011 Published: October 10, 2011 13309

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The Journal of Physical Chemistry A high and low recoil energies of the product H atom have not yet been explored. The above complementary views (nonadiabatic S1/S2 coupling vs S1/S0 internal conversion) seem to include all the possibilities for the very first step in the S1 state dynamics when the photoenergy is between 4.5 and 5.0 eV. Further, recent studies13,14 clearly support the view that the early time dynamics is that of nonadiabatic S1/S2 coupling.2,3 However, the dominant production of H atoms with high kinetic energy ~ state of the phenoxyl radical), (which is associated with the X as found for one-photon dissociation with Eexcite = 47132 or 43656 cm
1 (5.84 or 5.41 eV)6 or with 200 nm (6.2 eV),12 cannot be clearly explained by the nonadiabatic 1ππ/
1πσ/ coupling scheme of Lan et al.3 As the photon energy becomes larger than the energy of the CI1 of 1ππ*
1πσ*, which is located near 5.0 eV,4,11 additional possibilities have to be considered: the path through the prefulvenic CIpref of S1/S0 near 5.3 eV4 and also the involvement of the second 1ππ* state (S3) near 6.4 eV, as shown in Figure 1 of ref 11. When the photon energy becomes higher than the energy of the vertical excitation to the S2(1πσ*) state, 5.365 eV,13 another interesting but contentious possibility is dynamics initiated by direct excitation to the S2 state. The possibility of any involvement of direct excitation to the πσ* state has been completely neglected in previous studies due to the weak electronic oscillator strength of the S2(πσ*) r S0(ππ) transition. However, the possibility of direct (vibronically induced) excitation to the S2 state was deduced in section III-E of a very recent study,14 but the consequences of this direct excitation were not explored in detail. Some parts of the discussion of this phenol system, such as the early time dynamics for photon energies larger than 5.4 eV, seem as yet incompletely resolved. This study had two principal aims. The first was to extend a previous study3 to include the possible isotope effects of the replacement of the abstracting hydrogen atom of Ph
OH with a deuterium on the details of the dynamics. The main aim of this extension was to study the effects on the branching ratio of small changes in the spatial extension of the initial wave packet. The isotope effect on the time-scale of the dynamics can be treated with a simpler kinetic model, but the effects on the branching ratio cannot. The tunneling effect plays an important role in the nonadiabatic 1ππ*
1πσ* coupling because of the barrier height with respect to CI1 of approximately 0.5 eV, so the branching ratio determined by the combination of CI1 and CI2 can be significantly affected. Little discussion or consideration of the isotope effect on the branching ratio is found in previous studies of phenol and related systems. Further experimental studies of Ph-OD, as shown for the case of the thiophenol system,15 could provide additional insights into the detailed dynamics. The second target of the present study was to determine the consequences of treating the dark S2(1πσ*) state as the initial excited state rather than the bright S1(1ππ*) state, as was partially investigated in the previous theoretical study in conjunction with the phase effect of the coherent control of a branching ratio.16 Although the interplay of the two CIs turns out to have a profound influence on the wave packet dynamics of phenol when the initially excited state is the 1ππ* state,3 the effects of the first CI1 when the initially excited state is the 1πσ* state were previously unknown. This second aim was motivated by recent experimental studies of the photochemistry of phenol-d56 and thiophenol derivatives,15 for which the initially

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Figure 1. (a) Diabatic potential energy profile at θCCOH = 0, (b) diabatic potential energy surfaces Vii, and (c) the diabatic coupling terms Vij,i6¼j. This figure is adapted with permission from Lan et al.3. 2005 American Institute of Physics.

excited state was not the S1(1ππ*) state but the S2(1πσ*) state. Further examples of the possible direct photoexcitation to the dissociative 1πσ* excited state were discussed in a recent review.17 Recent studies of the photodissociation of tyrosine, a biological unit of phenol derivative, found ultrafast features with τ even less than 100 fs (fs);18 this observation also inspired us to explore the possibilities of the direct excitation to the πσ* state with a photon of high energy. Although the activations of the 16a(a00 ) and 18b(a0 ) modes have been observed in the product phenoxyl radical,10 a detailed study of the vibronic coupling responsible for the direct (vibronically induced) excitation to the πσ* state was not attempted in the present study.

’ COMPUTATIONAL METHOD The Hamiltonian operator of the Schrodinger equation to be solved for the phenol system in the above-mentioned 2D space3 consists of the following terms 1 0 1 0 1 0 0 V11 V12 V13 C B C B C B C H ¼ TN B @ 0 1 0 A þ @ V21 V22 V23 A V31 V32 V33 0 0 1 13310

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Figure 2. Eigenvalues (left-hand side) and the eigenfunctions (righthand side) of some vibration levels of the ground S0 electronic states of Ph
OH (upper) and Ph-OD (lower).

where the nuclear kinetic operator, TN, has the following form, as defined and used in the study of Lan et al.3 TN ¼


p 2 ∂2 p 2 ∂2
2μOH ∂r 2 2I ∂θ2

Exactly the same functional forms as used in the previous study3 were adopted here for the analytical representation of the diabatic potential energy surfaces (PESs; V11, V22, V33) and the diabatic couplings (V12, V23, V13), as shown in Figure 1. The indices 1, 2, and 3 refer to the diabatic S0(1ππ), 1πσ*, and 1ππ* states, respectively. The diabatic PESs were generated via a suitable unitary transformation of the adiabatic PESs computed by the state averaged CASSCF(10,10)/aug-cc-pVDZ level. The aug-cc-pVDZ set was further augmented with one diffuse s function and one set of p functions at oxygen, and two diffuse s and two sets of p functions at the dissociative hydrogen atom (see ref 3 for further details). The adiabatic PES of the ground S0 electronic state was constructed by diagonalizing the three by three matrix calculated with the above functions for Vij. The adiabatic PES of S0 was then represented on the fast Fourier transform (fft) grid space defined by 100 points of rOH (ranging from 1.0 au to 8.0 au) and 80 values of θCCOH (ranging from
π to +π radians). The vibration wavepackets of the adiabatic ground S0 electronic state were generated by solving the time-dependent Schrodinger equation with the Chebychev imaginary method,19 as implemented in the WavePacket program,20 with a time step of 0.1 fs. Once a selected wave packet of the S0 state is vertically excited onto the diabatic PESs of the 1ππ* state (V3) or the 1πσ* state (V2), the time-propagation of the excited wave packet is treated by solving the time-dependent Schrodinger equation with the

Figure 3. Results of the propagation after the vertical excitation from S0 to S1(1ππ*). The changes in the probabilities (populations) in the diabatic 1ππ*(P3), 1πσ*(P2), and S0(P1) states are shown on the left of the figure, and the snapshots of the propagating wave packets 20 fs after the excitation are shown on the right. The upper half of the figure shows the results for Ph-OH and the lower half shows the results for Ph-OD.

split-operator method,21 as included in the WavePacket program,20 with a time step of 0.1 fs. In order to propagate up to the near dissociation limit of the OH bond, the two-dimensional fft grid space was extended to include 400 points of rOH (ranging from 1.0 au to 29.0 au) and 80 points of θCCOH (ranging from
π to +π radians). To prevent artificial reflection of the dissociating parts of the wave packet at the edge of the fft grid space for rOH, a damping function, f(ri)=(ri-rmask)2 for ri g rmask, was used with rmask = 27.0 au. The time-dependent propagations were carried out for 3000 fs for Ph-OD in contrast to 200 fs for Ph
OH because of the much slower dynamics of Ph-OD due to the isotope effect, as is discussed in the following section. Except for the initial wavepackets shown in Figure 2, all quantities in Figures 3
6 of the present work are diabatic.

’ RESULTS AND DISCUSSION Initial Wave Packets. The vibration quantum numbers for the O
H stretch and the CCOH torsion mode are denoted nr and nθ, respectively. The eigenvalues of the (nr,nθ) vibration levels and the corresponding wave packets of the (0,0), (0,1), (1,0), and (1,1) vibration levels in the ground electronic S0 state are shown in Figure 2a and b for Ph-OH and Ph-OD, respectively. The magnitudes of the eigenvalues of phenol obtained with our 13311

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Figure 6. Same as Figure 5, but for the case (nr,nθ) = (1,2).

Figure 4. Percent populations of the diabatic ππ*(V3), πσ*(V2), and S0(V1) states, calculated at 200 fs for Ph-OH (at 3000 fs for Ph-OD), are represented by black, shaded, and white boxes, respectively. Note that the dissociation limit of S0(V1) corresponds to the excited electronic ~ (2σ) of the phenoxyl radical and a H atom of low kinetic energy. state A

Figure 5. Changes in the populations are shown in the boxes on the left, and snapshots of the wave packets propagating on each diabatic PES at 10 fs after the vertical excitation are shown on the right, for the case (nr, nθ) = (0,0). The existence of the ππ* state is completely neglected in scheme 1 in Table 1, but is included in scheme 2 in Table 1.

calculations are slightly different from the corresponding values of Lan et al. (for example, the eigenvalue of the (0,0) level is 2188 cm
1 according to our study, whereas a value of 2202 cm
1 was obtained by Lan et al.), but the gaps between our eigenvalues are the same as those of Lan et al.3 The isotope effect on the eigenvalues is evident: the gap between the (0,0) and the (0,1) levels decreases from 266 cm
1 in Ph-OH to 201 cm
1 in Ph-OD, and the difference between the (0,0) and the (1,0) levels decreases from 3895 to 2888 cm
1, as expected. Although the isotope effects on the wave functions (i.e., the wave packets) are equally discernible, note that the special extensions of the wave packet of Ph-OD (see the lower right of Figure 2) are slightly narrower than the corresponding extensions of Ph-OH (see the upper right of Figure 2). Propagation after Excitation to the 1ππ* State. All of the features of the dynamics of phenol after the excitation to the 1ππ*

state discussed in this subsection have already been discussed fully by Lan et al.3 Their main points are, however, reviewed here to set up the discussions in the following subsections concerning the isotope effects and the dynamics after the direct excitation to the 1πσ* state. When nr is zero, the initial wave packet vertically excited up to the 1ππ* state does not change its central position even after propagations of up to several hundreds of femtoseconds. Therefore, their time propagations are not shown here. Only a very small portion of the wave packet leaks out through the barrier of the first conical intersection, CI1, of 1ππ*
1 πσ*.3 The proportions of the population in the 1ππ* state after time-propagation for 200 fs are 95, 89, and 87% when nθ is 0, 1, and 2, respectively, as shown in the upper left of Figure 4. The lifetime of the S1 state has been reported to be 2.2
2.4 ps,13,22 and the above population losses (5, 11, 13%) within 200 fs imply that the tunneling rates of the actual system with 33 internal degrees of freedom are overestimated by the present 2-D model space. Once the vibration quantum number nr of the initial wave packet increases to 1, which corresponds to the excitation of the OH stretch mode, the wave packet excited to the 1ππ* state (V3 in Figure 3) quickly leaks out to the 1πσ* state (V2) through the first CI1 (represented by the first x mark at rOH = 1.16 Å) of 1 ππ*
1πσ* and then bifurcates into the 1πσ* state and the S0 state (V1) at the second CI2 (the second x mark at rOH = 1.96 Å) of 1πσ*
S0. The contour maps on the right of Figure 3a show the wave packets on the diabatic PESs of the three electronic states 20 fs after the excitation of the wave-packets corresponding to the (1,0), (1,1), and (1,2) vibration levels. As the time propagation proceeds, the population of the 1ππ* state (P3 on the left of Figure 3) gradually decreases while those of the 1πσ* and S0 states increase accordingly, as represented by P2 and P1 in Figure 3, respectively. The changes in the populations of the three states with propagation time depend upon the vibration levels of the initial wave-packets, as shown on the left of Figure 3. ~ (2σ) state of the The proportions dissociated to the excited A Ph-O radical, P1, calculated at 200 fs, turn out to be 69, 63, and 81% when nθ is 0, 1, and 2, respectively, with nr = 1. The results are summarized in the upper-middle part of Figure 4, with other cases. Lan et al. noticed the alternation of the ratios and mentioned a kind of odd-number effect.3 When the vibration quantum number nr of the initial wave packet increases to 2, the proportions dissociated to the ground state Ph-O radical are 63, 70, and 78% when nθ is 0, 1, and 2, respectively, as shown in the upper right of Figure 4. 13312

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~ /X ~ ) on the Table 1. Dependences of the Branching Ratio (A Quantum Numbers of the Initial Wave Packets of the S0 Statea scheme 0b

scheme 1

scheme 2

S0 f π* f CI1 f σ* f CI2 f

S0 f σ * f CI2 f

S0 f σ* f CI1 f σ* f CI2 f

(0,0)

0.41 [0.41]

0.41 [0.36]

(0,1)

1.63 [1.66]

1.24 [1.36]

(0,2)

2.35 [2.44]

1.46 [1.55]

(nr,nθ)

(1,0)

2.36 [2.82]

0.46 [0.45]

0.51 [0.41]

(1,1)

1.74 [2.99]

1.93 [1.92]

1.86 [1.60]

(1,2) (2,0)

4.99 [7.97] 1.74 [3.97]

2.85 [2.80] 0.49 [0.47]

2.09 [1.97] 0.52 [0.46]

(2,1)

2.45 [1.59]

2.16 [2.07]

2.14 [1.84]

(2,2)

3.73 [3.79]

3.02 [2.94]

2.72 [2.47]

The results corresponding to the direct excitation to the 1πσ* state are given in the columns for schemes 1 and 2. The branching ratios for PhOD are given in square brackets. b Our results for Ph-OH for scheme 0 are the same as previous results.3 a

Isotope Effect. When the dissociating hydrogen atom is replaced by a deuterium, the first noticeable isotope effect is the slow-down of the time-scale, as expected and demonstrated in the left of Figure 3b. In spite of the large difference in the time scale due to the isotope substitution, the overall features (the shape of the contour representation) of the propagating wavepackets of Ph-OD at 20 fs are very similar to those of the corresponding features of Ph-OH at 20 fs, as collated on the right of Figure 3, but the magnitudes of P2 and P1 in the Ph-OD case are much smaller than those of Ph-OH. When the initial wave packet of the (1,0) vibration level of Ph-OH was excited to the 1ππ* state, approximately s200 fs was required before the population of the 1ππ* state, P3, decreased down below 1%. In the Ph-OD case, the corresponding time is approximately 3000 fs due to the isotope effect. When nr = 0, the proportions of the populations remaining in the 1ππ* state of Ph
OH at 200 fs are 95, 89, and 87% for nθ of 0, 1, and 2, respectively, whereas the values are 97, 93, and 90% for Ph-OD, even at 3000 fs, as shown in the lower part of Figure 4. These changes also reflect the reduced tunneling effect that results from the isotope substitution. An earlier experiment on the radiationless decay of the S1 state of phenol reported a reduction in the decay rate of over 2 orders of magnitude,23 and a recent experiment observed that the lifetimes of the S1 states are 2.4 ns (Ph-OH) and 13.3 ns (Ph-OD).22 The main target of the present study of the isotope effect was the branching ratio of the high and low kinetic energies of the ~ ) and dissociated H atom, which correspond to the ground (X ~ ) electronic states of the dissociated phenoxyl radical, excited (A respectively. The branching ratios were calculated at 200 fs for Ph-OH but at 3000 fs for Ph-OD. When nr = 1, the proportions ~ (2σ) state of the Ph-O radical, P1 in dissociated to the excited A Figures 3 and 4, are for Ph-OH 69, 63, and 81% for nθ = 0, 1, and 2, respectively, in contrast to 73, 75, and 87%, respectively, for Ph-OD. The odd
even effect found for Ph-OH is now significantly weaker in the Ph-OD case. When nr = 2, on the other hand, the corresponding proportions are 63, 70, and 78% for Ph-OH and 78, 61, and 78% for Ph-OD, as shown in Figure 4. The odd
even effect reappears here in the isotope effect. The nodal structure of the initial wave packets is not changed by the

isotope substitution, so the above change in the odd
even effect seems to be caused by slight changes in the degree of the spatial extent of the initial wave packets and subsequent additional changes after the interference with the first CI1. The dependences of the branching ratio on (nr,nθ) are given in the second column (the column for scheme 0 of Table 1), along with those of the other cases discussed in the subsections below. These changes in the branching ratio due to isotope substitution provide useful information for future experimental studies; the consequences of this isotope effect have not previously been adequately explored and utilized in experimental studies of the phenol system. Dynamics after Direct Excitation to the 1πσ* State. The dynamics resulting from the direct excitation of the (0,0) initial wave packet to the 1πσ* state has been investigated in a study of optimal control simulations with a chirped laser field.16 The virtual dynamics initiated by direct excitation to the 1πσ* state by a continuous-wave (not chirped) light source, as examined in a very recent study,14 was investigated in this study to determine further details of the effects of the nodal shape of the initial wave packet, that is, the initial vibration level of the ground S0(1ππ) state. The virtual dynamics was described with two schemes in the present theoretical study. In the first scheme (scheme 1), the interference between the propagating wave packet and CI1 is completely neglected, that is, the CI between 1πσ* and 1ππ* is treated as if it does not exist. Scheme 1 corresponds to cases where the PES of the 1ππ* state is located above the PES of the 1 πσ* state, as in the case of pyrrole, and for which there is therefore no conical intersection with the 1ππ* state along the dissociation channel of the O
H bond. In the second scheme (scheme 2), the effects of CI1 are included by using the same diabatic coupling term V23, as described in the above subsections. Typical results for the two schemes for initial quantum numbers of (0,0) and (1,2) are shown in Figures 5 and 6, respectively. When the initial wave packet of the S0 state is vertically and directly excited up to the PES of the dissociating 1πσ* state, as anticipated, the wave packet propagates very quickly along the PES of 1πσ*, even when the quantum number nr is zero and ~ (2σ) and bifurcates at CI2 into two dissociation limits, the A 2 ~ ( π) states of the Ph-O radical. All the processes are almost X complete within approximately 20 fs, as shown by the changes in the Pi values on the left of Figures 5 and 6. Almost no isotope effect is evident on this time scale in these cases. Some snapshots of the propagating wave packets at 10 fs are shown on the right of Figures 5 and 6. The proportion of the wave packet trapped in the 1 ππ* state due to the inclusion of CI1 in scheme 2 is shown by the contour map on the PES of V3, in the lower-middle areas of Figures 5 and 6. The proportion trapped in the 1ππ* state in scheme 2 increases as the value of nθ increases, so the difference between schemes 1 and 2 also increases with nθ. The branching ~ /X ~ (corresponding to P1/P2) for the (0,0) initial wave ratio of A packet for scheme 1 is calculated to be 0.41. The dependence of the branching ratio on the vibration quantum numbers of the initial wave packet is summarized in the last two columns of Table 1. The branching ratios corresponding to those shown in Figure 4 are also included in the second column (scheme 0) of Table 1 for easier comparison. The branching ratios of the PhOD system are given in parentheses in Table 1. Several interesting results are evident in Table 1. First, the magnitudes of the effects of CI1 on the virtual dynamics are rather small, and the branching ratio is not much altered in most cases; the values in the fourth column (scheme 2) are qualitatively the 13313

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The Journal of Physical Chemistry A same as the corresponding values in the third column (scheme 1), except for the initial wave packet with (nr = 0, nθ = 2). This effect arises because the magnitude of V23 is rather small, as shown in Figure 1c. The branching ratios of the initial wave packets with (1,0), (1,2), and (2,0) depend significantly on whether the excited state is 1ππ* (scheme 0) or 1πσ* (schemes 1 and 2). Note also that the higher the value of nθ, the larger the effect of CI1, that is, the larger the difference between the branching ratios of schemes 1 and 2. This result arises because the magnitude of V23 becomes larger as θ increases, as shown in Figure 1c. A higher value of nθ implies that a higher proportion of the initial wave packet is spread over a larger range of θ. Although the time-scale of the changes in the probabilities (relative populations, Pi) according to scheme 2 is slightly retarded as the value of nθ increases, most of the dynamics are completed within about 50 fs, even when nθ is 2. This time scale is comparable to and shorter than the conclusion of a recent experiment: 150 fs was suggested as an upper limit for H-atom elimination from phenol.18 Unfortunately, the effects of internal vibration relaxation (IVR) from the vibronic coupling modes, which is responsible for the direct excitation from S0 to the 1πσ* state, to the active reaction path (the stretch of the O
H bond) was not included in the present study. The most significant difference between the dynamics of scheme 0 (initial excitation to the 1ππ* state) and schemes 1 and 2 (direct excitation to the 1πσ* state) is the drastic inversion of the branching ratio for quantum numbers (1,0) and (2,0), that is, the ratio changes from 2.36 (scheme 0) to 0.46/0.51 (scheme 1/ scheme 2) for (1,0) and from 1.74 to 0.49/0.52 for (2,0). As shown and explained by Lan et al.,3 the initial wave packets of the (1,0) and (2,0) vibration quantum numbers have no nodal structure along the θ direction (the CCOH dihedral angle) when excited to the 1ππ* state, but bifurcate into two parts on the PES of 1πσ* after the interaction with CI1 and acquire a node along the line of θ = 0 due to the opposite phases of the two parts. The ~ state of the population diabatically dissociating to the ground X Ph-O radical is therefore suppressed, and the branching ratio becomes as large as 2.36 for the (1,0) initial wave packet and 1.74 for the (2,0) initial wave packet. However, when the same initial wave packet of (1,0) or (2,0) is excited directly to the 1πσ* state and propagates along its PES, the results of our study show that the dominant part of the wave packet propagates diabatically ~ of Ph-O. The along the PES of the 1πσ* state and dissociates to X roles of CI1 and CI2 are very small here because the magnitudes of the diabatic couplings, V12 and V23, are zero along the line of θ = 0, as can be seen in Figure 1c. Only a very small proportion of the wave packets spread along the θ direction during the ~ state propagation dissociate (bifurcate at CI2) to the excited A ~ ~ of the Ph-O radical. As a result, the branching ratio A/X becomes as small as 0.4. An experimental study of the dependence of the branching ratio on the initial vibration state was reported recently by Hause et al.,6 and the authors explained their observations by using the previous theoretical results of Lan et al.3 The energy of the onephoton light they used was Eexcite = 47132 or 43656 cm
1 (5.84 or 5.41 eV),6 which is sufficiently high to produce direct excitation to the 1πσ* state. Their results (the light traces in Figure 5a,c of ref 6) clearly show that the dominant dissociation ~ state of Ph-O. The results of scheme 0, which product is the X correspond to those of Lan et al., do not provide an explanation for this result, but the small branching ratio, 0.41, predicted by scheme 2 is in good agreement with the experimental results. The

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distribution of H-atom kinetic energy, that is, the solid lines in figure 2 of ref 12, which was determined by the excitation of phenol-h6 and phenol-d5 molecules at 200 nm (6.2 eV), also corresponds to the branching ratio of scheme 2 rather than that of scheme 0. Hause et al. also carried out (IR + UV) two-photon photodissociation (vibrationally mediated) experiments and observed ~ state; note noticeable enhancement of the Ph-O product in the A the dark traces in Figures 5a,c of ref 6. By using the results of Lan et al., they interpreted this enhancement as the result of the initial O
H stretch excitation in the vibrationally mediated step. The results in Table 1, however, show that this interpretation is incorrect, that is, the branching ratios of the initial wave-packets of the (1,0) and (2,0) vibration quantum numbers are approximately 0.4
0.5 according to scheme 2, that is, almost the same as in the case of the initial wave packet of (0,0). The large branching ratios of the initial wave packets for nθ g 1 in Table 1 imply that when the photodissociation is initiated by direct excitation to the 1 πσ* state, it is not the initial excitation of the O
H stretch but the excitation of the CCOH torsion in the ground electronic state of Ph-OH that is the main reason for the enhancement of the Ph-O ~ state in the vibrationally mediated two-photon product in the A experiment.6 The energy gaps between the vibration levels of the CCOH torsion mode are however very small, just several hundreds of cm
1. Thermal averaging between the vibration levels of the torsion mode also needs to be considered here. Another point revealed by the results in Table 1 is that the isotope effect on the branching ratio is prominent when the initially excited state is 1ππ*, but it is not so large when the initially excited state is 1πσ*. This result can be easily explained, because the tunneling effect plays an important role when the wave packet initially excited to the 1ππ* state leaks out to the PES of the 1πσ* state through CI1. The tunneling effect plays little role in the case of direct excitation to the πσ* state. We expect that this significant difference could be useful to a future experimental study as a guide to the degree of participation of ~ /X ~ the direct excitation scheme. If the isotope effect on the A branching ratio is large, then the initial step of the dynamics is governed by nonadiabatic S1/S2 coupling. If not, the direct (vibronically induced) excitation from S0 to S2 is another possibility.

’ SUMMARY AND CONCLUSION The time-dependent quantum wave packet propagation method was used to reinvestigate the photochemistry of phenol.3 Although the functional forms and diabatic coupling terms of a previous study of the diabatic PES were used here, the scope of the simulations was extended to include the isotope effect due to substitution of the dissociating hydrogen with deuterium. Our study also considered the dynamics initiated by direct excitation to the 1πσ* state, aiming to provide further insight into recent results of a vibrationally mediated two-photon experiment6 and the ultrafast time scale (