Photodissociation Dynamics of Propargyl Alcohol at 212 nm: The OH

Jan 6, 2010 - Photodissociation dynamics of propargyl alcohol (HC≡C−CH2OH) at 212 ... Ji-Hye Lee , Tae-Yeon Kang , Chan-Ho Kwon , Hyon-Seok Hwang ...
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J. Phys. Chem. A 2010, 114, 2053–2058

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Photodissociation Dynamics of Propargyl Alcohol at 212 nm: The OH Production Channel Ji Hye Lee, Hyonseok Hwang, Chan Ho Kwon, and Hong Lae Kim* Department of Chemistry, Institute for Molecular Science and Fusion Technology, Kangwon National UniVersity, Chunchun 200-701, South Korea ReceiVed: September 24, 2009; ReVised Manuscript ReceiVed: December 8, 2009

Photodissociation dynamics of propargyl alcohol (HCtC-CH2OH) at 212 nm in the gas phase was investigated by measuring rotationally resolved laser-induced fluorescence spectra of OH (2Π) radicals exclusively produced in the ground electronic state. From the spectra, internal energies of OH and translational energy releases to products were determined. The electronic transition at 212 nm responsible for the OH dissociation was assigned as the πCtC f π*CtC transition by time-dependent density functional theory calculations. In addition, an energy barrier at the exit channel along the reaction coordinate on the excited electronic potential energy surface was identified by ab initio calculations. The observed energy partitioning among the fragments was successfully modeled by the so-called “barrier-impulsive model”. Introduction There have been several spectroscopic studies of propargyl alcohol, which have mainly focused on vibration-rotation interaction and intramolecular vibrational energy redistribution in the ground electronic state. Among isomers of propargyl alcohol, the gauche form has been identified as a stable isomer, and the potential function for internal rotation of the hydroxyl group has a minimum at 121° from the trans position from the observed microwave spectrum.1-3 Frequency and time domain spectroscopic studies (Raman,4,5 high resolution IR,6,7 transient absorption spectroscopy8) of propargyl alcohol show fast energy redistribution from the initially excited acetylenic C-H stretching vibration, which was explained by the large number of bath states including vibration-rotation interaction with no special effect of low frequency OH torsional vibration.9 Structures and dynamics of propargyl alcohol in the ground electronic state have widely been studied,10-12 and yet studies of this molecule in the excited electronic state are sparse. Photodissociation dynamics of a molecule should depend upon the nature of the excited state and the shape of the potential energy surface along the reaction coordinate leading to individual dissociation channels. Kinetics and the detailed mechanism of dissociation of the molecule upon electronic excitation by irradiation of light thus manifest the physical properties of the molecules in the excited electronic state. An electronic absorption spectrum of the parent molecule, energy, and angular distribution of the fragments observed in the experiments could provide essential information on the shape of the potential energy surface in the excited electronic state. The potential energy surface should be obtained by quantum chemical calculations, but for polyatomic molecules, it is impossible to calculate the full potential energy surfaces in the excited electronic state. Thus, the potential energy curve along the reaction coordinate, the observed dissociation channel, would be calculated under reasonable approximations, from which the dissociation dynamics can be understood in detail. Photodissociation of propargyl alcohol producing OH was investigated by irradiation with 193 nm light generated by an * Corresponding author. Tel.: 82-33-250-8492. Fax: 82-33-253-7582. E-mail: [email protected].

ArF excimer laser where the energy distribution among the products was obtained and compared to that from other unsaturated alcohols such as allyl alcohol.13 The observed energy distribution was explained by the so-called barrier-impulsive model (or hybrid model). In the previous study, however, the barrier energy and structure of the molecule on top of the barrier required for calculation of the energy distribution upon applying the model were ambiguous because of lack of theoretical calculations. In addition, the UV absorption spectrum would have helped to understand the nature of the excited state and the photodissociation dynamics. In the present study, the UV absorption spectrum has been obtained, and the photodissociation dynamics at 212 nm, the long wavelength side of the absorption spectrum, has been investigated by measuring the rotationally resolved laser-induced fluorescence spectrum of the OH radicals exclusively produced in the ground electronic state. The observed electronic transitions have been identified taking advantage of quantum chemical molecular orbital calculations. In addition, energy partitioning among the fragments has been obtained from the observed spectrum of OH and compared to the model calculations on the basis of the potential energy curve obtained from quantum chemical ab initio calculations, and the detailed photodissociation dynamics have been discussed. Experiments The experiments were carried out in a low pressure flow cell with conventional photolysis-probe geometry. The cell, a cube made of stainless steel with four arms (each 30 cm long), was evacuated to a pressure of 10-3 Torr by a mechanical pump. The gaseous sample was slowly flowed through the cell at a pressure of 50 mTorr from a reservoir that contained liquid propargyl alcohol and the vapor in equilibrium at ambient temperature. The sample pressure was controlled by two needle valves. The liquid propargyl alcohol (states purity of 98%) was purchased from Aldrich and used without further purification. The 212 nm vertically polarized photolysis light (typically 1 mJ/pulse, 4 mm diam) was generated by mixing after doubling of the fundamental output of a dye laser (Continuum ND-6000) pumped by the second harmonic of an Nd:YAG laser (Continuum Surelite). The fundamental output of the dye laser at

10.1021/jp9091865  2010 American Chemical Society Published on Web 01/06/2010

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Lee et al. TABLE 1: Results of Molecular Orbital Calculations using Gaussian 03 for Propargyl Alcohol vertical energy (eV) 6.04 6.48 6.70 6.85

Figure 1. UV absorption spectrum of propargyl alcohol in the gas phase taken by a VARIAN Cary-100 UV-vis spectrophotometer with the cell path length of 1 cm and the sample pressure of 50 Torr.

636 nm was frequency doubled in a KDP crystal, and then the fundamental and the doubled outputs were mixed in a BBO crystal to generate the 212 nm photolysis light. The mixing efficiency was about 5% when a half-wave plate for UV was placed in the beam path to match the polarization directions. The probe light to measure the laser-induced fluorescence spectra of OH, employing the X(2Π) f A(2Π) electronic transition at 306-320 nm, was a doubled output of another dye laser (Lumonics, HD-500) pumped by the second harmonic of an Nd:YAG laser (Lumonics, YM-800). The two laser beams were collinearly or perpendicularly introduced to the cell through the arms, which contain baffles to minimize scattered radiation. The delay between the photolysis and probe, typically about 100 ns, was controlled with a digital pulse and delay generator. The power of the probe light, which was about 30 µJ/pulse (∼4 mm diam), was kept as low as possible to avoid saturation of the spectra. The fluorescence signal was detected with a photomultiplier tube (Hamammatsu, R-212UH) perpendicularly mounted relative to the two laser beams through cutoff filters and collection lens. The measured signal was fed to a digital sampling oscilloscope, and integrated fluorescence signals were recorded. A 50 mTorr pressure and 100 ns delay between the photolysis and probe laser pulses ensure measurements of nascent product energy distribution. The fluorescence spectra were corrected with variation of the photolysis and probe laser powers, and the data were collected and stored on a personal computer. The line width of the probe laser output was measured by rotationally resolved gaseous I2 spectra near 620 nm, which was found to be 0.07 cm-1 at fwhm. This laser line profile was deconvoluted from the measured line profiles to estimate the actual Doppler profiles in the spectra. Results A. Electronic Transitions. The UV absorption spectrum of propargyl alcohol in the gas phase was taken and presented in Figure 1. The spectrum shows continuously increasing absorption starting from around 240 nm with structures near 200 nm. To identify the electronic transitions responsible for these peaks, quantum chemical molecular orbital calculations were carried out using the Gaussian 03 program package.14 First, the density functional theory (DFT) calculations were performed to obtain the equilibrium structure on the ground state at the B3LYP/6311++G(p,d) level. The gauche form has the global minimum at the potential energy curve for the internal rotation of OH at

orbital assignment

CI expansion contribution

oscillator strength

πCtC(15) f σ*O-H(16) πCtC(14) f σ*O-H(16) πCtC(15) f π*CtC(17) πCtC(15) f π*CtC(20) n(13) f σ*O-H(16) πCtC(15) f π*CtC(17)

0.6011 0.5327 0.4349 0.3202 0.4511 0.3466

0.0024 0.0329 0.0111 0.0132

the dihedral angle of 52° similar to the results by Hirota.2 The trans isomer has a higher energy by 6 kJ/mol than the cis isomer, and a mixture of 90% cis and 10% trans isomers is present at room temperature. Next, vertical excitation energies from this global minimum were calculated by the time dependent-density functional theory (TD-DFT) calculations at the B3LYP/6311++G(p,d) level. The calculated energies and molecular orbital assignments participating in the observed electronic transition are summarized in Table 1. The transitions responsible for the absorption are mainly the πCtC f σ*O-H and the πCtC f π*CtC transitions, but the electronic state corresponding to σ*O-H should be expected to be repulsive and lead to H-atom rupture from the parent molecule. On the other hand, the state associated with π*CtC should be bound, and dissociation should favor the lower energy channel. On the basis of this qualitative argument, the electronic transition at 212 nm that yields OH radicals is assigned to the πCtC f π*CtC transition. The vertical energies and related molecular orbitals near the transition energy of interest obtained by the TD-DFT calculations are listed in Table 1. The vertical transition takes place at the Franck-Condon region, transferring the equilibrium geometry of the ground state to the excited state resulting in the UV spectrum. The S1 state that corresponds to the two doublet ground state products would have several local minima on the excited potential surface. The T00 transition should be to a global minimum on the S1 excited surface, whose structure would be different from the equilibrium structure on the ground state. The parent molecule excited to a place on the excited potential energy surface at the Franck-Condon region that has π*CtC character experiences surface crossing to the exit channel leading to the dissociation products, which is the C-OH bond breaking channel in the present study. The detailed decay mechanism could be investigated only by the full multidimensional potential energy surface including the Franck-Condon and the asymptotic product region, which is impossible at present. However, it is suggested that the dissociation of OH from propargyl alcohol should take place after the surface crossing. B. Energy Partitioning among Fragments. The laserinduced fluorescence spectra of OH produced from photodisociation of propargyl alcohol at 212 nm were measured employing the X(2Π) f A(2Π) electronic transition (Figure 2). In the spectra, the 0-0 and 1-1 bandheads of the ro-vibronic transitions are shown, and the well-resolved P-, Q-, and R-branch rotational transitions are observed. The individual rotational transitions are assigned on top of the spectra according to Dieke and Crosswhite.15 Normalized rotational population distributions were obtained by relative intensities of the observed lines corrected by appropriate line strength factors,16 and Boltzmann-type plots are presented in Figure 3. Shown in the plot is a slight population built up at the lowest J levels due to collisional rotational energy relaxation. Form the linear regression neglecting data at the lowest 2-3 J levels, the rotational temperatures were deduced, from which the average rotational energies of 12.0 ( 0.8 and 9.5 ( 0.8 kJ/mol were obtained for

Photodissociation Dynamics of Propargyl Alcohol

Figure 2. Laser-induced fluorescence spectrum of OH produced from photodissociation of propargyl alcohol at 212 nm employing the A r X electronic transition of OH.

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Figure 4. Doppler profile of the P1(2) rotational transition of OH. The dashed line is the laser line profile, and the solid lines are the actual Doppler profile and the best fit with convolution of the laser line profile.

TABLE 2: Energy Partitioning (in kJ/mol) among Products with Fractions of the Available Energy from Photodissociation of Propargyl Alcohol at 212 nm for the OH W′′ ) 0 State available energy 212 nm

193 nm

a

Figure 3. Boltzmann-type plots of rotational population distribution of OH obtained from the spectrum in Figure 2.

V′′ ) 0 and V′′ ) 1, respectively. The vibrational population ratio between V′′ ) 0 and V′′ ) 1 of OH was also obtained from the relative intensities of the rotational transitions in the (0,0) and (1,1) vibronic bands corrected by the reported Franck-Condon factors,17 which is 0.92/0.08. The translational energy of the OH fragments was measured from the Doppler broadened rotational lines. In the present experimental setup, when both the linearly polarized photolysis and the probe laser beams are collinearly propagated, the probe direction is perpendicular to the polarization direction of the photolysis laser beam, whereas the probe direction is parallel to the polarization direction of the photolysis laser beam when the two laser beams are propagated perpendicular to each other. In both geometries, the observed Doppler profiles of the rotational transitions are Gaussian-like under the resolution of our laser, which implies isotropic velocity distribution of the OH fragments. The Doppler profiles reflecting anisotropic velocity distribution can also be smeared by fast collisional relaxation, resulting in the Gaussian-like profiles. As pointed out earlier, however, the dissociation of OH after the surface crossing would take time for rotation of the parent molecule and the directional memory can be destroyed. In addition, as compared to the relaxation of alignment/orientation by collisions, translational energy relaxation should be much slower.18 One might argue that even for the isotropic velocity distribution, the Doppler profiles for different rotational branch transitions should

252.1 experiment prior impulsive BIMa 307.8 experimentb BIMc

〈Er(OH)〉

〈fr(OH)〉

〈Et(sys)〉

〈ft〉

12.0 ( 0.84 31.0 9.31 11.3

0.048 0.12 0.037 0.045

148.6 ( 23.9 45.9 241.6 135.5

0.59 0.18 0.96 0.54

13.8 ( 1.0 13.7

0.045 0.045

148 ( 23 143.6

0.48 0.47

Barrier-impulsive model. b Reference 13. c Present study.

be distinct due to the V-j correlation developed at an instance of dissociation,19 but the shape difference in the profiles could not be resolved in the present study. The Doppler profile of the P1(2) rotational transition is presented in Figure 4 together with the observed laser line profile. The average translational energy of the OH fragments was calculated from the second moment of the observed profiles after deconvolution of the laser line profile, and the center of mass translational energy release in the fragments for the OH rotational state N ) 2 was then calculated to be 148.6 ( 23.9 kJ/mol. The observed partitioning of the available energy to the products is summarized in Table 2. C. F1/F2 and Λ-Doublet Ratios. The observed OH ratios between the two different spin-orbit states, F1(2Π3/2)/ F2(2Π1/2), and between the Λ-doublet states are presented in Figures 5 and 6, respectively. In the present study, the F1/F2 ratio shows some propensity in the F1 state and no appreciable propensity in any Λ-doublet state on the average. The origin of the propensity in one of the spin-orbit state is not clear, but it should be related to the relative time for dissociation to the electron precession and/or singlet-triplet surface interaction.20 If the dissociation is relatively slow, an electron correlation should somehow determine the final spin-orbit state of the product. However, the Λ-doublet propensity unambiguously originates from the dissociation dynamics.21,22 If the OH rotation arises from the impulse at the dissociation, the pπ orbital generated from the dissociation should then lie in the plane of rotation, resulting in the population of the Π(A′) Λ-doublet state. The Π(A′′) state is populated, however, when the force perpendicular to the plane of rotation such as torsional vibration of OH in the parent molecule is exerted. According to the

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Figure 5. Population ratios between the two spin-orbit states of OH as a function of the rotational quantum numbers.

Figure 6. Population ratios between the two Λ-doublet states of OH as a function of the rotational quantum numbers.

selection rule, the Q-branch rotational transition should be induced from the Π(A′′) state, whereas the P- and R-branch transitions should be induced from the Π(A′) state. Thus, from relative intensities between the different rotational branch transitions, the Λ-doublet population ratio can be measured. In the present study of photodissociation of propargyl alcohol, a statistical Λ-doublet population ratio was observed with deviation from the statistical distribution at high J levels. This deviation, however, probably originates from large experimental uncertainties from small signal intensities at high J levels, and, on the average, it is concluded that no appreciable Λ-doublet propensity is observed. Discussion Mechanisms of photodissociation followed by an electronic transition are in general classified as (1) direct, fast dissociation from repulsive excited states, (2) slow dissociation from the vibrationally hot ground electronic state after rapid internal conversion, and (3) indirect dissociation from different excited states resulting from extensive potential couplings such as intersystem crossing.23 In each case, the dissociation dynamics are vastly different, and thus the resulting physical properties of the product systems are different. The dissociation dynamics can be modeled by an impulsive and a statistical model for cases 1 and 2, respectively. However, for case 3, the physical properties of the final products such as energy partitioning among products cannot be expected by a simple model, because the dissociation dynamics should be governed by the shape of the potential energy surface leading to the individual product channels. The enthalpies of formation of propargyl alcohol, propargyl radical, and OH radical are 55.3 for the cis form (61.3 kJ/mol for the trans form), 340.6, and 39.3 kJ/mol, respectively.13,24 The enthalpy of the reaction producing OH is calculated to be

Lee et al. 324.1 kJ/mol considering the 90:10 cis and trans mixture of propargyl alcohol. Thus, the available energy that is the photon energy at 212 nm (564.3 kJ/mol) minus the enthalpy of reaction was calculated to be 252.1 kJ/mol, including 11.9 kJ/mol average thermal energy of the parent molecule, which would be distributed among products. When the dissociation of OH from propargyl alcohol takes place from the repulsive state, the energy partitioning of the available energy among products can be estimated by the impulsive model.25,26 In this model, upon initial electronic excitation, an abrupt turn-on of repulsive force between atoms of the breaking bond is assumed, which results in large translational energy release to the products. Invoking linear and angular momentum conservations, the average translational and rotational energies of the OH fragments were calculated employing the equilibrium geometry calculated from the DFT calculations mentioned above according to the Franck-Condon principle. The calculated center of mass translational energy released to the products and average rotational energy of OH are 241.6 and 9.31 kJ/mol, respectively, which are significantly different from the experimentally measured values. In addition, the vertical energies obtained from quantum chemical molecular orbital calculations are too large for the parent molecule to reach any (nσ*C-O) or (πσ*C-O) state at 212 nm evidenced by the UV absorption spectrum. Therefore, it can be concluded that the dissociation of OH should indirectly occur. A statistical model can be applied to obtain the energy partitioning among products when the dissociation is slow on the vibrationally hot ground electronic surface after the internal conversion from the initially prepared state upon photon absorption. A simple prior model in this case assumes that the available energy should be distributed among all product degrees of freedom with equal probability.27 Thus, the population of the individual rotational state of OH is proportional to the number of accessible quantum states in the propargyl fragment at the energy, E ) Eav - EOH (v,J). The number of vibrational states of the parpargyl radical was directly counted with fundamental frequencies obtained by the similar DFT calculations at the B3LYP/6-311++G(p,d) level. The calculated average rotational energy of OH from the rotational population distribution is 31.0 kJ/mol. In addition, the average translational energy was also calculated employing the same prior model to be 45.9 kJ/mol, which is very different from the measured values. Therefore, the dissociation should indirectly take place on the excited potential energy surface. When the dissociation occurs on the electronically excited state, the dissociation dynamics should be governed by the shape of the potential energy surface leading to the products. In the case of dissociation where there exists an energy barrier at the exit channel along the reaction coordinate, the barrier-impulsive model can be applied to estimate the energy partitioning among the products.28 The barrier-impulsive model has long been applied to calculate energy partitioning among products for various unimolecular decomposition reactions with an exit channel barrier such as molecular elimination of HX (X ) F, Cl) from haloalkanes.29,30 In this model, it is assumed that the available energy above the barrier is statistically partitioned among products and the rest is partitioned impulsively from the top of the barrier. On the ground state, the unimolecular decomposition of simple bond rupture producing two radical products has no reverse barrier for association in general, but on the excited state, the association reaction of two radicals sometimes has a barrier because of a structural difference between the ground and excited states.31 Although the barrier-

Photodissociation Dynamics of Propargyl Alcohol

J. Phys. Chem. A, Vol. 114, No. 5, 2010 2057 the barrier at the exit channel along the reaction coordinate clearly appears (1.7 Å C-O bond distance). The molecular structure on top of the barrier is also depicted in the figure. The TD-DFT calculations usually provide lower vertical energies for single point calculations with fixed geometries than the CIS calculations.32 Thus, to improve the energy, the TD-DFT calculations for the S1 excited state were carried out with the optimized CIS geometries, from which the reverse barrier energy, Eimp, was calculated to be 105.4 kJ/mol. The barrier-impulsive model successfully estimated the energy partitioning among products for the photodissociation of ethylene.33 In this model, the energies of the fragments A and B can be calculated as

ET ) ETstat - ETimp ETimp )

ERimp(A) ) ETimpbA2µAB/IA

Figure 7. Potential energy curves on the ground and S1 excited states leading to the OH production channel in propargyl alcohol. The “b” are the energies on the ground state obtained by the DFT calculations, “4” are the energies on the S1 state obtained by the CIS calculations, and “O” are obtained by the TD-DFT calculations.

impulsive model has mostly been applied to the reactions on the ground electronic state, it would be applied to the reaction on the excited electronic state when the barrier at the exit channel exits. In this case, it is assumed that the parent molecule spends some time, such as a few vibrational periods, at the Franck-Condon region and is dissociated impulsively on top of the barrier. Thus, the amount of energy of the reverse barrier, Eimp, would be partitioned impulsively, and the rest of the available energy, Estat ) Eav - Eimp, is statistically partitioned among the products. To test this hybrid model in the present study, the shape of the potential energy surface along the reaction coordinate should be investigated, and if there is an energy barrier, the geometry of the transition state should be tested for energy disposal. To figure out the shape of the potential energy surface, first the potential energies of the parent molecule on the ground electronic state were calculated as a function of the C-O bond distance by the DFT calculations (Figure 7). The energy of the molecule at equilibrium was first calculated, and then optimized structures and energies were obtained as the C-O bond distance was enlarged by 0.1 Å steps up to 3.0 Å where the molecule is assumed to be dissociated at this distance. These calculations were performed at the B3LYP/6-311++G(p,d) level. The available energy for the dissociation of OH from propargyl alcohol at 212 nm from these calculations was found to be 251.9 kJ/mol as compared to 252.1 kJ/mol from the literature mentioned above.13 Similar results were obtained by ab initio calculations at the MP2/6-311++G(d, p) level, which is not shown in the figure. For the potential energy surface on the excited electronic state, the optimized structure and energy of the molecule on the S1 state were obtained by the ab initio CIS calculation with the 6-311++G(d,p) basis set with the same C-O bond distance as that of the equilibrium structure on the ground state. Next, the same CIS calculations were performed for the molecule with the C-O bond extending up to the dissociation limit, 3.0 Å. The potential energy curve as a function of the C-O bond distance is shown in Figure 7, where

Eimp 1 + bA2µAB/IA + bB2µAB/IB

ERimp(B) ) ETimpbB2µAB/IB where b’s are impact parameters of the fragments, µAB is the reduced mass, and Ifrag is the moment of inertia of the fragments about an axis through the center of mass of the respective fragment, perpendicular to the plane containing the center of mass and the two separating atoms. The impact parameter bA is given by r sin ℵA, where r is the distance from the dissociating atom to the center of mass of the corresponding fragment and ℵA is the angle between the bond to be broken and a line from the center of the fragment to the atom that is getting separated. The statistical energy partitioning among products for Estat of the available energy was calculated employing the prior model. Using this model and the obtained Eimp from the potential energy surface calculations, the rotational energy of OH and the center of mass translational energy release including the energy statistically partitioned were calculated to be 11.3 and 135.5 kJ/mol, respectively, which are in good agreement with those measured within the experimental uncertainties. It was also found that almost all of the reverse barrier energy was transformed into product translation, whereas the rotational energy of the OH fragments mostly comes from statistical energy partitioning. The fact that the rotational energy of OH mostly originates from the statistical energy partitioning should result in no appreciable propensity among the two Λ-doublet states of OH. As mentioned earlier, in the study of photodissociation of propargyl alcohol at 193 nm, energies of the fragments were ambiguously estimated employing the hybrid model without any potential energy calculations. Here, in addition, the translational energy release to the fragments and the rotational energy of OH were calculated using the present results and found to be 143.6 and 13.7 kJ/mol, respectively, which are in good agreement with the measured values.13 The measured and calculated energies of the fragments are listed in Table 2. Summary The photodissociation dynamics of propargyl alcohol at 212 nm in the gas phase was investigated by measuring the rotationally resolved laser-induced fluorescence spectra of OH

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produced in the ground state. The electronic absorption at 212 nm leading to dissociation of OH is assigned to the πCtC f π*CtC transition from which the dissociation takes place on the S1 excited state potential energy surface after surface crossing. The ground and S1 excited state potential energy curves along the dissociation coordinate were obtained by the DFT and ab initio quantum chemical calculations. The obtained S1 surface shows an exit channel barrier along the reaction coordinate, and the measured energy partitioning among products is successfully explained by the barrier-impulsive model. Acknowledgment. This work was financially supported by the Korea Research Foundation (C00128). References and Notes (1) Bolton, K.; Owen, N. L.; Sheridan, J. Nature 1968, 217, 164. (2) Hirota, E. J. Mol. Spectrosc. 1968, 26, 335. (3) Pearson, J. C.; Drouin, B. J. J. Mol. Spectrosc. 2005, 234, 149. (4) Malinovsky, A. L.; Makarov, A. A.; Ryabov, E. A. JETP 2008, 106, 34. (5) Malinovsky, A. L.; Doljikov, Yu. S.; Makarov, A. A.; Ogurok, N. D. D.; Ryabov, E. A. Chem. Phys. Lett. 2006, 419, 511. (6) Hudspeth, E.; McWhorter, D. A.; Pate, B. H. J. Chem. Phys. 1998, 109, 4316. (7) Green, D.; Holmberg, R.; Lee, C. Y.; McWhorter, D. A.; Pate, B. H. J. Chem. Phys. 1998, 109, 4407. (8) Yoo, H. S.; McWhorter, D. A.; Pate, B. H. J. Phys. Chem. A 2004, 108, 1380. (9) Makarov, A. A.; Malinovsky, A. L.; Ryabov, E. A. J. Chem. Phys. 2008, 129, 116102. (10) Lister, D. G.; Palmieri, P. J. Mol. Struct. 1976, 32, 355. (11) Travert, J.; Lavalley, J. C.; Chenery, D. Spectrochim. Acta, Part A 1979, 35, 291.

Lee et al. (12) Marshall, K. T.; Hutchinson, J. S. J. Phys. Chem. 1987, 91, 3219. (13) Dhanya, S.; Kumar, A.; Upadhyaya, H. P.; Prakash, D. N.; Rameshwar, D. S. J. Phys. Chem. A 2004, 108, 7646. (14) Gaussian 03; Gaussian, Inc.: Pittsburgh, PA, 2003. (15) Dieke, G. H.; Crosswhite, H. M. J. Quant. Spectrosc. Radiat. Transfer 1962, 2, 97. (16) Chidsey, I. L.; Crosley, D. R. J. Quant. Spectrosc. Radiat. Transfer 1980, 23, 187. (17) Loque, J.; Crosley, D. R. J. Chem. Phys. 1998, 109, 439. (18) Shin, S. K.; Kang, T. Y.; Park, C. R.; Kim, H. L. J. Phys. Chem. A 2000, 104, 1400. (19) North, S. W.; Hall, G. E. J. Chem. Phys. 1996, 104, 1864. (20) Lee, K. W.; Lee, K. S.; Jung, K. H.; Volpp, H. R. J. Chem. Phys. 2002, 117, 9266. (21) Andresen, P.; Rothe, E. W. J. Chem. Phys. 1985, 82, 3634. (22) Hanazaki, I. Chem. Phys. Lett. 1993, 201, 301. (23) Schinke, R. Photodissociation Dynamics; Cambridge University Press: Cambridge, 1993. (24) McMillan, D. F.; Golden, D. M. Annu. ReV. Phys. Chem. 1982, 33, 493. (25) Busch, G. E.; Wilson, K. R. J. Chem. Phys. 1972, 56, 3626. (26) Tuck, A. F. J. Chem. Soc., Faraday Trans. 2 1977, 73, 689. (27) Levin, R. D.; Bernstein, R. B. Molecular Reaction Dynamics and Chemical ReactiVity; Oxford Univ. Press: New York, 1987. (28) Zamir, E.; Levin, R. D. Chem. Phys. 1980, 52, 253. (29) Arunan, E.; Wategaonkar, S. J.; Setser, D. W. J. Phys. Chem. 1991, 95, 1539. (30) Dong, E.; Setser, D. W.; Hase, W. L.; Song, K. J. Phys. Chem. A 2006, 110, 1484. (31) Robinson, P. J.; Holbrook, K. A. Unimolecular Reactions; Wiley: New York, 1972. (32) Cramer, C. J. Essentials of Computational Chemistry; Wiley: New York, 2002. (33) Chang, A. H. H.; Hwang, D. W.; Yang, X. M.; Mebel, A. M.; Lin, S. H.; Lee, Y. T. J. Chem. Phys. 1999, 110, 10810.

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