Photodissociation of CH3I: A Full-Dimensional (9D) Quantum

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Photodissociation of CH3I: A Full-Dimensional (9D) Quantum Dynamics Study Christian R. Evenhuis† and Uwe Manthe* Theoretische Chemie, Fakult€at f€ur Chemie, Universit€at Bielefeld, Universit€atsstr. 25, D-33615 Bielefeld, Germany ABSTRACT: The photodissociation of methyl iodide in the A band is studied by full-dimensional (9D) wave packet dynamics calculations using the multiconfigurational time-dependent Hartree approach. The potential energy surfaces employed are based on the diabatic potentials of Xie et al. [J. Phys. Chem. A 2000, 104, 1009] and the vertical excitation energy is taken from recent ab initio calculations [Alekseyev et al. J. Chem. Phys. 2007, 126, 234102]. The absorption spectrum calculated for exclusively parallel excitation agrees well with the experimental spectrum of the A band. The electronic population dynamics is found to be strongly dependent on the motion in the torsional coordinate related to the H3-C-I bend, which presumably is an artifact of the diabatic model employed. The calculated fully product state-selected partial spectra can be interpreted based on the reflection principle and suggests strong coupling between the C-I stretching and the H3-C-I bending motions during the dissociation process. The computed rotational and vibrational product distributions typically reproduce the trends seen in the experiment. In agreement with experiment, a small but significant excitation of the total symmetric stretching and the asymmetric bending modes of the methyl fragment can be seen. In contrast, the umbrella mode of the methyl is found to be too highly excited in the calculated distributions.

I. INTRODUCTION Methyl iodide photodissociation is the prototypical example of a polyatomic molecular photodissociation process. It serves as a benchmark for testing experimental techniques and has provided advances in the theoretical understanding of photodissociation processes. Given the vast literature on the subject, we will not attempt to give a comprehensive discussion of the existing research and refer to detailed reviews, for example, to refs 1-5. Only theory based on “first principles’’ and recent experiments studying methyl iodide photodissociation will be discussed in the following. Ab initio potentials for the relevant electronically excited states of methyl iodide in the A band were first developed by Amatatsu et al.6 in 1991. The potentials included three diabatic potential energy surfaces (PESs) and three diabatic potential coupling surfaces characterizing the 3Q0 and 1Q1 states (see Figure 1 for the schematic one-dimensional picture of the PESs). The six-dimensional potentials provided a full description of the motion in all coordinates except the three C-H distances and described the conical intersection between the PESs. Considering the state of the art in the early 1990s, this was a significant achievement. Quantum dynamics studies using these PESs appeared immediately after the trajectory calculations included in the work of Amatatsu et al.:6 three-dimensional wave packet dynamics calculations by Guo1,7 based on a H3-C-I pseudotriatomic model were followed by five-dimensional calculations2,8 using the multiconfigurational time-dependent Hartree (MCTDH)9,10 approach. In the later calculations, only the four asymmetric methyl stretching and bending motion were frozen. The MCTDH approach, which facilitates accurate quantum dynamics calculations for systems with higher dimensionality than tractable by r 2011 American Chemical Society

standard wave packet techniques, was introduced around this time and the methyl iodide photodissociation studies2,8 provided the first benchmark application of the approach. The above-mentioned theoretical studies1,2,7,8 based on the PESs of Amatatsu et al. generally yielded product distributions which were in decent agreement with experiment. However, the computed absorption spectra were significantly blue-shifted compared to experiment. Thus, comparisons of product distributions between theory and experiments performed at a given excitation wavelength were problematic. Further developments followed: Amatatsu et al. extended their work and published full-dimensional PESs11 in 1996. It is noteworthy that these potentials are presumably still the only full-dimensional ab initio PESs available which describe photodissociation for molecules consisting of more than three to four atoms. Four-dimensional MCTDH calculations12 studied resonance Raman spectra. To address the problem of the blue-shifted absorption spectrum, Xie et al.3 performed new ab initio calculations and developed improved potential parameters for the fulldimensional PESs of Amatatsu et al.11 Xie et al. also performed three-dimensional wave packet calculations for CH3I and CD3I using the pseudotriatomic model on this new PESs. The absorption spectrum computed for the new PESs showed a reduced but still existing blue shift compared to experiment.3 Special Issue: Victoria Buch Memorial Received: October 31, 2010 Revised: December 21, 2010 Published: February 10, 2011 5992

dx.doi.org/10.1021/jp1103998 | J. Phys. Chem. A 2011, 115, 5992–6001

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Figure 1. PESs plotted as a function of the C-I distance. All other coordinates are frozen at their value at the Franck-Condon point.

The discrepancy in the vertical excitation energy between the theoretical results from Amatatsu and co-workers3,6,11 and the experiment spurred further ab initio studies.13-16 Recent detailed ab initio studies by Alekseyev et al.15,16 suggested possible shortcomings in the earlier ab initio results and presented more accurate electronic structure data. While giving high quality ab initio data along one-dimensional cuts through the adiabatic PESs, these studies did not provide PESs that could be used in detailed dynamical calculations. Neither a diabatization nor a description of correlated multidimensional features of the potential have been attempted in this electronic structure focused work. Thus, the PESs of Xie et al.3 still provide the best potentials available for multidimensional dynamics studies of the photodissociation of methyl iodide. Paralleling the progress made in theory, new experimental studies investigating the photodissociation of CH3I in the A band appeared.4,5,17-21 Rotational and vibrational distributions of the photodissociation products have been studied in great detail using modern experimental techniques4,17-19 and femtosecond pump-probe experiments5,20,21 analyzed the dynamics in real time. The experiments of Eppink and Parker4,17 also investigated the minor vibrational channels in more detail. Besides the dominant vibrational excitation of the methyl umbrella mode, they also found excitation of the methyl products in the symmetric stretching mode and the asymmetric bending modes. These results provided one of the motivations for the present work. While five-dimensional wave packet calculations studying methyl iodide photodissociation were published already in 1993,8 existing quantum dynamics calculations using the best available PESs had exclusively been based on the threedimensional pseudotriatomic model.3,5 Although this model captures most of the essential dynamics of methyl iodide photodissociation, it can only describe umbrella vibrations of the methyl fragment and employs a restricted description of the rotation of the methyl product. To provide a more detailed theoretical description, the present work will present accurate full-dimensional wave packet calculations studying methyl iodide photodissociation using the best available PESs.3 To this end, it employs the MCTDH approach, which since its initial application to methyl iodide photodissociation2,8,12 has arguably been established as the most efficient scheme to simulate polyatomic quantum dynamics accurately (see refs 22-31 for examples of benchmark applications and important methodological developments of the MCTDH approach). The present work should also demonstrate the wealth of data

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which can be obtained from accurate multidimensional quantum dynamics simulations. This data facilitates a detailed theoretical analysis of polyatomic system displaying many degrees of freedom and can provide insights which could not be gained from analyzing only experimentally available information. The article is organized as follows: the article starts with detailing the system description (section II) and the quantum dynamics techniques employed (section III). The actual results will be presented and discussed in section IV: First, the computed absorption spectra and the electronic population dynamics are studied (sections IV.A and IV.B) comparing results obtained in full and reduced dimensionality. Next, section IV.C focuses on fully stateresolved partial spectra and gives a detailed physical interpretation of the results of the present numerical simulation. Finally, rotational and vibrational product distributions are presented (sections IV.D and IV.E) and compared to experiment. At the end of this article, section V briefly summarizes the central conclusions and discusses further perspectives.

II. SYSTEM DESCRIPTION A. Coordinates and Kinetic Energy Operator. The present work employs the coordinate system suggested in ref 32: the six coordinates F, ϑF, jF, θ, φ, and χ describe the CH3 fragment, while the three coordinates R, ϑR, and jR characterize the position of the iodine atom relative to the methyl group. The coordinate system is based on a 3 þ 1 Radau construction for the CH3 group, which introduces three symmetrically defined C-H Radau vectors. The body fixed coordinate system is defined by the methyl group using these vectors: the trisector of the three C-H Radau vectors is taken as the z-axis and the first of the three C-H Radau vectors defines the x-z plane of the body fixed frame. To define the position of the iodine atom relative to this frame of reference, the polar coordinates R,ϑR, and jR associated with the Jacobi vector connecting the CH3 center of mass with the I atom are used. The coordinate θ related to the umbrella angle is given by the angle between the z-axis and any of the C-H Radau vectors. F, ϑF, and jF are hyperspherical coordinates related to the lengths r1, r2, and r3 of the three Radau vectors:

r1 ¼ F cos ϑF r2 ¼ F sin ϑF cos jF

ð1Þ

r3 ¼ F sin ϑF sin jF Thus, the coordinate F is related to the totally symmetric C-H stretch vibration of the methyl group, while the coordinates ϑF and jF describe the two asymmetric C-H stretching vibrations. The coordinates φ and χ are the angles that locate the projections of the two Radau vectors not used in the definition of the body fixed frame in the molecular x-y plane.32 They describe the asymmetric bending of the methyl group. The derivation of the kinetic energy operator corresponding to these coordinates has also been described in ref 32. The present work does not use the “quasi-exact” version of the kinetic energy operator but resorts to the approximate “mean field C3v” kinetic energy operator. This operator is significantly simpler than the more rigorous one and the errors introduced, which are in the 10 cm-1 range,32 are negligible, considering the accuracy required in the present study. Incorporating the volume element into the definition of the kinetic energy operator (except for a sin ϑR factor, which is not included to retain the typical form of 5993

dx.doi.org/10.1021/jp1103998 |J. Phys. Chem. A 2011, 115, 5992–6001

The Journal of Physical Chemistry A the angular momentum operator), the resulting kinetic energy operator for vanishing total angular momentum reads (see also ref 33 for further details on the derivation)

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Table 1. Values of the Parameters in Kinetic Energy Operator

1 ∂ 1 ^J2 þ 2μR ∂R 2 2μR R 2 R " 1 ∂2 1 ∂2 þ 2 2 2 2mH ∂F F sin ϑF ∂j2F

^¼ T

2

1 1 ∂ ∂ 1 pffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffi sin ϑF 2 F ∂ϑF sin ϑF sin ϑF ∂ϑF aθ 1 ∂ ∂ 1 pffiffiffiffiffiffiffiffiffiffiffi sin3 θ þ 2 pffiffiffiffiffiffiffiffiffiffiffi ∂θ sin3 θ F sin3 θ ∂θ aφ þ cφ cot2 θ 1 ∂ ∂ 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ γðφ, χÞ F2 ∂φ γðφ, χÞ γðφ, χÞ ∂φ þ

aχ þ cχ cot2 θ 1 ∂ ∂ 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffi γðφ, χÞ þ 2 ∂χ γðφ, χÞ F γðφ, χÞ ∂χ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ∂ aθφ 1 ∂ pffiffiffiffiffiffiffiffiffi 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi sin θcos θ 3 γðφ, χÞ þ 2 ðpffiffiffiffiffiffiffiffiffiffiffi 3 ∂φ γðφ, χÞ F sin θ ∂θ p ffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi ∂ 1 1 ∂ pffiffiffiffiffiffiffiffiffiffiffi 3 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi γðφ, χÞÞ þ cos θ sin θ ∂θ sin3 θ γðφ, χÞ ∂φ aθy ∂ b cot θ ∂ ^J R , y - 2i φy ^J - 2i 2 ∂φ R , y F ∂θ F2 bχx cot θ ∂ a þ c cot2 θ ∂ ^J R , x - 2i χz χz ^J - 2i ∂χ ∂χ R , z F2 F2 ay ax az þ cz cot2 θ ^2 JR , z - 2 ^JR2 , x - 2 ^JR2 , y F2 F F bxz cot θ ^ ^ ðJ R , x J R , z þ ^J R , z^J R , x Þ ð2Þ F2 (Please note that atomic units are assumed if not otherwise noted and 9h= 1 is used throughout this work). Here mH is the mass of hydrogen, μR is the reduced mass associated with the R coordinate, and 4 1 2 2 γðφ, χÞ ¼ pffiffiffi ½1 þ ðφ - π=3Þ 1 þ ðχ - πÞ ð3Þ 3 3 3 The operators ^̂J R,x, ^̂J R,y, ^̂J R,z, and ^̂J2R = ^̂J 2R,x þ ^̂J 2R,y þ ^̂J 2R,z denote the usual angular momentum operators associated with the rotation of the CH3-I Jacobi vector relative to the body fixed frame. Table 1 gives the coefficients present in eq 2 (Please note that the original work of ref 32 contained some typos. The corrected values from ref 33 are used in Table 1). The present work only considers the case of vanishing total angular momentum. Because all moments of inertia of the methyl fragment are comparatively large, the moments of inertia of the complete CH3-I system at any relevant geometry must also be large, so the separation of overall rotation from the internal motions of the CH3-I system is a good approximation on the relevant time scale. Consequently, the rotational state distributions of the dissociation fragments can be obtained by combining the results for vanishing total angular momentum with the initial rotational distribution (corresponding, e.g., to the specific experimental setup) using standard angular momenta coupling schemes (see ref 34 for a detailed discussion of the description of the rotational states of CH3 described within the present coordinates and kinetic energy operator).

aθ

1 þ 2Δϑ2 þ (4/3)Δj2 þ (1/3)Δφ2 þ (1/9)Δχ2

aφ

(3/2) þ (15/8)Δϑ2 þ 3Δj2

cφ

3 þ 6Δϑ2 þ 4Δj2 þ (3/2)Δφ2 þ (5/6)Δχ2

aχ

(9/2) þ (99/8)Δϑ2 þ 3Δj2

cχ aθφ

9 þ 18Δϑ2 þ 12Δj2 þ (15/2)Δφ2 þ (6/4)Δχ2 √ [1/(4 3)][-9Δϑ2 þ 8Δj2 þ 7Δφ2 - (7/3)Δχ2]

aθy

(3/2)Δϑ2 - (4/3)Δj2 - (5/6)Δφ2 þ (1/18)Δχ2

bφy

31/2(-1 - (11/4)Δϑ2 - (2/3)Δj2 - (3/4)Δφ2 - (1/36)Δχ2)

bχx

-3 - (15/4)Δϑ2 - 6Δj2 - (15/4)Δφ2 - (17/12)Δχ2

aχz

-3 - (21/2)Δϑ2

cχz

-6 - (57/4)Δϑ2 - 6Δj2 - (15/4)Δφ2 - (17/12)Δχ2

ax

2 þ (5/2)Δϑ2 þ 4Δj2 þ 2Δφ2 þ (4/3)Δχ2

ay az

2 þ (11/2)Δϑ2 þ (4/3)Δj2 þ (4/3)Δφ2 - (2/9)Δχ2 3 þ (21/2)Δϑ2

cz

5 þ 13Δϑ2 þ 4Δj2 þ 2Δφ2 þ 4Δχ2 2 þ (5/2)Δϑ2 þ 4Δj2 þ 2Δφ2 þ (4/3)Δχ2

bxz

Δϑ = 0.0030, Δj2 = 0.0045, Δφ2 = 0.010, Δχ2 = 0.030 2

B. Potential Energy Surfaces. To describe the dynamics of the electronically excited methyl iodide, the present work uses the nine-dimensional coupled diabatic potentials of Amatatsu et al.11 with the modified potential parameters of Xie et al.3 In addition to the parameter modification, two further changes to the original potentials of ref 11 have been made. First, the simple methyl force field VCH3 used in the original work of Amatatsu et al. (see eq 1 of ref 11) has been replaced by the recent accurate CH3 PES of Medvedev et al.35 This modification was made so that the vibrational states of the methyl fragment produced by the dissociation process are more accurately described. Because the asymptotic methyl potential appears as a separate additive term in the diabatic PESs, the exchange of the CH3 potentials can be done without further affecting other aspects of the diabatic potentials of Amatatsu et al. Second, nonanalytic terms present in potentials, as defined in ref 11, have been removed. In the original definition of the potentials, the function ζ(S4a,S4b,S5a,S5b) has been used to partially characterize how the diabatic potential coupling is influenced by the asymmetric stretching motions (described by the coordinates S4a and S4b) and the asymmetric bending motions (described by the coordinates S5a and S5b) of the methyl group. ζ is defined using the sum of the two angles ζ1 = arctan(S5b/S5a) and ζ2 = arctan(S4b/S4a). However, ζ1 is undefined at any geometries where S5b = S5a = 0 and ζ2 becomes undefined at any geometries where S4b = S4a = 0. As a consequence, the resulting ζ values vary extremely rapidly with geometry if the CH3 group is approximately C3v symmetric. This rapid variation of the potential is unphysical and would render exact quantum dynamics calculations that include the respective coordinates essentially infeasible. To avoid this problem, we resorted to the simple solution to remove any terms from the potential that involve ζ1 or ζ2 (which is equivalent to set ζ equal to zero in all expressions). The description of the electronic ground state PES of methyl iodide combines the empirical potential from previous work12 (which is partly based on an older empirical potential36) with the ab initio CH3 PES of Medvedev et al.: ref Vground ¼ V1 ðrI , θH Þ þ V3 ðθI Þ þ VCH3 - VCH ðθH Þ 3

ð4Þ

Here coordinates are based on the actual vectors connecting the atoms (in contrast to the Radau- or Jaboci-type vectors used in 5994


The Journal of Physical Chemistry A the kinetic energy operator and the wave function representation): rI is the distance between the carbon and the iodine atom, θI is the H3-C-I bending angle, and θH is the “real’’ umbrella angle of the CH3 group (see previous work2,8 for a more detailed description of these coordinates). The potentials V1 and V3 are taken from ref 12. VCH3 denotes the CH3 PES of eq (θH) is the one-dimensional cut of VCH3 Medvedev et al. VCH 3 along the umbrella angle computed with all other coordinates fixed at the equilibrium geometry values of CH3I. The subtracref (θH) is required to compensate for the double tion of VCH 3 counting of the umbrella potential in V1 and VCH3. The energy difference between the ground and excite state potentials was fixed by employing recent ab initio results of Alekseyev et al.:15 their value of the vertical energy difference between the ground state PES and the 3Q0 PES at the ground state equilibrium geometry, 4.901 eV, was used to determine the energy of the ground state PES relative to the coupled excited state PESs. This corresponds to resetting the parameter e0 in V1 from ref 12 to -0.0912 Hartree = -2.481 eV. As in the work of Guo and co-workers1,3,7 and previous MCTDH work on methyl iodide photodissociation,2,8,12 the transition dipole moments are assumed to be coordinate independent.

III. WAVE PACKET PROPAGATION AND ANALYSIS All quantum dynamics calculations presented employ the MCTDH approach.9,10 The vibrational ground state on the ground electronic state is obtained by propagation in imaginary time. Subsequent propagation in real time on the coupled excited state surfaces yields the dynamical observables, for example, absorption spectra and product distributions. The vibrational states of CH3 required for the calculation of the product distributions are computed using the state-averaged MCTDH approach.37 The potential energy integrals appearing in the MCTDH equations of motion are evaluated using the correlation DVR (CDVR) approach.38 The integration is performed using a constant mean field (CMF) integration scheme.39 Specifically, the CMF2 approach of ref 40 is employed. Standard harmonic oscillator discrete variable representations (DVRs)41-43 and fast Fourier transform (FFT) schemes44 are used to represent the single-particle function (SPFs) in the coordinates F,ϑF,jF,θ,φ,χ and R,jR, respectively. The grid in R covers a range from 3.44 bohr to 12.61 bohr and guarantees converged results for the propagation times considered. The frequencies and equilibrium positions of the harmonic oscillator DVRs are determined at the Franck-Condon point. In the coordinate ϑR the cot-Legendre-DVR of ref 45 is employed which allows one to appropriately account for the singularities in the kinetic energy operator at ϑR = 0. The corresponding grid extends to a maximum angle of 1.0. The number of timeindependent grid points employed in the real time propagation is given in Table 2. Table 2 also gives the number of SPFs employed in final MCTDH propagations. Extended tests varying the number of SPFs in all coordinates have been performed to ensure convergence of the propagated wave function describing the methyl iodide photodissociation. The reduced dimensional calculations presented employ the same basis set sizes as their full-dimensional counterparts for their active coordinates . The vibrational states of methyl obtained by state-averaged MCTDH calculations using the basis set given in Table 2 agree

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Table 2. Wavefunction Representations (nκ, Number of Single-Particle Functions; Nκ, Number of Time-Independent Grid Points or Basis Functions) CH3I coordinates

nκ

CH3 Nκ

nκ

Nκ

F

3

10

4

10

ϑF,jF

4

7

4

7

θ

4

40

8

40

φ,χ

3

12

6

12

R ϑR

5 8

768 48

jR

7

32

elec. states

3

3

within subwavenumber accuracy with the results of previous computations employing the same Hamiltonian.32 Compared to these previous calculations which considered a maximum of 36 vibrational states, the present convergence tests increased the number of vibrational states considered to 60. The total absorption cross section σ(E), the partially and fully resolved cross sections with respect to the final states n of the fragments σn(E), and the product distributions are obtained from the wave function Ψ(t) propagated in real time. Here the initial wave function Ψ(0) is given by the ground state wave function ΨG of the ground electronic state put on a excited state PES by applying the appropriate transition dipole moment operator μ̂: Ψ(0) = μ̂ΨG The total absorption cross section is given by * + Z ^ 2πE ¥ iðEþE0 Þt - iHt e Ψð0Þe Ψð0Þ dt σðEÞ ¼ 3c - ¥ ¼

Z ¥ 4πE Re½ eiðE þ E0 Þt ΨðtÞdt 3c 0

ð5Þ

^ denotes the Hamiltonian, c is the velocity of light, E0 is Here H the ground state energy, and Re[x] is the real part of x. Introducing appropriate projection operators P̂n onto the final states in question, partially or fully state-resolved cross sections can similarly be calculated by Fourier analyzing the wave function projected onto the final states in the asymptotic limit: Z ^ ^ 0 ^ 2πE ¥ iðEþE0 Þt ^n e - iHt 0 ÞΨð0Þædt e ÆΨð0Þje - iHt 0 lim ðeiHt P t f ¥ 3c - ¥ Z t0 2πE ^n Ψðt 0 Þædt ¼ eiðEþE0 Þt ÆΨðt 0 - tÞjP lim 3c t 0 f ¥ - t0 Z t0 4πE ^n Ψðt 0 Þædt lim ¼ Re½ eiðEþE0 Þt ÆΨðt 0 - tÞjP ð6Þ 3c t0 f ¥ 0

σ n ðEÞ ¼

For the present system, taking t0 = 70 fs assures a converged description.

IV. RESULTS AND DISCUSSION A. Absorption Spectra. Figure 2 shows the absorption spectrum computed for excitation to the 3Q0 state (parallel transition). Results computed in full and reduced dimensionality are displayed together with the experimentally observed absorption spectrum for the A band.4,46 The reduced dimensionality 5995



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Figure 2. Absorption spectra calculated for parallel transitions (X f 3 Q0) in full and reduced dimensionality are displayed together with the experimental spectrum. All spectra are scaled to have the same maximum intensity.

calculations include the coordinates R, ϑR, and θ as active coordinates in the three-dimensional (3D) model. This choice of coordinates corresponds to the coordinates used in the quantum dynamics studies of Guo and co-workers1,3,7 and describes the CH3-I distance, the amplitude of the H3-C-I bending, and the CH3 umbrella motion explicitly. The fivedimensional (5D) model additionally includes the H3-C-I torsion described by the coordinate φR and the symmetric methyl stretch described by the coordinate F in the dynamical treatment. Coordinates that were not included in the dynamical treatment were frozen at their values at the Franck-Condon point. One finds that the agreement between all spectra is quite good and that differences between the theoretical spectra computed in full and reduced dimensionality are small. Spectra computed in lower dimensionality tend to be shifted to slightly higher energies. However, the differences only range from 0.01 to 0.03 eV. This finding demonstrates that, not surprisingly, the absorption spectrum is mainly determined by the motion in only a small number of coordinates: R, ϑR, and θ. The agreement between the calculated spectrum based on exclusively parallel excitation (X f 3Q0) and the experimental spectrum for the A band is also quite good. The theoretical spectrum computed in full dimensionality is slightly red-shifted by about 0.05 eV and about 10% broader than the experimental one. The improved agreement compared to the theoretical work of ref 3 is mainly caused by using of the improved vertical excitation energy computed by Alekseyev et al.15 in the potential modeling. It should be noted that above comparison only considers the contribution of the parallel excitation (X f 3Q0) in the computed spectra. This choice is consistent with the conclusions drawn by Eppink and Parker4 from their experimental study. They concluded that the contributions of the perpendicular transitions to the A band are irrelevant due to their small intensity. However, this conclusion disagrees with ab initio calculations for the transition dipole moments performed by Amatatsu et al.11 and Alekseyev et al.16 These theoretical studies indicated that the total intensity resulting from the perpendicular X f 1Q1 transition should be as high as 20%. Such a contribution would significantly broaden the high energy tail of the spectrum.11,16 Because the present study is not concerned with electronic structure calculations, we presently are not able to contribute to the resolution of this discrepancy. We can only mention that the present study yields an absorption spectrum in

Figure 3. Populations of the electronic states obtained from fulldimensional and reduced-dimensional calculation as a function of time. The upper panel displays the population of the 3Q0 state. The populations of the A0 and A00 states of the 1Q1 level are shown in the lower panel.

good agreement with experiment if exclusively perpendicular excitation is considered. B. Electronic Population Dynamics. The time evolution of the electronic populations after broad band excitation into the 3 Q0 state is displayed in Figure 3. The upper panel shows the probability of being in the 3Q0 electronic state. About 10 fs are required to reach the conical intersection between the 3Q0 and 1 Q1 surfaces, after which significant population transfer occurs for a period of about 15 fs until the wave packet has passed beyond the coupling region. This feature is common to the 5D and 9D results. The 3D results show a similar pattern, however here the population transfer starts somewhat earlier. Also, in the 3D results a minor damped oscillatory structure can be seen later at times up to 40 fs. These structures result from electronic recurrences and are more pronounced in lower dimension dynamics as the coherence of the nuclear wave function is longer lived. More importantly, when the final extend of the population transfer from the 3Q0 electronic state to the two 1Q1 electronic states is compared, significant differences depending on the dimensionality of the description employed are found. While the differences between the 5D result and the full-dimensional description are small and within the intuitively expected range, the 3D modeling shows more than twice as much population transfer compared to 5D and 9D. It should be noted that this finding is independent of the particular value of jR chosen in the 3D calculations: essentially indistinguishable results have been obtained using different fixed values of jR in the 3D model. In the full-dimensional results one additionally sees that the populations of the A0 and A00 states of the 1Q1 level differ by about 20% while the corresponding populations in the 5D calculation are equal. The surprising dependence of the population transfer on the dimensionality of the dynamical model and the unequal populations of the A0 and A00 states of the 1Q1 level require an 5996


The Journal of Physical Chemistry A explanation. This can be obtained by studying the jR dependence of the diabatic potential couplings. The diabatic model employed by Amatatsu et al.6,11 bases its symmetry consideration on a Cs reference symmetry. The three diabatic states numbered 1, 2, and 3 are one diabatic 1Q1 state transforming according to the A0 irreducible representation, one diabatic 1Q1 state transforming according to A00 , and the diabatic 3Q0 state (which transforms according to A0 ). Correspondingly, the diabatic potential couplings V13, V23, and V12 transform as A0 , A00 , and A00 , respectively. However, considering a C3v reference symmetry, the diabatic states 1 and 2 should transform as the A0 (E) and A00 (E) components of the E representation and the diabatic state 3 as A1. The corresponding diabatic potential couplings V13 and V23 should therefore transform as the A0 (E) and A00 (E) components of the E representation. This symmetry is correctly reflected in the parts of the Amatatsu et al. potential which dependent on the CH3 asymmetric bending and stretching coordinates. It is, however, not correctly described by the parts depending on the H3-C-I bending coordinates ϑ and j (see eqs 7-9 of ref 11). With respect to ϑ and j, V13 and V23 of refs 3, 6, and 11 transform as the A1 and A2 irreducible representations of C3v. This improper modeling of the H3-C-I bending dependence of the diabatic potential couplings only affects dynamical calculations which include torsional motion. The significant difference found between the 3D calculations which do not include the torsional coordinate jR and the more elaborate 5D and 9D calculations, which include the torsional coordinate can be attributed to this peculiarity of the diabatic modeling employed in refs 3, 6, and 11. It also explains the broken symmetry of the populations of the A0 (1Q1) and A00 (1Q1) states in the 9D calculations where torsional motion and asymmetric vibrations in the methyl group are included. It should be noted that this problem should have surfaced earlier. Although the torsional coordinate had been included in earlier five-dimensional dynamical studies2,8 that employed the potential of ref 6, the reduced-dimensional model employed in these studies used a torsional coordinate that accidentally included parts of the overall rotation and strongly overestimated the effective mass associated with this coordinate. To correct for this error the inverse mass type factor 1/(μIr2I sin2 θI) þ 2/(3mHr2H sin2 θH) in the kinetic energy of ref 2 would have to be replaced by 1/(μIr2I sin2 θI) þ 2/(3mHr2H sin2 θH sin2 θI). Due to this overestimation of the effective mass, the torsional motion was effectively frozen and the calculation could not test the torsional potentials. Beside the calculations studying parallel excitation to 3Q0 surface, full-dimensional quantum dynamics calculations have also been performed for perpendicular excitation to the 1Q1(A0 ) electronic state. If the wave packet is started on the 1Q1 PES no significant electronic population transfer to the diabatic 3Q0 electronic state is found: the population of the diabatic 3Q0 state never exceeds one percent. This result is not surprising as the diabatic 1Q1 state corresponds to an excited adiabatic state at the Franck-Condon geometry and to the ground adiabatic state in the asymptotic limit. Thus, staying on the diabatic 1Q1 PES during the passage of the conical intersection corresponds to a nonadiabatic transition from the excited to the ground state and at the same time avoids a nondiabatic transition. As discussed extensively in refs 47-50, such a type of process is strongly favored compared to a nondiabatic transition (diabatic 1Q1 to diabatic 3Q0) which would avoid changing the adiabatic electronic PES.

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Figure 4. Final electronic state resolved partial cross sections for parallel excitation (X f A(3Q0)). All cross sections are scaled to show identical electronic state resolved integral cross sections.

Switching from the time-dependent picture to the energydependent one and restricting the further discussion to the results of our full-dimensional calculations, Figure 4 shows the electronically state resolved cross sections calculated for exclusively parallel transition. In Figure 4, all three spectra have been scaled to show equal energy-integral absorption cross sections. To this end, the spectra of the 3Q0, A0 (1Q1), and A00 (1Q1) electronic states have been divided by the electronic populations 0.952, 0.0214, and 0.0262, respectively, seen in Figure 3. One can see that the energy profile is nearly identical for all electronic states. Only a small relative red shift of the 1Q1 spectra can be found. Correspondingly, the I/I* product distribution resulting from parallel transition (X f 3Q0) is approximately energy independent. The small relative shift of the spectra gives rise to an approximately linear decrease of the relative yield of I products from 0.063 at E = 4.3 eV (288 nm) to 0.042 at E = 5.3 eV (233 nm). C. Fully State Resolved Partial Spectra. The most detailed information about the dissociation process is given by the fully state-resolved partial spectra. These are calculated using eq 6 with projection operators P̂n which specify all quantum states of the photodissociation products: the electronic state of the iodine atom and the vibrational and rotational states of the methyl fragment. Here these spectra will be denoted as σx,(ν1,ν2,ν3l ,ν4l ),J,K. The index x takes the values g or e for iodine produced in the (degenerate) ground electronic state (I channel) or the spin-orbit excited electronic state (I* channel), respectively, (ν1,ν2,νl33νl44) denotes the vibrational state of the methyl fragment using the notation of Medvedev et al.,35 ν1, ν2, ν3, and ν4 are the number of quanta of excitation in the symmetric stretch, umbrella, asymmetric stretch, and asymmetric bending modes, respectively. The rotational state of the methyl is characterized by the usual quantum numbers J and K for its total angular momentum and its angular momentum component for rotation around the CH3 symmetry axis. Noting that σx,(ν1,ν2,ν3l ,ν4l ),J,K depends quadratically on the transition dipole moment μ, we will use the appropriately μ-rescaled values σx,(ν1,ν2,νl3 ,νl4 ),J,K/μ2 instead of σx,(ν1,ν2,νl3 ,νl4 ),J,K. Because the size of the μ’s is somewhat uncertain (see the discussion in the previous subsection), avoiding any unnecessary reference to explicit μ’s seems advantageous. Considering that eight vibrational states of the methyl product (of the up to 60 ones included in the analysis) show significant final populations and rotational population with Js beyond 10 that are still sizable in the I channel, it is obviously impossible to 3

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3

3

3

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4

4



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The above results suggested an interpretation based on the reflection principle (see, e.g., ref 51 for an excellent review of standard interpretation concepts for photodissociation processes). Consider the most simple application of reflection principle in one dimension: modeling the ground state potential Vg(x) as a standard harmonic oscillator, Vg(x) = mω2x2/2, and the excited state potential Ve(x) as approximately linear in the vicinity of the Franck-Condon point, Ve(x) = v0 þ v1 3 x constants), the ground state wave function is (v0 and v1 denote 2 N 3 e-(1/2)mωx and the reflection principle would predict an approximate absorption spectrum σðE1D Þ ¼ c 3 e - mωððE1D - ν0 Þ=ν1 Þ

Figure 5. Fully state resolved-partial spectra σe,(0,0,0,0),j,0, σe,(0,1,0,0),j,0, and σe,(0,2,0,0),j,0 (see text for details) for parallel excitation and the I* product channel are displayed in panels a, b, and c, respectively. The spectra are plotted as a function of E-Evib, where E is the energy of the absorbed photon and Evib is the vibrational energy of the generated methyl fragment.

present the complete set of fully state-resolved data. Thus, our presentation of fully state-resolved data focuses on the general trends and shows only results for the dominant channels. Only parallel excitation will be considered here. Figure 5 displays the most intense partial spectra. I* products and vibrational excitation only in the umbrella mode is found here. To demonstrate an important feature of all fully state-resolved partial spectra, the spectra have been plotted as a function of the photon energy E minus the vibrational energy Evib of the generated methyl product. One then finds that all spectra show an approximately identical energy profile: they can be well represented using a simple Gaussian GðEÞ ¼ c 3 e - ððE - E0 Þ=ΔEÞ

2

ð7Þ

Importantly, the width parameter approximately takes an identical value of ΔE = 0.30 eV for all spectra displayed independent of the specific vibrational and rotational state of the products. The center of the Gaussian is also essential independent of the rotational state. It varies only comparatively weakly depending on the vibrational state: E0 values of 4.64, 4.67, and 4.70 eV are found for ν2 = 0, ν2 = 1, and ν2 = 2, respectively. This slight increase of about 0.03 eV per quantum of ν2 excitation is only a fraction of the vibrational energy present in the CH3 fragment: the vibrational excitation energies for the two excited states are Evib(ν2 = 1) = 591 cm-1 = 0.073 eV and Evib(ν2 = 2) = 1265 cm-1 = 0.155 eV.

2

ð8Þ

The connection between this simple 1D absorption spectrum and the fully state-resolved partial spectra discussed above is obvious. The width parameter ΔE in eq 7 can be straightforwardly identify with the constant v1/(mω)1/2 in eq 8. Thus, a simple interpretation based on the reflection principle is supported by the state-independent value of ΔE seen in Figure 5. Understanding the state-dependence of the center of the Gaussian, E0, requires a more elaborate discussion. The results presented in Figure 5 imply that E0 is independent of the rotational product state. On the first sight this finding seems to differ from expectations based on the reflection principle: considering that the energy E1D in eq 8 should naively be identified with the energy E - Erot - Evib available in the dissociation coordinate R, one would first expect the center of the partial spectra to be blueshifted by Erot þ Evib, depending on the rotational and vibrational energy of the methyl fragment produced. While this type dependence can be approximately verified for the different vibrational states (note that the partial spectra have been plotted as a function of E - Evib in Figure 5), Figure 5 demonstrated the center positions of partial spectra are essentially independent of Erot. To explain this finding, one has to assume that the rotational motion (described by the coordinates ϑR and jR) and the motion in the dissociation coordinate R are strongly coupled. Energy can be very efficiently be transferred between these motions during the dissociation process, consequently, both motions essentially share a common pool of energy. At the Franck-Condon point, only the amount of energy present in this common energy pool is determined. E1D in eq 8 then must be identified with E - Evib (instead of E - Erot - Evib) because rotational energy should not be seen as a type of energy separable from the kinetic energy present in the dissociation coordinate at the Franck-Condon point. The detailed investigation of Figure 5 also has shown that the peak positions of the partial spectra are not completely independent of E - Evib. Complete independence would have implied that the vibrational motion is separable from the dissociative and rotational motion. Obviously this separation is not perfect and the peak positions are slightly shifted toward higher energies as the vibrational energy increases. This implies that the “effective vibrational frequency” in the umbrella mode at the FranckCondon point slightly exceeds the umbrella frequency of the free methyl radical. Considering that the steric hindrance of the umbrella motion due to the presence of iodine atom at the Franck-Condon point, such shift towards a higher “effective frequency” seems to be perfectly physically reasonable. The above discussion considered dissociation resulting in iodine atoms in the electronically excited state which is the 5998



Figure 6. Fully state-resolved partial spectra σg,(0,1,0,0),J,3, σg,(0,2,0,0),J,3, and σg,(0,3,0,0),J,3 (see text for details) for parallel excitation and the I product channel are displayed in panels a, b, and c, respectively. The spectra are plotted as a function of E - Evib, where E is the energy of the absorbed photon and Evib is the vibrational energy of the generated methyl fragment.

dominant channel. Figure 6 presents the most intense partial spectra from iodine atoms produced in the electronic ground state. The contributions from the two components of the degenerate 1Q1 electronic state have been summed together in these spectra. It should also be noted that here the dominant contribution is found in the rotational states with K = 3 and K = -3 (see next subsection for a detailed discussion). Results for opposite K values are identical due to symmetry and thus only the results for positive K’s are shown in Figure 6. Regarding the line shape of the partial spectra, the same conclusions as discussed above for Figure 5 are valid also for the results presented in Figure 6. The partial spectra are approximately Gaussians with an identical width parameter ΔE = 0.30 eV. The peak positions are approximately independent of the amount of rotational excitation. In contrast to Figure 5, this independence is not as perfect here which might be related to the generally higher level of rotational excitation present. In general, the peak positions are shifted to slightly lower energies. This is related to the fact that nonadiabatic transitions from the initially populated 3Q0 electronic state to the 1Q1 electronic state are more probable if the kinetic energy in the R coordinate is smaller. Thus, nonadiabatic transitions are more likely to occur for wave packet components with low energy and the 1Q1 partial spectra should be slightly shifted toward lower energies compared to their 3Q0 counterparts. This can actually be seen in a comparison of the spectra in Figures 5 and 6.

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D. Rotational Product Distributions. The above discussion has centered on the energy profiles of the fully state-resolved partial spectra. Now the absolute size of the contributions of the different rotational and vibrational product states should be considered. Figure 5 shows that the rotational product distributions in the I* channel are cold and always peak at a value of J = 2. The rotational product distributions in the I channel are significantly hotter and peak at values of J = 8 to J = 9 (see Figure 6). The difference between the rotational product distributions is induced by the conical intersection: the coordinate ϑR, which asymptotically describes rotation, acts as coupling coordinate in the neighborhood of the conical intersection. As outlined for example in refs 47-50, a wave packet moving on the lower adiabatic PES through the region of the conical intersection tends to show large amplitude motion in the coupling coordinate. In contrast, a wave packet on the upper adiabatic PES typically contracts in the coupling coordinate. In methyl iodide photodissociation (after parallel excitation), products in I or I* channels correspond to wave packets transferred to the lower or upper adiabatic PES, respectively. Correspondingly, products in I or I* channels can be expected to show large or small amplitude motions in the coupling coordinate. This finally results in either a large or a small degree of rotational excitation. These theoretical results agree well with experimental findings as discussed in detail in previous work.2 Although these conclusions where based on older experimental data there are supported by recent experimental results.19 Recent experiments19 have found that the rotational temperature in the I* channel is independent of the vibrational excitation for a given excitation wavelength and depends only weakly on the excitation wavelength. This finding is in good agreement with the results presented in Figure 5. Peak positions E0 are independent of the rotational quantum number and levels of rotational excitation are independent of the vibrational state. For the I channel studied in Figure 6, the E0’s were found to slightly increase with increasing rotational excitation. Thus, the rotation product distributions resulting from Figure 6 show a decrease of rotation excitation with decreasing energy and increasing wavelength. This again is in agreement with the trends reported in recent experimental work.19 However, the increase of the rotational temperature with increasing vibrational excitation in the I channel reported in ref 19 can not be explained by the present theoretical results. The preferential value of the K quantum number taken by the photodissociation products strongly correlates with electronic state as already previously discussed in ref 2. The results of the present work show again that K = 0 states vastly dominate in the I* channel, while K = (3 states dominate in the I channel. This correlation is an immediate consequence of the analytic form of the ϑR- and jR-dependent diabatic coupling terms in the PES employed.2 Additionally, small but significant contributions from the other states with |K| e 5 have been found in the present work. These contributions result from diabatic coupling terms that depend on the asymmetric bending and stretching coordinates of the methyl group. Such terms were not considered in previous quantum dynamics studies. E. Vibrational Product Distributions. Figures 5 and 6 show fully state-resolved partial spectra plotted as a function of E Evib. While this presentation is best suited for a theoretical analysis of the present numerical results, experiments measure product distributions and spectra as a function of energy of the absorbed photon E or, equivalently, of the corresponding 5999



Figure 7. Vibrational product distributions are shown as a function of the wavelength of the absorbed photon. Panels a and b show results for the I* and I channels after parallel excitation.

wavelength λ. Vibrational product distributions at a given E or λ, thus, strongly depend on the relative energy shift of the different vibrationally resolved partial spectra. The values of Evib and E0 discussed in section IVC are of central importance for the vibrational product distributions observed at a given photon energy. Vibrational product distributions for the I* and I channel (after parallel excitation) obtained from the fully state-resolved partial spectra by summation over all rotational states are displayed in Figure 7 as a function of λ. Excitation of the umbrella vibration provides the dominant contributions. Except for the umbrella excited states, populations reaching significant levels have been found only for states showing a small degree of excitation in the symmetric stretching or the asymmetric bending vibrations. Figure 7 also shows the results for these minor but still significant vibrational channels: all final vibrational states that contribute for more than 0.5% to the total amount of product considering broad band excitation are plotted. In addition to the large contributions from vibrational ground state of methyl and the umbrella excited states (0,ν2,0,0) with ν2’s up to 5, smaller contributions from the symmetric stretching excited state (1,0,0,0) and the

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asymmetric bending doubly excited state (0,0,0,20) are found in Figure.7a. Because the I channel contributes only about 4% to the total population, here only data for the more prominent vibrational channels (0,ν2,0,0) with ν2’s between 0 and 5 is presented. Other vibrational states yield (broad band) contributions of less than 4% of the I population or, equivalently, less than 0.2% of the total (I þ I*) population. (Many of the contributions which individually make up for less than 0.2% of the total wave packet can not be extracted from the present MCTDH wave function with sufficient accuracy. Therefore, such data is generally not presented. It could be obtained using higher integration accuracies and larger basis sets in the MCTDH calculations.) The general trends seen for the vibrational product distributions agree with experimental results.4,17-19,52-54 Excitation of the umbrella vibration is found to strongly dominate the product distributions and the I channel shows higher levels of excitation than the I* one. Excitation of the symmetric stretch vibration at smaller wavelength and excitation of the asymmetric bending mode have been reported as minor channels in recent experimental studies.4,17 Therefore, the experimental trends regarding the extend of excitations in the different vibrational levels of the methyl product agree well with the present theoretical findings. Comparing the extend of vibrational excitation in the umbrella vibration more quantitatively, significant differences between the present theoretical results and experimental findings are found. For the I* channel, experiments clearly show vibrational product distributions peaking at ν2 = 0 for all wavelengths. Vibrational populations of 0.85 at 304 nm,18 0.76 at 266 nm,4 and 0.66 at 248 nm52 have been reported. In contrast, in the present calculations ν2 = 0 is the dominating channel only at wavelength above 270 nm and the calculated populations for the ν2 = 0 state are significantly smaller at all wavelengths. Correspondingly, the populations of the umbrella mode excited vibrational states are always too high. Considering the I channel, a similar quantitative disagreement between the present results and experiment can be seen. Recent experiments at 304 nm18 yield populations of 0.38, 0.58, 0.18, and 0.07 for states with vibrational quantum numbers ν2 of 0, 1, 2, and 3, respectively. At 248 nm, populations of 0.24, 0.34, 0.23, and 0.13, respectively, have been measured (see ref 7). Thus, compared to experiment the present calculations significantly overestimate the excitation of umbrella vibration for products in the I channel. This result is somewhat surprising since previous quantum dynamics calculations1-3,7 using the Amatatsu et al. potentials3,6,11 showed significantly better agreement between theory and experiment.

V. CONCLUSIONS AND PERSPECTIVE Accurate full-dimensional quantum dynamics calculations for the photodissociation of methyl iodide have been presented for the first time. The theoretical results allow one to study the dissociation dynamics of this polyatomic system in full detail. By analyzing the simulation data a detailed understanding of the dynamics can be gained. The strong coupling between the C-I distance and the H3-C-I bending motions can be demonstrated by analyzing the fully rotationally and vibrationally stateselected absorption cross sections. The CH3 vibrations are found to be approximately but not perfectly separable. Vibrational excitation of the symmetric stretch mode or the asymmetric bending modes of the methyl group can be identified as minor channels. 6000


The Journal of Physical Chemistry A All these results demonstrate that full-dimensional MCTDH simulations can provide a very helpful tool to gain a profound understanding of the dissociation dynamics of polyatomic molecules. Beside checking consistency between experimental data and computed numbers, the wealth of data provided by fulldimensional quantum dynamics calculations can greatly simplify the development of interpretational concepts and provide a route toward physical understanding. The present study also highlights a persistent problem in the dynamical simulation of methyl iodide photodissociation. While the potential energy surfaces developed by Amatatsu and coworkers3,6,11 provided a pioneering contribution to the detailed investigation of polyatomic photodissociation processes, the present results also clearly indicate significant shortcomings even of the most recent potential.3 More accurate potentials for the excited electronic states of methyl iodide are obviously a prerequisite for further progress.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Present Address †

Department of Chemistry, Stanford University, Stanford, California 94305, United States.

’ ACKNOWLEDGMENT The authors gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (Sonderforschungsbereich 613). ’ REFERENCES (1) Guo, H. Chem. Phys. Lett. 1991, 187, 360. (2) Hammerich, A. D.; Manthe, U.; Kosloff, R.; Meyer, H.-D.; Cederbaum, L. S. J. Chem. Phys. 1994, 101, 5623. (3) Xie, D.; Guo, H.; Amatatsu, Y.; Kosloff, R. J. Phys. Chem. A 2000, 104, 1009. (4) Eppink, A. T. J. B.; Parker, D. H. J. Chem. Phys. 1998, 109, 4758. (5) de Nalda, R.; Dura, J.; Garcia-Vela, A.; Izquierdo, J. G.; GonzalezVazqurez, J.; Banares, L. J. Chem. Phys. 2008, 128, 244309. (6) Amatatsu, Y.; Morokuma, K.; Yabushita, S. J. Chem. Phys. 1991, 94, 4858. (7) Guo, H. J. Chem. Phys. 1992, 96, 6629. (8) Manthe, U.; Hammerich, A. D. Chem. Phys. Lett. 1993, 211, 7. (9) Meyer, H.-D.; Manthe, U.; Cederbaum, L. S. Chem. Phys. Lett. 1990, 165, 73. (10) Manthe, U.; Meyer, H.-D.; Cederbaum, L. S. J. Chem. Phys. 1992, 97, 3199. (11) Amatatsu, Y.; Yabushita, S.; Morokuma, K. J. Chem. Phys. 1996, 104, 9783. (12) Gerdts, T.; Manthe, U. J. Chem. Phys. 1997, 107, 6584. (13) Aljitha, D.; Fedorov, D. G.; Finley, J. P.; Hirao, K. J. Chem. Phys. 2002, 117, 7068. (14) Aljitha, D.; Wiezbowska, M.; Lindh, R.; Malmqvist, P. A. J. Chem. Phys. 2004, 121, 5761. (15) Alekseyev, A. B.; Liebermann, H.-P.; Buenker, R. J.; Yurchenko, S. N. J. Chem. Phys. 2007, 126, 234102. (16) Alekseyev, A. B.; Liebermann, H.-P.; Buenker, R. J. J. Chem. Phys. 2007, 126, 234103. (17) Eppink, A. T. J. B.; Parker, D. H. J. Chem. Phys. 1999, 110, 832. (18) Li, G.; Shin, Y. K.; Hwang, H. J. J. Phys. Chem. A 2005, 109, 9226. (19) Rubio-Lago, L.; Garcia-Vela, A.; Arregui, A.; Amaral, G. A.; Banares, L. J. Chem. Phys. 2009, 131, 174309.

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Photodissociation of CH3I: A Full-Dimensional (9D) Quantum

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