Full-Dimensional Quantum Dynamics of Vibrationally Mediated

Article pubs.acs.org/JPCA

Full-Dimensional Quantum Dynamics of Vibrationally Mediated Photodissociation of NH3 and ND3 on Coupled Ab Initio Potential Energy Surfaces: Absorption Spectra and NH2(Ã 2A1)/NH2(X̃ 2B1) Branching Ratios Jianyi Ma,*,†,‡ Changjian Xie,‡,§ Xiaolei Zhu,∥ David R. Yarkony,*,∥ Daiqian Xie,*,§ and Hua Guo*,‡ †

Institute of Atomic and Molecular Physics, Sichuan University, Chengdu, Sichuan 610065, China Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States § Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210093, China ∥ Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, United States ‡

ABSTRACT: Vibrationally mediated photodissociation of NH3 and ND3 in the A band allows the exploration of the excited-state potential energy surface in regions that are not accessible from the ground vibrational state of these polyatomic systems. Using our recently developed coupled ab initio potential energy surfaces in a quasi-diabatic representation, we report here a full-dimensional quantum characterization of the Ã ← X̃ absorption spectra for vibrationally excited NH3 and ND3 and the corresponding nonadiabatic dissociation dynamics into the NH2(Ã 2A1) + H and NH2(X̃ 2B1) + H channels. The predissociative resonances in the absorption spectra have been assigned with appropriate quantum numbers. The NH2(Ã 2A1)/NH2(X̃ 2B1) branching ratio was found to be mildly sensitive to the initial vibrational excitation prior to photolysis. Implications for interpreting experimental data are discussed.

1. INTRODUCTION The traditional photoexcitation typically accesses a small Franck−Condon region on the electronically excited potential energy surface (PES) due to the compact nature of the groundstate wave function. By vibrationally pumping the molecule before photoexcitation, different regions of the excited-state PES can be explored, which might lead to quantitatively or qualitatively different dissociation dynamics. This so-called vibrationally mediated photodissociation (VMP) has been shown in several prototypical systems, such as H2O and NH3, to be a powerful tool to explore the mode specificity and bond selectivity in reactive systems.1,2 The first absorption band of ammonia near 50000 cm−1 is dominated by a long progression of nearly equally spaced diffuse peaks, assignable to the umbrella mode excitations (2n).3,4 This spectrum can be attributed to the significant change of the minimal energy structure from the C3v pyramidal ground (X̃ 1A1) state to the D3h trigonal planar first excited (Ã 1A2″) state. These 2n features are predissociative, with lifetimes ranging from femtoseconds to picoseconds, depending on the umbrella quantum number and isotopic substitutions. The finite lifetimes stem from the quasi-bound nature of the Ã state PES in the Franck−Condon region. On the other hand, © 2014 American Chemical Society

the dissociation products include both the ground and excited states of NH2, with the former often dominating, indicating a breakdown of the Born−Oppenheimer approximation. Experimental studies of the absorption spectra,5−10 product internal state distributions and branching ratios,11−21 and dissociation lifetimes22,23 have been reported. The ample experimental data made the photodissociation of ammonia a prototypical system for understanding an array of important issues in polyatomic systems, such as tunneling, mode specificity, nonadiabatic transitions, and intramolecular vibrational energy redistribution (IVR).1,2,24−26 Concomitantly, theoretical studies have helped to reveal the topography of the Franck−Condon region and the seam of the conical intersection,27−33 which are responsible for unique nonadiabatic dynamical features of ammonia photodissociation.34−44 Due to the importance of quantum effects such as tunneling, a faithful characterization of the multidimensional dynamics requires quantum mechanics on accurate PESs. Very recently, four of the current authors have reported highly Special Issue: David R. Yarkony Festschrift Received: June 9, 2014 Revised: July 17, 2014 Published: July 18, 2014 11926

dx.doi.org/10.1021/jp5057122 | J. Phys. Chem. A 2014, 118, 11926−11934

The Journal of Physical Chemistry A

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accurate coupled PESs in a quasi-diabatic representation determined from high-level ab initio data, energies, energy gradients, and derivative couplings at a large number of nuclear configurations.45,46 Full-dimensional quantum dynamical calculations using these PESs have quantitatively reproduced a wide array of experimental data for the photodissociation of NH3 and ND3, including the position, width, and intensity of the predissociative resonances, as well as the NH2(Ã 2A1)/ NH2(X̃ 2B1) branching ratio.45,46 Very recently, the final state distributions of the NH2(X̃ 2B1) fragment have been calculated and found to agree with experimental data very well.47 These recent theoretical studies significantly improved our understanding of this prototypical system. Strong mode specificity and bond selectivities have been reported in the VMP of ammonia.48−56 One of the most intriguing findings is the strong mode selectivity in the nonadiabatic dissociation dynamics. Unlike the commonly observed dominance of the ground-state NH2(X̃ 2B1) channel, excitation in the antisymmetric stretching mode (ν3) of NH3 followed by photolysis was found to lead to predominately adiabatic dissociation to the excited state NH2(Ã 2A1).52,53,56 The strong mode selectivity in controlling the nonadiabatic dynamics has not yet been elucidated. In fact, previous theoretical studies based on semiclassical42 and quantum dynamics43 have failed to reproduce the mode-specific NH2(Ã 2A1)/NH2(X̃ 2B1) branching ratios inferred from these experiments. In this work, we explore the VMP of ammonia using the same dynamical model developed in our recent work.45−47 We determine the absorption spectra including several low-lying vibrational states of NH3 and ND3 and provide assignments based on the wave functions of these Ã -state predissociative resonances. In addition, we compute the NH2(Ã 2A1)/ NH2(X̃ 2B1) branching ratios for these states in an attempt to understand the experimentally reported mode selectivity. This work is organized as follows. Section 2 outlines the quantum dynamics method used to compute the absorption spectra and NH2(Ã 2A1)/NH2(X̃ 2B1) branching ratios. The results are presented and discussed in section 3. In section 4, a summary is given.

Figure 1. PESs of the two lowest-lying states of NH3. The equilibrium geometry of NH3 is shown for both the ground and excited states.

r2, respectively, and j20̂ = (j1̂ + j2̂ )2 due to the fact that the total angular momentum is set to zero. The total wave function, which is expressed as a vector

⎛ΦA ⎞ |Φ⟩ = ⎜⎜ ⎟⎟ ⎝ ΦX ⎠

has two components for the two electronic states. They are expanded in terms of the parity (p) adapted basis Φ A/X, p =

2

1 ∂2 + ∑− 2μi ∂ri 2 i=0

∑ i=0

+ p|j1 − m⟩|j2 m⟩)

(4)

p = ±1

(5)

To make the basis compact, we have used a nondirect product approach61 for the radial coordinates. In particular, different numbers of vibrational basis functions for the two nonreactive coordinates, namely, r1 and r2, were used in two different r0 regions. The discretization parameters are listed in Table 1. To facilitate the evaluation of the action of the potential energy operators, the wave function is transformed into a grid where the potential energy operators are diagonal. This pseudospectral method is quite efficient because only small onedimensional transformations are involved.62 The Condon model was assumed, and the vibrational eigenfunctions on the ground electronic state were placed vertically on the excited electronic state PES. The propagation of the wave packet vector

2

ji ̂

2μi ri2

12

|j1 j2 m , p⟩ = (2 + 2δm ,0)−1/2 (|j1 m⟩|j2 − m⟩

(1)

2

p ΨiA/X, |i ⟩|i1⟩|i2⟩|j1 j2 m , p⟩ 0i1i 2j j m 0

where ΨA/X,p i0i1i2j1j2m are the coefficients of the wave functions in the discrete representation.59 Here, i0 denotes the DVR (discrete variable representation)60 grid index for the radial coordinate r0, while i1 and i2 label the vibrational basis functions for the radial directions of r1 and r2, respectively. |j1j2m,p⟩ is the angular FBR (finite basis representation) defined by parity-adapted products of the spherical harmonics

in which I is a two-dimensional identity matrix. Hd is the 2 × 2 diabatic potential energy matrix defined in our recent work,46 which was improved from our earlier version45 by having the correct asymptotic behavior. In Figure 1, the coupled PESs for the two electronic states of NH3 are shown. The kinetic energy operator (KEO) expressed in the (2 + 1) Radau−Jacobi coordinates for the NH3 system can be written as (ℏ = 1)57,58 T̂ =

∑ i0i1i 2j1 j2 m

2. THEORY Following our recent work,46 the six-dimensional Hamiltonian (J = 0) is conveniently given in a quasi-diabatic representation as follows H = T̂ I + H d

(3)

(2)

where r0 is Jacobi radial coordinate, r1 and r2 are two Radau radial coordinates, μ0, μ1, and μ2 are the corresponding reduced masses, θ1(θ2) is the angle between vectors r1⃗ (r2⃗ ) and r0⃗ , and φ is the relative azimuthal angle between r1⃗ and r2⃗ in body fixed frame. j1̂ and j2̂ are the angular momentum operators for r1 and

⎛ ΨA ⎞ k Ψk = ⎜⎜ ⎟⎟ X ⎝ Ψk ⎠ 11927



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Table 1. Numerical Parameters (in au) Used in Wave Packet Calculations grid/basis ranges and sizes

largest values of j1, j2 and m damping function for r0a damping functions for r1 and r2a flux position for r0 propagation steps a

NH3

ND3

r0 ∈ (1.2,14.0), N0 = 100 for 1 ≤ i0 ≤ 21, DVR r1, r2 ∈ (1.2,4.5), N1 = N2 = 21 for 22 ≤ i0 ≤ 100, basis N1 = N2 = 6 24

r0 ∈ (1.2,14.0), N0 = 120 for 1 ≤ i0 ≤ 23, DVR r1, r2 ∈ (1.2,4.5), N1 = N2 = 23 for 24 ≤ i0 ≤ 120, basis N1 = N2 = 6 27

αD = 0.1, r0,D = 11.1 αD = 0.1, ri,D = 3.1

αD = 0.1, r0,D = 11.1 αD = 0.1, ri,D = 3.1

r0,f = 10.0 13000

r0,f = 10.0 18000

P A/X(E) =

× Im

⎡

∑ (2 − δk ,0)e−ik′ ϑ⎢δ(r0 − r0f )

The position of the dividing surface (r0f), as given in Table 1, is located in the dissociation asymptote beyond the conical intersection. Finally, the predissociative resonances in the absorption spectra from various vibrational states of NH3(X̃ ) and ND3(X̃ ) were assigned based on their nodal structures in the corresponding wave functions.

3. RESULTS AND DISCUSSION Convergence tests have been performed with regard to the size of the grid, the propagation steps, and the position of the dividing surface. Table 1 lists all of the numerical parameters used in the final dynamical calculations. Due to the involvement of excited vibrational modes, the grids are larger than those used in our earlier work.46 Here, the basis set size is about 2.0 × 108 for NH3 and 3.5 × 108 for ND3. In Table 2, the energy and assignments of low-lying vibrational states of NH3 in the ground electronic state are

(6)

⎛ Ψi ⎞ Ψ0 = ⎜ ⎟ ⎝0⎠

Table 2. Vibrational Energy Levels of NH3(X̃ ) in cm−1

in which Ψi represents the wave function on the ground electronic state PES obtained using the iterative Lanczos algorithm.64,65 For VMP, several low-lying vibrational wave functions have been first determined and used in the photodissociation calculations. The Hamiltonian in eq 6 was scaled to the spectral range of (−1,1) via Hs = (H − H+I)/H−. The spectral medium (H+ = (Hmax + Hmin)/2) and half-width (H− = (Hmax − Hmin)/2) were determined by the spectral extrema, Hmax and Hmin, which can be readily estimated. Finally, the wave packet was damped near the edge of the grids in all three radial coordinates. The damping functions (D) and parameters are listed in Table 1. The Ã ← X̃ absorption spectra were obtained from the discrete cosine Fourier transform of the Chebyshev autocorrelation functions Ck ≡ ⟨ΨA0 |ΨAk ⟩66 1 πH − sin ϑ

∑ (2 − δk ,0) cos(k ϑ)Ck k=0

∂ A/X⎤ Ψk ′ ⎥ ∂r0 ⎦ (8)

with Ψ1 = DHsΨ0 and

S(E ) =

⎣

k ′= 0

was performed with the Chebyshev propagator63 k≥2

∑ (2 − δk ,0)e−ik ϑΨkA/X k=0

The damping function is defined as D = exp[−αD(r − rD)2], r ≥ rD.

Ψk = 2DHsΨk − 1 − D2 Ψk − 2

1 2πμ0 (H ) sin ϑ2 − 2

Theo.

(7)

where ϑ = arccos E is the Chebyshev angle and k is the Chebyshev order. For narrow resonances, we have also determined their complex energies (En − iΓn/2) from the Chebyshev correlation functions using a low-storage filter diagonalization method.67,68 Due to the large grids needed to resolve the NH2 internal state distributions, we choose in this work to compute only the total probabilities in the A and X channels using a flux method69

ν1

νp2

νl33

νl44

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0

+

0

0

0 0− 1+ 1− 0+ 0− 2+ 2− 3+ 1+ 1− 3− 0+ 0− 0+ 0− 0+ 0− 0+ 0−

0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 11 11

0 00 00 00 11 11 00 00 00 11 11 00 20 20 22 22 00 00 00 00

this work

ref 45

expt.45

0 0.45 969.14 991.42 1624.78 1625.38 1683.83 1914.50 2421.15 2582.88 2610.76 2909.62 3210.05 3211.02 3237.13 3237.98 3316.89 3317.46 3420.24 3420.43

0 0.45 974.36 997.65 1622.55 1623.76 1679.27 1918.57 2420.94

0 0.79 932.43 968.12 1626.28 1627.37 1597.47 1882.18 2384.15 2540.53 2586.13 2895.51 3216.10 3217.78 3240.44 3241.62 3336.11 3337.10 3443.68 3443.99

given. These calculated results are compared with available experimental values. It can be seen from the table that our theoretical results are in reasonably good agreement with the experimental values. Understandably, the agreement is not as good as some spectroscopically accurate ground-state PESs,70,71 which are often semilocal and empirically adjusted to reproduce spectroscopic data, thus not suitable for photodissociation studies. However, the results reported here are significantly 11928



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better than those41 based on the ab initio global PES of Li et al.33 Finally, we note that the vibrational energy levels on the improved PESs46 are very close to those obtained using the previous version of our PESs,45 indicating that the improvements of the PESs detailed in ref 46 have a very limited impact on the Franck−Condon region. Figure 2 displays the calculated A-band absorption spectra for four low-lying vibrational states (00, 11, 31, and 41) of

Figure 3. Calculated absorption spectra from the 00, 11, 31, and 41 states of ND3(X̃ 1A1).

also the maximum observed in experimental spectra.5,7 As discussed before, the excitation of the umbrella mode is attributed to the transition from the pyramidal X̃ state to the planar Ã state. No other modes are evident in the absorption spectra despite some differences in the corresponding N−H bond length. The positions and widths of the peaks have been determined, and they are listed in Tables 3 and 4 for NH3 and ND3, respectively. The results on the improved PESs46 are quite similar to those reported in our earlier work.45 Comparing Figures 2 and 3 reveals much narrower line widths for ND3 due apparently to the tunneling nature of the predissociation and IVR. In addition, the width of the first overtone (21) of NH3 and ND3 is narrower than that of the fundamental (00), in agreement with experimental observations.4,6,7,10,72 The calculated absorption spectra from the first symmetric stretching overtones (the 11 states) have two dominant progressions (2n and 112n), where the 112n progression is more intense. The dominance of the 112n progression is likely due to the similarity in the symmetric stretching potentials of the two electronic states. This weaker 2n progression peaks at 23, while the stronger 112n progression peaks at 1128. The latter are significantly shorter lived, as shown in Table 3, due presumably to the ease of overcoming the dissociation barrier.

Figure 2. Calculated absorption spectra from the 00, 11, 31, and 41 states of NH3(X̃ 1A1).

NH3(X̃ ). The corresponding spectra for ND3 are given in Figure 3. For each vibrational state, there are two separate spectra with even and odd parities, which are represented in red and blue colors in the figures. They originate from the neardegenerate pair of tunneling states in the ground electronic state. The energies in these figures are referenced to the band origins, which are lower than the experimental values by 796 and 676 cm−1 for NH3 and ND3, respectively. We have also ignored the nuclear spin statistics of the para and ortho forms of ammonia in plotting these spectra, which only affects the intensities. In agreement with experimental observations,5,7 the absorption spectra from the 00 states are dominated by long progressions in the umbrella (ν2) mode. In addition, the absorption spectrum peak at 25 (28) for NH3 (ND3), which is 11929



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Table 3. Calculated Positions and Widths (both in cm−1) of Predissociative Vibrational Features in the A-Band Absorption Spectra from Vibrationally Excited NH3(X̃ ) NH3 00

11

31

41

band

E

Γ

band

E

Γ

band

E

Γ

band

E

Γ

00 21 22 23 24 25 26 27 28 29 210 211 212 213

0 886 1781 2689 3600 4501 5404 6319 7249 8195 9154 10120 11091 12064

35.4 23 36 73.2 143.4 207.8 245.8 255.4 248.4 238.6 237.2 245.4 259.6 278.4

00 21 22 23 24 25 1124 1125 1126 1127 1128 1129 11210

0 886 1781 2689 3600 4501 5647 6716 7751 8758 9726 10713 11693

35.4 23 36 73.2 144.6 207.6 466 535 466 398 343 377 384

2531 2631 2731 2831 2931 21031 21131

5777 6657 7580 8505 9438 10384 11323

240 240 247 258 288 336 411

2141 2241 2341 2441 2541 2641 2741 2841 2941 21041 21141

1950 2889 3825 4772 5734 6703 7667 8660 9445 10418 11314

145 134 153 174.4 225.4 311.6 425.2 559.2 370 418 556

Table 4. Calculated Positions and Widths (both in cm−1) of Predissociative Vibrational Features in the A-Band Absorption Spectra from Vibrationally Excited ND3(X̃ ) ND3 00

11

31

41

band

E

Γ

band

E

Γ

band

E

Γ

band

E

Γ

00 21 22 23 24 25 26 27 28 29 210 211 212 213 214 215

0 653 1308 1966 2631 3310 3996 4694 5399 6108 6822 7540 8261 8985 9712 10443

2.2 1.0 21.4 27 31.6 33.6 27.2 24.6 27.6 35.6 48 65.4 86.6 113.8 146.6 211.4

00 21 22 23 24 25 1123 26 1124 27 1125 28 1126 1127 1128 1129 11210 11211 11212

0 653 1308 1966 2631 3310 3581 3996 4309 4694 5029 5398 5806 6507 7280 7974 8708 9435 10161

2.2 1.0 21.4 27 31.8 33.8 136.6 27.2 159.2 25.6 180.6 27 216.8 170 149.6 188 216 247 297

2531 2631 2731 2831 2931 21031 21131

5061 5767 6480 7200 7913 8633 9346

178 157 174 217 254 305 374

2141 2241 2341 2441 2541 2641 2741 2841 2941 21041 21141 21241 21341 21441

1490 2172 2862 3513 4220 4874 5566 6272 6958 7678 8401 9119 9843 10570

18.8 27 56.8 146.2 202.8 148 143.4 172.6 187.6 149.4 164 180.4 203.2 220

spectra are almost identical, and thus, only one is included in the figure. The absorption spectra from the first bending overtones 41 consist of only a single progression featuring the combination states 2n41. The progression peaks at 2541 for NH3 and 2841 for ND3. The widths of these peaks are quite large, suggesting strong predissociation. There are no experimental absorption spectra for vibrationally excited NH3 and ND3; therefore, a direct comparison between theory and experiment is not possible. However, Bach et al. have measured the action spectra for the VMP of NH3 by measuring the H product as a function of the photolysis wavelength. Comparison with their experimental data50,53 reveals that the agreement is excellent for the photodissociation from both the ground (00) and excited (11 and 31) vibrational states of NH3(X̃ ) in the same energy range, as shown in Figure

In addition to these two progressions, there are some weaker features that are not assigned. Excitation from the first antisymmetric stretching overtone, namely the 31 states, results in two progressions (2n31 and 2n41), with the 2n31 progression much more intense. The 2n progression is absent because of selection rules, but some bending excitation is present. All NH3 peaks are broad and overlapping, which makes the assignment particularly difficult. Consequently, their widths listed in Table 3 are, strictly speaking, estimates. The assignments were achieved only with the help of the ND3 assignment, which is much easier given the narrower peaks and clear nodal structures in the corresponding wave functions. Note that the 31 mode should be doubly degenerate, but the lack of permutation symmetry in the coordinates used in the calculation renders them nondegenerate by about 0.1 cm−1. However, their absorption 11930



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method to obtain the rotational constants of the A-state resonances.9 They argued that a perturbing state, the 43 state, must exist near the 24 state in order to account for the asymmetry of the spectral feature. Interestingly, they also found asymmetry in the 00 and 21 levels of ND3 through anomalous centrifugal distortion constants,9 due to an unidentified perturbation. The Fermi resonance mentioned above cannot provide this perturbation for the band origin (00) or the 21 level owing to the mass dependence of the frequency. Tang and Imre have attributed the asymmetry in the absorption spectra of the 00 states to ν1 excitations accidentally overlapping with the positions of 2n states with a different parity.34 However, these authors have used empirical PESs with some arbitrary modifications. We did not find any evidence, from either the parity-resolved absorption spectra or the wave functions, that the ν1 excitation was involved. Another possible candidate for the perturbing states is the lower triplet state of ammonia, which has roughly the same umbrella frequency.73 However, the perturbation of individual vibrational levels, as opposed to a uniform perturbation, implies intersections of the triplet and singlet PESs at non-D3h configurations. Previous ab initio calculations have found that the triplet-state PES is essentially parallel to the singlet one along the umbrella coordinate.29 Our own extensive search also failed to locate a crossing between the two electronic states in the Franck−Condon region. As a result, we have no choice but to discount this possibility. At present, we are unable to offer a definitive theoretical identification for the experimentally implied states that perturb the 2n levels. However, we speculate that these states might be highly excited vibrational levels on the ground (X̃ 1A1) electronic state of ammonia that are accidentally degenerate with the 2n state on the excited (Ã 1A″2 ) electronic state. Whether this speculation is valid has to await further experimental verification. Overall, the excellent theory−experiment agreement in Figure 4 is already very satisfactory. Figure 5 displays the calculated NH2(Ã 2A1) percent fractions for the photodissociation of the four initial vibrational states.

4. The agreement is striking. However, there are significant differences in the assignment between the calculated and

Figure 4. Comparison between measured action spectra50 and calculated absorption spectra from the 00, 11, and 31 states of NH3(X̃ 1A1). The combs on each panel mark the position of resolved band origins in simulated spectra. The black vertical lines mark the previous assignment of the measured actions spectra. The experimental data are taken from Table 1 of ref 50.

measured VMP spectra. In the experiment, for example, the bending (ν4) mode was suggested to be nearly degenerate with the umbrella (ν2) mode, leading to 1:1 Fermi resonances. However, the computed frequencies are ν4 = 1064 and ν2 = 886, cm−1, based on our absorption spectra in which the anharmonicity was taken into consideration. While the ν2 frequency is similar to the experimental value of 892 cm−1, the ν4 frequency differs from the suggested experimental value of 906 cm−1 by ∼12%. In the experiment of Bach et al.,50 it was found necessary to include the ν4 states in order to account for the asymmetry of the spectral envelope in some VMP action spectral features. For example, the action spectrum near 48000 cm−1 for the 00 photodissociation was assigned to 22 with a small component of 42. A similar perturbation was also invoked by Henck et al., who used the microwave optical double resonance (MODR)

Figure 5. Calculated branching ratios for the VMP from the 00, 11, 31, and 41 states of NH3(X̃ 1A1). The upper and lower panels are for even and odd parities.

The fractions are difficult to converge above 7.4 (7.0) eV for NH3 (ND3) due to the large memory requirement; therefore, no data are shown in that energy range. We note that the fractions for the vibrationless states have been shown in our previous work to agree well with experimental data.46 It is clear 11931



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from the figure that the product nonadiabatic branching is only mildly sensitive to the initial vibrational excitation. In particular, the VMP from 31 does not produce a fraction qualitatively different from the rest. (The percent fractions from both 31 states are essentially the same; therefore, only one is included in the figure.) This theoretical result is at odds with the claim that the VMP of the 31 state is dominated by adiabatic dissociation. We note that the experimental translational distributions for the H fragment were inferred from two different (Doppler time-offlight52,53 and velocity mapping ion imaging56) detecting methods, from which the branching ratios were inferred. However, some significant quantitative differences that exist between the experimental kinetic energy distributions were attributed to the probe laser pulse.56 On the other hand, the results reported here are consistent with the conclusion reached in our earlier reduced-dimensional quantum mechanical work43 and in the semiclassical trajectory study by Bonhommeau et al.,42 both of which are based on the same alternative pair of coupled PESs.33 At present, the origin of this theory− experiment discrepancy is unclear, but it might be associated with the internal excitation in the NH2 fragment. Figure 6 shows the calculated ND2(Ã 2A1)/ND2(X̃ 2B1) percent fractions for the photodissociation of the four initial

However, the agreement of the action spectra for VMP reported here and excellent agreement with absorption spectra, nonadiabatic branching ratios, and product distributions for the photodissociation of vibrationally unexcited NH3 and ND3 demonstrated in our earlier work45−47 clearly establish the accuracy of the PESs and their coupling used here. The remaining discrepancies between theory and experiment that still exist for VMP in this ostensibly simple system are puzzling. Our theoretical results fail to reproduce the pronounced mode selectivity for nonadiabatic dynamics reported for the VMP of NH3.52,53,56 However, we note that the lack of strong mode specificity in the nonadiabatic branching ratio is consistent with previous theoretical studies based on another set of diabatic PESs.42,43 While it is possible that some unknown factors are absent in our model, it is more likely that the experimental branching ratio indirectly inferred from the measurement of the H translational energy distribution might need to be reinterpreted. To this end, we plan to map out all NH2 rovibrational states in the VMP of NH3 in the near future. This is computationally expensive but might offer some clues as to the origin of the discrepancy. It is also our hope that further experiments will be motivated by the apparent disagreement underscored by the present study. For example, a systematic study of the ND3 might help to shed further light on the VMP dynamics. The direct detection of the NH2 fragment might also help to reveal new insights.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: *E-mail: *E-mail: *E-mail:

[email protected] (J.M.). [email protected] (D.R.Y.). [email protected] (D.X.). [email protected] (H.G.).

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS J.M. thanks the National Natural Science Foundation of China (21303110) for support. The work at NJU was funded by the National Natural Science Foundation of China (Grants 21133006 and 91221301). The UNM and JHU teams were funded by the National Science Foundation Grant CHE0910828 to H.G. and the U.S. Department of Energy Grant DE-FG02-91ER14189 to D.R.Y. We are grateful to Fleming Crim and Andreas Bach for many stimulating discussions and for pointing to the possibility of the triplet state and asymmetry of spectral shapes found in ref 10.

Figure 6. Calculated branching ratios for the VMP from the 00, 11, 31, and 41 states of ND3(X̃ 1A1). The upper and lower panels are for even and odd parities.

vibrational states. They have similar behavior to the NH3 results, showing in particular very weak mode specificity.

4. CONCLUSIONS We report here an extensive full-dimensional quantum dynamical study of the VMP of NH3 and ND3 on accurate coupled PESs of the two lowest-lying electronic states. While our absorption spectra reproduce all major peaks in the experimental action spectra, the theoretical assignments of the predissociative resonances accessed by VMP agree with some experimental assignments but differ in others. Specifically, we found little evidence for the involvement of the bending (ν4) mode of the A-state ammonia, as proposed in prior experimental studies. The ν4 frequency was also found to differ significantly from the umbrella frequency (ν2). As a result, a previously suggested 1:1 Fermi resonance between the two modes seems unlikely. In addition, our theoretical model is unable to shed light on the identity of the putative perturbing states implicated in several experimental studies for the 2n states of both NH3 and ND3.9,50

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REFERENCES

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