Non-adiabatic processes play an important role in photochemistry, but the mechanism for conversion of electronic energy to chemical energy is still poorly understood. To explore the possibility of vibrational control of non-adiabatic dynamics in a prototypical photoreaction, namely, the A-band photodissociation of NH 3 ( X ̃ 1 A 1 ) , full-dimensional state-to-state quantum dynamics of symmetric or antisymmetric stretch excited NH 3 ( X ̃ 1 A 1 ) is investigated on recently developed coupled diabatic potential energy surfaces. The experimentally observed H atom kinetic energy distributions are reproduced. However, contrary to previous inferences, the NH 2 ( A ̃ 2 A 1 ) /NH 2 ( X ̃ 2 B 1 ) branching ratio is found to be small regardless of the initial preparation of NH 3 ( X ̃ 1 A 1 ) , while the internal state distribution of the preeminent fragment, NH 2 ( X ̃ 2 B 1 ) , is found to depend strongly on the initial vibrational excitation of NH 3 ( X ̃ 1 A 1 ) . The slow H atoms in photodissociation mediated by the antisymmetric stretch fundamental state are due to energy sequestered in the internally excited NH 2 ( X ̃ 2 B 1 ) fragment, rather than in NH 2 ( A ̃ 2 A 1 ) as previously proposed. The high internal excitation of the NH 2 ( X ̃ 2 B 1 ) fragment is attributed to the torques exerted on the molecule as it passes through the conical intersection seam to the ground electronic state of NH3. Thus in this system, contrary to previous assertions, the control of electronic state branching by selective excitation of ground state vibrational modes is concluded to be ineffective. The juxtaposition of precise quantum mechanical results with complementary results based on quasi-classical surface hopping trajectories provides significant insights into the non-adiabatic process.

The breakdown of the Born-Oppenheimer approximation represents a common occurrence in chemistry, particularly in photoreactions which convert photon energy to chemical energy.1 In these processes, a single adiabatic potential energy surface (PES) is no longer sufficient and multistate non-adiabatic dynamics is required. Non-adiabatic interactions are frequently attributable to conical intersections (CIs), which facilitate transitions to distinct adiabatic channels accessible from the electronic degeneracy.2,3 For example, a CI is known to be responsible for the photo-isomerization of the retinal chromophore, rhodopsin, necessary for vision.4 To gain detailed understanding of non-adiabatic dynamics induced by CIs, prototypical processes involving photodissociation of small molecules are often used because their coupled PESs and dynamics can be accurately determined from first principles.

A “holy grail” of this field is laser control of the outcome of a non-adiabatic reaction.3 Some time ago, Crim and coworkers reported that such control can be realized in the photodissociation of ammonia by pre-exciting NH 3 ( X ̃ 1 A 1 ) to distinct vibrational levels prior to photolysis.5–7 This remarkable paradigm has been particularly influential in the field of non-adiabatic dynamics3 and as a result a clear theoretical understanding is highly desired.

The photodissociation of NH3 in its A band near 50 000 cm−1 involves two coupled electronic states,8 providing a prototypical example of non-adiabatic dynamics.9 Fig. 1 shows a CI (part of an extended four-dimensional seam) connecting the two electronic states in the dissociation pathway,10–12 which is responsible for non-adiabatic transitions. Two product channels H + NH 2 ( A ̃ 2 A 1 ) and H + NH 2 ( X ̃ 2 B 1 ) are accessible via adiabatic and non-adiabatic pathways, respectively.

FIG. 1.

Three-dimensional representation of the coupled PESs of NH3 as a function of RN-H and out-of-plane angle θ.

FIG. 1.

Three-dimensional representation of the coupled PESs of NH3 as a function of RN-H and out-of-plane angle θ.

Close modal

Many groups, focusing on photodissociation of ammonia from its ground vibrational state, have reported experimental detection of both product channels,5–7,13–22 and showed that the photodissociation is dominated by non-adiabatic production of NH 2 ( X ̃ 2 B 1 ) . However, in the experiments of Crim and coworkers, vibrationally mediated photodissociation (VMP)23 of ammonia from excited vibrational states was investigated using IR-UV double resonance excitation. The kinetic energy distribution of the H fragment was measured using either the Doppler-time of flight,6 H-atom Rydberg tagging,5 or velocity map ion imaging techniques.7 Interestingly, all experiments found a strong dependence on the prepared vibrational state of NH 3 ( X ̃ 1 A 1 ) . In particular, the H atom distribution produced in the VMP from the 31 state (v3 = 3444 cm−1) was found to be uniformly slow whereas that produced by pre-exciting the 11 state (v1 = 3336 cm−1) consists of a mixture of fast and slow hydrogen atoms. These authors concluded that the former must be dominated by electronically excited NH 2 ( A ̃ 2 A 1 ) via the adiabatic pathway, with the latter dominated by NH 2 ( X ̃ 2 B 1 ) produced non-adiabatically. This remarkable control of non-adiabatic dynamics was rationalized in terms of mode specificity in accessing the CI connecting the two electronic states.

Theoretical studies of the mode-specific non-adiabatic dissociation of NH3 have been unable to confirm the experimental claim. The earlier quasi-classical trajectory (QCT) study of Truhlar and coworkers24 and reduced-dimensional quantum dynamical calculations by some of us25 on a set of ab initio based coupled PESs26,27 failed to uncover any significant difference in the NH 2 ( A ̃ 2 A 1 ) /NH 2 ( X ̃ 2 B 1 ) branching ratio for various VMP processes. This was confirmed by more recent full-dimensional multi-channel quantum calculations28 on very accurate coupled PESs also based on ab initio data.29 We emphasize that the latter work has reproduced almost all measurements, including absorption spectra and final state distributions of the NH2 fragment for the A-band photodissociation of the vibrational ground state of NH3,29–31 thus firmly establishing the accuracy of the PESs and their couplings.

Here, we report state-of-the-art quantum-state resolved full-dimensional quantum non-adiabatic calculations that re- solve the theory-experiment discrepancy. Our results reproduce the experimental H atom kinetic energy distributions, but reinterpret the experimental data in terms of different NH 2 ( X ̃ 2 B 1 ) internal excitations rather than a difference in the NH 2 ( A ̃ 2 A 1 ) /NH 2 ( X ̃ 2 B 1 ) branching ratio. The 2 × 2 quasi-diabatic PESs were determined from high-level ab initio data29,31 using a novel method described in our recent publications.32,33 The full-dimensional quantum calculations of the final state-resolved photodissociation dynamics of NH3 have been discussed in detail before,31 so only a brief outline is given here. Assuming vertical excitation, the initial wave packet on the excited NH 3 ( A ̃ 1 A 2 ) state PES was chosen to be one of several low-lying vibrational eigenfunctions of NH 3 ( X ̃ 1 A 1 ) , simulating the experiments of Crim and coworkers.5–7 The wave packet is propagated using the real Chebyshev propagator34 and the final state populations were determined in the dissociation asymptote by projecting onto the fragment eigenstates.31 Both the NH 2 ( A ̃ 2 A 1 ) and NH 2 ( X ̃ 2 B 1 ) fragments are included and their ro-vibrational state distributions allow for the unambiguous determination of the electronic state associated with measured H atom kinetic energy distributions at the experimental energy. The calculation details are given in supplementary material.35 

In Fig. 2, the calculated and measured H atom kinetic energy distributions for the VMP from the 11 state of NH 3 ( X ̃ 1 A 1 ) are compared at two energies used in the measurements (46 208 and 48 911 cm−1). The calculated distributions were generated by Gaussian convolution with a fixed full-width-half-maximum (FWHM) of 200 cm−1. At the lower energy (Fig. 2(a)),5 the NH 2 ( A ̃ 2 A 1 ) channel is closed and only NH 2 ( X ̃ 2 B 1 ) fragments are produced. It can also be seen that both the theoretical and experimental distributions are broad and have many oscillatory structures, which correspond to rotational excited states of NH 2 ( X ̃ 2 B 1 , v 2 = 0 , 1 ) with the well-known NKa propensity.13,36,37 These NH2 states have roughly the same population, as shown in the supplementary material,35 resulting in a H atom kinetic energy distribution extending to the highest allowed energy. Since this energy (46 208 cm−1) corresponds to the 0 0 0 resonance peak in the absorption spectrum, its distribution is very similar to that reported by us for photodissociation of vibrationally unexcited NH3,31 but with a lower intensity due to unfavorable Franck-Condon overlap. At the higher energy (Fig. 2(b)),7 however, some NH 2 ( A ̃ 2 A 1 ) is produced, but the population is small, consistent with our recent non-final-state resolved calculation.28 The theory-experiment agreement is quite satisfactory as the overall shapes and line spacing of the measured distributions are well reproduced, although some differences are seen at low energies. We note in passing that it is difficult to detect slow H atoms experimentally.

FIG. 2.

Comparison of calculated H atom kinetic energy distributions for the 11 VMP with (a) experimental result of Bach et al.5 at the total energy of 46 208 cm−1 and (b) with experimental result of Hause et al.7 at the total energy of 48 911 cm−1.

FIG. 2.

Comparison of calculated H atom kinetic energy distributions for the 11 VMP with (a) experimental result of Bach et al.5 at the total energy of 46 208 cm−1 and (b) with experimental result of Hause et al.7 at the total energy of 48 911 cm−1.

Close modal

A similar theory-experiment comparison is presented in Fig. 3 for VMP from the 31 state of NH 3 ( X ̃ 1 A 1 ) at the experimental energy of 49 972 cm−1.7 Note that there are two degenerate states for the asymmetric stretching mode. However, as we illustrate in the supplementary material,35 both give very similar results. As a result, the average of the two is presented here. As shown in Fig. 3(a), the calculated H atom kinetic energy distribution also compares favorably with experiment,7 and the contribution from the NH 2 ( A ̃ 2 A 1 ) state in low kinetic energy range is limited as discussed below. Unlike the 11 VMP shown in Fig. 2, the distribution for the 31 VMP is dominated by slow H atoms. However, consistent with our earlier work,28 only a small population for NH 2 ( A ̃ 2 A 1 ) , comparable to albeit larger than, that in the 11 VMP is predicted. Instead, it is shown in Fig. 3(b) that the slowly recoiling H atom can be largely attributed to the strong internal excitation of the NH 2 ( X ̃ 2 B 1 ) fragment. Indeed, the NH2 fragment is dominated by populations with high vibrational excitations, with bending (v2) quanta up to 6, and the NKa propensity preserved. These attributions contrast strongly with those made in the experimental studies5–7 where the slow H distribution in the 31 VMP is attributed to the production of the excited adiabatic H + NH 2 ( A ̃ 2 A 1 ) channel.5–7 The theoretical results unequivocally indicate that the earlier experimental attribution is unlikely to be correct.

FIG. 3.

(a) Comparison of the calculated H atom kinetic energy distribution for the 31 VMP with experimental result of Hause et al.7 at the total energy of 49 972 cm−1. (b) Population distribution of the NH 2 ( X ̃ 2 B 1 ) fragment with ro-vibrational assignments.

FIG. 3.

(a) Comparison of the calculated H atom kinetic energy distribution for the 31 VMP with experimental result of Hause et al.7 at the total energy of 49 972 cm−1. (b) Population distribution of the NH 2 ( X ̃ 2 B 1 ) fragment with ro-vibrational assignments.

Close modal

The production of highly bending excited NH 2 ( X ̃ 2 B 1 ) fragments in ammonia photodissociation is well known. In the studies by Stavros and coworkers, NH 2 ( X ̃ 2 B 1 ) fragments with v2 up to 9 were detected.19,20 The more recent work of Rodriguez et al. also reported that NH 2 ( X ̃ 2 B 1 ) fragments with up to v2 = 4 have been seen from the 2 0 4 dissociation.22 In addition, the rotational excitation in these vibrational levels is extreme, peaking near the highest possible rotational levels,22 very similar to that shown in Fig. 3(b). Note that geometry changes during the course of the dissociation encourage the H-N-H angle deformation since the equilibrium H-N-H angle is 144° and 103° for NH 2 ( A ̃ 2 A 1 ) and NH 2 ( X ̃ 2 B 1 ) , while it is 120° for NH 3 ( A ̃ 1 A 2 ) . As we explain below, the rotational excitation can be attributed to the torque exerted on the NH2 fragment by the recoil of the H atom at non-planar geometries13,36,37 and the effect of out-of-plane derivative couplings during the non-adiabatic transition. To shed light on the high bending and rotational excitations of the NH 2 ( X ̃ 2 B 1 ) fragment, we have carried out quasi-classical surface hopping trajectory studies on the same set of coupled PESs as that used in the quantum dynamical studies. (For details on the calculations and additional results, see supplementary material.35) Three trajectories have been randomly selected from the 31 VMP process to illustrate the nuclear motion and the effect of g and h vectors on the electronic energy redistribution. Here, g is the energy difference gradient vector and h is the energy difference scaled derivative coupling vector.38 The evolution of these trajectories, including the non-adiabatic transitions, is provided in supplementary material and in the associated movie files.35 

Significant excursion on the excited A state PES is seen, in which the frustrated dissociation is not dissimilar to the roaming dynamics found in recent studies.39 However, these excited state dynamics are not the main reason for the bending excitation in the NH 2 ( X ̃ 2 B 1 ) fragment. Instead, the bending and rotational excitations in the NH 2 ( X ̃ 2 B 1 ) fragment are largely gained during non-adiabatic transitions near the CI seam. The forces acting on these trajectories immediately before and after the hop can be described by the g and h vectors. The g and h vectors for each of the three trajectories at the geometry where the last surface hopping event takes place are shown in Fig. 4. As shown in that figure, the g and h vectors of three typical trajectories are dominated by linear combinations of three motions: the translational motion of departing H atom, the out-of-plane umbrella motion that becomes the head-over-heels rotation of NH2, and the bending of the H-N-H angle. These vectors suggest that the high rotational and bending excitations in the NH 2 ( X ̃ 2 B 1 ) fragment can be attributed to the force acting on the molecule as it transitions from the A to X state.

FIG. 4.

The g and h vectors for three typical trajectories leading to high v2 excitation in NH 2 ( X ̃ 2 B 1 ) . Trajectories are given in supplementary material.35 

FIG. 4.

The g and h vectors for three typical trajectories leading to high v2 excitation in NH 2 ( X ̃ 2 B 1 ) . Trajectories are given in supplementary material.35 

Close modal

As seen in Fig. 4 and also in our previous investigation of the CI seam,40 the contribution of the departing hydrogen atom motion diminishes as the NH distance and H-N-H angle increase. At large distances, the bending motion and head-over-heels rotation become components of a perturbed H-N-H Renner-Teller intersection, with the pair of degenerate bends at asymptotic linear geometries becoming the g and h vectors. Note that the intersection seam joins into the Renner-Teller intersection when the NH distance is infinity, where g and h vectors will vanish because the model Hd is defined in internal coordinates and cannot treat rotational motions. However, this does not affect the simulation at all because the coordinates only start to vanish at much larger NH distance (>4 Å) than the distance of the surface hopping events. This implies that if the molecule undergoes a non-adiabatic transition at large NH distances and near linear H-N-H angles, the majority of the electronic energy will be converted into internal energies of the NH2 moiety in the form of rotation and H-N-H bend, and very little energy will be converted into the kinetic energy of departing hydrogen atom. This would cause significant higher excitation levels in H-N-H angle bend and rotation and at the same time produce slow hydrogen atom products. This is consistent with the findings of both the experimental measurements and quantum dynamics results presented in this paper. As seen in Fig. S6, when compared with the 11 process, the VMP process through the 31 state experiences surface hopping events at a much larger NH distance and H-N-H angles. This observation might be due to the fact that the former encounters the CI seam where the N-H distances are more symmetric,12 but this speculation needs further confirmation. In any event, we conclude that where the surface hop occurs is key and that location depends on the mode excited.

The results presented here resolve the long-standing controversy related to the mode specific control of non-adiabatic transitions in the photodissociation of ammonia. The calculated H atom kinetic energy distributions for VMP for several low-lying vibrational states of NH 3 ( X ̃ 1 A 1 ) are in satisfactory agreement with experiment. Specifically, the distribution is broad for the 11 VMP, but narrow for the 31 VMP and dominated by slow H. In all cases, the NH 2 ( A ̃ 2 A 1 ) /NH 2 ( X ̃ 2 B 1 ) branching ratio is small and comparable, thus ruling out the mode specific control of the electronic branching. Instead, our results indicate that the NH 2 ( X ̃ 2 B 1 ) internal excitation is high for the 31 VMP, resulting from the change of force at the CI seam, which ultimately leads to the inverted rotational state distribution with the NKa propensity and excitation of the NH 2 ( X ̃ 2 B 1 ) bending (v2) mode. Thus, while proposed control of electronic state branching via VMP is unlikely to be operative in this system, mode-specific control of vibrational energy distribution is found and reflects where near the seam, the non-adiabatic transition occurs.

The NJU group was supported by the National Natural Science Foundation of China (21133006, 21403104, and 91221301), the Chinese Ministry of Science and Technology (2013CB834601), and Chinese Postdoctoral Science Foundation (2014M551552). J.M. thanks National Natural Science Foundation of China (21303110). The JHU team was supported by National Science Foundation grant (CHE-1361121 to D.R.Y.). H.G. thanks the U.S. Department of Energy (DF-FG02-05ER15694 to H.G.) for generous support.

1.
M.
Klessinger
and
J.
Michl
,
Excited States and Photochemistry of Organic Molecules
(
VCH
,
New York
,
1995
).
2.
H.
Köppel
,
W.
Domcke
, and
L. S.
Cederbaum
,
Adv. Chem. Phys.
57
,
59
(
1984
).
3.
D. R.
Yarkony
,
Chem. Rev.
112
,
481
(
2011
).
4.
B. G.
Levine
and
T. J.
Martínez
,
Annu. Rev. Phys. Chem.
58
,
613
(
2007
).
5.
A.
Bach
,
J. M.
Hutchison
,
R. J.
Holiday
, and
F. F.
Crim
,
J. Chem. Phys.
118
,
7144
(
2003
).
6.
A.
Bach
,
J. M.
Hutchison
,
R. J.
Holiday
, and
F. F.
Crim
,
J. Phys. Chem. A
107
,
10490
(
2003
).
7.
M. L.
Hause
,
Y. H.
Yoon
, and
F. F.
Crim
,
J. Chem. Phys.
125
,
174309
(
2006
).
8.
V.
Vaida
,
W.
Hess
, and
J. L.
Roebber
,
J. Phys. Chem.
88
,
3397
(
1984
).
9.
M. N. R.
Ashfold
,
G. A.
King
,
D.
Murdock
,
M. G. D.
Nix
,
T. A. A.
Oliver
, and
A. G.
Sage
,
Phys. Chem. Chem. Phys.
12
,
1218
(
2010
).
10.
R.
Runau
,
S. D.
Peyerimhoff
, and
R. J.
Buenker
,
J. Mol. Spectrosc.
68
,
253
(
1977
).
11.
M. I.
McCarthy
,
P.
Rosmus
,
H.-J.
Werner
,
P.
Botschwina
, and
V.
Vaida
,
J. Chem. Phys.
86
,
6693
(
1987
).
12.
D. R.
Yarkony
,
J. Chem. Phys.
121
,
628
(
2004
).
13.
J.
Biesner
,
L.
Schnieder
,
J.
Schmeer
,
G.
Ahlers
,
X.
Xie
,
K. H.
Welge
,
M. N. R.
Ashfold
, and
R. N.
Dixon
,
J. Chem. Phys.
88
,
3607
(
1988
).
14.
J.
Biesner
,
L.
Schnieder
,
G.
Ahlers
,
X.
Xie
,
K. H.
Welge
,
M. N. R.
Ashfold
, and
R. N.
Dixon
,
J. Chem. Phys.
91
,
2901
(
1989
).
15.
E. L.
Woodbridge
,
M. N. R.
Ashfold
, and
S. R.
Leone
,
J. Chem. Phys.
94
,
4195
(
1991
).
16.
D. H.
Mordaunt
,
M. N. R.
Ashfold
, and
R. N.
Dixon
,
J. Chem. Phys.
104
,
6460
(
1996
).
17.
R. A.
Loomis
,
J. P.
Reid
, and
S. R.
Leone
,
J. Chem. Phys.
112
,
658
(
2000
).
18.
J. P.
Reid
,
R. A.
Loomis
, and
S. R.
Leone
,
J. Chem. Phys.
112
,
3181
(
2000
).
19.
K. L.
Wells
,
G.
Perriam
, and
V. G.
Stavros
,
J. Chem. Phys.
130
,
074308
(
2009
).
20.
N. L.
Evans
,
H.
Yu
,
G. M.
Roberts
,
V. G.
Stavros
, and
S.
Ullrich
,
Phys. Chem. Chem. Phys.
14
,
10401
(
2012
).
21.
A. S.
Chatterley
,
G. M.
Roberts
, and
V. G.
Stavros
,
J. Chem. Phys.
139
,
034318
(
2013
).
22.
J. D.
Rodriguez
,
M. G.
Gonzalez
,
L.
Rubio-Lago
, and
L.
Banares
,
Phys. Chem. Chem. Phys.
16
,
406
(
2014
).
23.
F. F.
Crim
,
Annu. Rev. Phys. Chem.
44
,
397
(
1993
).
24.
D.
Bonhommeau
,
R.
Valero
,
D. G.
Truhlar
, and
A. W.
Jasper
,
J. Chem. Phys.
130
,
234303
(
2009
).
25.
W.
Lai
,
S. Y.
Lin
,
D.
Xie
, and
H.
Guo
,
J. Phys. Chem. A
114
,
3121
(
2010
).
26.
S.
Nangia
and
D. G.
Truhlar
,
J. Chem. Phys.
124
,
124309
(
2006
).
27.
Z. H.
Li
,
R.
Valero
, and
D. G.
Truhlar
,
Theor. Chem. Acc.
118
,
9
(
2007
).
28.
J.
Ma
,
C.
Xie
,
X.
Zhu
,
D. R.
Yarkony
,
D.
Xie
, and
H.
Guo
,
J. Phys. Chem. A
118
,
11926
(
2014
).
29.
X.
Zhu
,
J.
Ma
,
D. R.
Yarkony
, and
H.
Guo
,
J. Chem. Phys.
136
,
234301
(
2012
).
30.
J.
Ma
,
X.
Zhu
,
H.
Guo
, and
D. R.
Yarkony
,
J. Chem. Phys.
137
,
22A541
(
2012
).
31.
C.
Xie
,
J.
Ma
,
X.
Zhu
,
D. H.
Zhang
,
D. R.
Yarkony
,
D.
Xie
, and
H.
Guo
,
J. Phys. Chem. Lett.
5
,
1055
(
2014
).
32.
X.
Zhu
and
D. R.
Yarkony
,
J. Chem. Phys.
137
,
22A511
(
2012
).
33.
X.
Zhu
and
D. R.
Yarkony
,
J. Chem. Phys.
140
,
024112
(
2014
).
34.
H.
Guo
,
J. Chem. Phys.
108
,
2466
(
1998
).
35.
See supplementary material at http://dx.doi.org/10.1063/1.4913633 for details of the quantum dynamics and QCT calculations and additional results.
36.
R. N.
Dixon
,
Mol. Phys.
68
,
263
(
1989
).
37.
R. N.
Dixon
,
Mol. Phys.
88
,
949
(
1996
).
38.
D. R.
Yarkony
,
J. Phys. Chem. A
101
,
4263
(
1997
).
39.
A. G.
Suits
,
Acc. Chem. Res.
41
,
873
(
2008
).
40.
X.
Zhu
and
D. R.
Yarkony
,
Mol. Phys.
108
,
2611
(
2010
).

Supplementary Material