^{1}, Rosendo Valero

^{1}, Donald G. Truhlar

^{1,a)}and Ahren W. Jasper

^{2}

### Abstract

Using previously developed potential energy surfaces and their couplings, non-Born–Oppenheimer trajectory methods are used to study the state-selected photodissociation of ammonia, prepared with up to six quanta of vibrational excitation in the symmetric or antisymmetric stretching modes of . The predicted dynamics is mainly electronically nonadiabatic (that is, it produces ground electronic state amino radicals). The small probability of forming the excited-state amino radical is found, for low excitations, to increase with total energy and to be independent of whether the symmetric or antisymmetric stretch is excited; however some selectivity with respect to exciting the antisymmetric stretch is found when more than one quantum of excitation is added to the stretches, and more than 50% of the amino radical are found to be electronically excited when six quanta are placed in the antisymmetric stretch. These results are in contrast to the mechanism inferred in recent experimental work, where excitation of the antisymmetric stretch by a single quantum was found to produce significant amounts of excited-state products via adiabatic dissociation at total energies of about 7.0 eV. Both theory and experiment predict a broad range of translational energies for the departing H atoms when the symmetric stretch is excited, but the present simulations do not reproduce the experimental translational energy profiles when the antisymmetric stretch is excited. The sensitivity of the predicted results to several aspects of the calculation is considered in detail, and the analysis leads to insight into the nature of the dynamics that is responsible for mode selectivity.

We are grateful to Zhen Hua Li for helpful assistance and to Hua Guo for helpful discussions. This work was supported in part by the National Science Foundation through Grant No. CHE07-04974 and in part by the United States Department of Energy Grant No. DE-AC04-94-AL85000, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences.

I. INTRODUCTION

II. METHODS

A. Dynamics

B. Trajectory harmonic initial conditions

C. Potential energy surfaces and vibrational states

D. Mode populations

III. RESULTS

A. Hydrogen-atom kinetic energy distributions

B. Choice of coupled-surface trajectory and initial conditions algorithms

C. Effect of large initial excitations

D. Effect of the diabatic coupling

E. Intermode couplings

F. Reaction mechanism

IV. CONCLUDING REMARKS

### Key Topics

- Excited states
- 42.0
- Dissociation
- 27.0
- Photodissociation
- 20.0
- Ground states
- 17.0
- Vibrational states
- 17.0

## Figures

Energy as a function of the longest N–H bond distance for the two lowest adiabatic states of based on fitted adiabatic surfaces from Ref. 55. The three N–H distances are denoted as . The minimum of the electronic state is planar with ( symmetry). The saddle point is planar with and ( symmetry), and the lowest-energy conical intersection is also planar. The minimum of the state is tetrahedral with . The zero of energy is the minimum of the ground electronic state. Reactant (i.e., ) as well as product (i.e., ) ZPEs are indicated. The vibrationally adiabatic curves for four sets of vibrational quantum numbers (see Fig. 2 for labeled curves) are represented above the segment of the reaction path comprised between the minimum of the electronic state and its saddle point. The energies of all the remaining vibrational levels studied in the present work are also indicated. Note that the diagram is only schematic (not to scale) between 1 and 5 eV and beyond 2 Å to make relevant quantities more discernible.

Energy as a function of the longest N–H bond distance for the two lowest adiabatic states of based on fitted adiabatic surfaces from Ref. 55. The three N–H distances are denoted as . The minimum of the electronic state is planar with ( symmetry). The saddle point is planar with and ( symmetry), and the lowest-energy conical intersection is also planar. The minimum of the state is tetrahedral with . The zero of energy is the minimum of the ground electronic state. Reactant (i.e., ) as well as product (i.e., ) ZPEs are indicated. The vibrationally adiabatic curves for four sets of vibrational quantum numbers (see Fig. 2 for labeled curves) are represented above the segment of the reaction path comprised between the minimum of the electronic state and its saddle point. The energies of all the remaining vibrational levels studied in the present work are also indicated. Note that the diagram is only schematic (not to scale) between 1 and 5 eV and beyond 2 Å to make relevant quantities more discernible.

Blowup of a key portion of Fig. 1 showing vibrationally adiabatic potential curves for the (0000), (1000), (0010), and (0600) states and energy levels for the remaining states studied in the present work. Vibrational quanta for and are indicated in bold to avoid confusion. The zero of energy is the minimum of the ground electronic state.

Blowup of a key portion of Fig. 1 showing vibrationally adiabatic potential curves for the (0000), (1000), (0010), and (0600) states and energy levels for the remaining states studied in the present work. Vibrational quanta for and are indicated in bold to avoid confusion. The zero of energy is the minimum of the ground electronic state.

H kinetic energy distributions at the end of FSTU/SD and simulations compared to experimental results of Hause *et al.* (Ref. 14) for . The maximum of the experimental distribution is normalized to 1, and the maxima of the theoretical distributions to 0.75 for ease of comparison.

H kinetic energy distributions at the end of FSTU/SD and simulations compared to experimental results of Hause *et al.* (Ref. 14) for . The maximum of the experimental distribution is normalized to 1, and the maxima of the theoretical distributions to 0.75 for ease of comparison.

H kinetic energy distributions at the end of FSTU/SD and simulations compared to experimental results of Hause *et al.* (Ref. 14) for . The maximum of the experimental distribution is normalized to 1, and the maxima of the theoretical distributions to 0.75 for ease of comparison.

*et al.* (Ref. 14) for . The maximum of the experimental distribution is normalized to 1, and the maxima of the theoretical distributions to 0.75 for ease of comparison.

Probability of producing excited-state products as a function of total energy for and (squares); and (rhombi); and (triangles); and , ; , ; , ; , ; and , (circles); and , ; , ; , ; , ; and , (crosses).

Probability of producing excited-state products as a function of total energy for and (squares); and (rhombi); and (triangles); and , ; , ; , ; , ; and , (circles); and , ; , ; , ; , ; and , (crosses).

Effective quantum number from single-surface calculations with , , and , (b) 0.01, (c) 0.1, and (d) 1/6.

Effective quantum number from single-surface calculations with , , and , (b) 0.01, (c) 0.1, and (d) 1/6.

Effective quantum number from single-surface calculations with , , and , (b) 0.01, (c) 0.1, and (d) 1/6.

Generalized-normal-mode vibrational frequencies in the adiabatic electronically excited state along the reaction path connecting the well to the saddle point . The frequencies were computed with the reaction coordinate (taken as the MEP in isoinertial coordinates downhill from the saddle point to the excited-state minimum) projected out. The curves reflect an adiabatic correlation of the vibrational modes.

Generalized-normal-mode vibrational frequencies in the adiabatic electronically excited state along the reaction path connecting the well to the saddle point . The frequencies were computed with the reaction coordinate (taken as the MEP in isoinertial coordinates downhill from the saddle point to the excited-state minimum) projected out. The curves reflect an adiabatic correlation of the vibrational modes.

Vibrational frequencies in the adiabatic electronically excited state along the reaction path connecting the well to the saddle point . These frequencies were computed without projecting out the reaction coordinate; when a frequency becomes imaginary it is plotted as a negative number. The curves reflect an approximate diabatic correlation of the vibrational modes.

Vibrational frequencies in the adiabatic electronically excited state along the reaction path connecting the well to the saddle point . These frequencies were computed without projecting out the reaction coordinate; when a frequency becomes imaginary it is plotted as a negative number. The curves reflect an approximate diabatic correlation of the vibrational modes.

## Tables

Excited-state populations as a function of initial vibrational state. For each method, results are ordered by increasing total energy.

Excited-state populations as a function of initial vibrational state. For each method, results are ordered by increasing total energy.

Excited-state populations obtained with the FSTU method as a function of initial vibrational state. Results are ordered by increasing total energy.

Excited-state populations obtained with the FSTU method as a function of initial vibrational state. Results are ordered by increasing total energy.

Percentage of trajectories that dissociate after hops for , , and for different values of the diabatic coupling. [All calculations in this table employ a Wigner distribution for the modes with . The umbrella mode frequency is ; .]

Percentage of trajectories that dissociate after hops for , , and for different values of the diabatic coupling. [All calculations in this table employ a Wigner distribution for the modes with . The umbrella mode frequency is ; .]

Average time of the first downward hop, percentage of trajectories that dissociate on the ground electronic state without attempting any upward hop, average fraction of attempted upward hops that are allowed, and average final probability for the excited electronic state, when or for different values of the diabatic coupling. [All calculations in this table employ a Wigner distribution for the modes with . The umbrella mode frequency is ; .]

Average time of the first downward hop, percentage of trajectories that dissociate on the ground electronic state without attempting any upward hop, average fraction of attempted upward hops that are allowed, and average final probability for the excited electronic state, when or for different values of the diabatic coupling. [All calculations in this table employ a Wigner distribution for the modes with . The umbrella mode frequency is ; .]

Average time , average adiabatic energy gap , average maximum N–H distance , and average nonplanarity angle at the last downward hop. [All calculations in this table employ a Wigner distribution for the modes with . The umbrella mode frequency is ; .]

Average time , average adiabatic energy gap , average maximum N–H distance , and average nonplanarity angle at the last downward hop. [All calculations in this table employ a Wigner distribution for the modes with . The umbrella mode frequency is ; .]

Excited-state FSTU populations as a function of initial vibrational state for trajectories initiated at the state saddle point. Results are ordered by increasing total energy. [All calculations in this table employ a QC distribution for the modes with . The umbrella mode frequency is , and the initial conditions are EU (i.e., is unrestricted).]

Excited-state FSTU populations as a function of initial vibrational state for trajectories initiated at the state saddle point. Results are ordered by increasing total energy. [All calculations in this table employ a QC distribution for the modes with . The umbrella mode frequency is , and the initial conditions are EU (i.e., is unrestricted).]

Classification of trajectories by their number of outer turning points and the potential surface to which they dissociate, for three pairs of initial vibrational states. [The (0010), (1000) calculations in this table are FSTU/SD calculations that employ a Wigner distribution for the modes with . The (0120) and (2100) calculations employ FSTU and a QC distribution. The (0340) and (4300) calculations employ FSTU and a Wigner distribution. The umbrella mode frequency is always , and the initial conditions correspond to .]

Classification of trajectories by their number of outer turning points and the potential surface to which they dissociate, for three pairs of initial vibrational states. [The (0010), (1000) calculations in this table are FSTU/SD calculations that employ a Wigner distribution for the modes with . The (0120) and (2100) calculations employ FSTU and a QC distribution. The (0340) and (4300) calculations employ FSTU and a Wigner distribution. The umbrella mode frequency is always , and the initial conditions correspond to .]

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