^{2}P

_{J}) + H

_{2}→ LiH(X

^{1}Σ

^{+}) + H: Influence by vibrational excitation and translational energy

^{1}, King-Chuen Lin

^{1,a)}and Yu-Ming Hung

^{2}

### Abstract

*Ab initio* potential energy surfaces and the corresponding analytical energy functions of the ground 1A′ and excited 2A′ states for the Li(2^{2}P) plus H_{2}reaction are constructed. Quasiclassical trajectory calculations on the fitted energy functions are performed to characterize the reactions of Li(2^{2}P) with H_{2}(*v* = 0, *j* = 1) and H_{2}(*v* = 1, *j* = 1) as well as the reaction when the vibrational energy is replaced by collision energy. For simplicity, the transition probability is assumed to be unity when the trajectories go through the crossing seam region and change to the lower surface. The calculated rotational distributions of LiH(*v* = 0) for both H_{2}(*v* = 0, *j* = 1) and H_{2}(*v* = 1, *j* = 1) reactions are single-peaked with the maximum population at *j*′ = 7, consistent with the previous observation. The vibrational excitation of H_{2}(*v* = 1) may enhance the reaction cross section of LiH(*v*′ = 0) by about 200 times, as compared to a result of 93–107 reported in the experimental measurements. In contrast, the enhancement is 3.1, if the same amount of energy is deposited in the translational states. This endothermic reaction can be considered as an analog of late barrier. According to the trajectory analysis, the vibrational excitation enlarges the H–H distance in the entrance channel to facilitate the reaction, but the excess energy may not open up additional reaction configuration.

The authors wish to thank Dr. Po-Yu Tsai for help with the rotational energy analysis. The computation was conducted in National Center for High Performance Computing. This work was supported by the National Taiwan University under contract no. 97R0318 and the National Science Council of Taiwan, Republic of China under contract no. NSC 97–2113-M-002–010-MY2.

I. INTRODUCTION

II. PES CALCULATIONS AND THREE-BODY FITTING

III. QUASICLASSICAL TRAJECTORY CALCULATIONS

IV. RESULTS AND DISCUSSION

A. Reaction cross section

B. Vibrational and rotational state distributions

C. Influence of vibrational excitation and translational energy

V. CONCLUSION

### Key Topics

- Chemical reaction cross sections
- 37.0
- Excited state reaction dynamics
- 32.0
- Hydrogen reactions
- 32.0
- Photochemical reactions
- 16.0
- Surface crossings
- 13.0

## Figures

Contour plot of the 2A′ surface as a function of LiH distance (*R* _{3}) and HLiH bending angle (*ϕ*), while the other LiH distance (*R* _{1}) is fixed at 1.6 Å, the equilibrium bond length of a free LiH. The reference potential energy of 0 eV corresponds to a C_{2v} configuration in which the distance between Li and the center of H_{2} is 7.0 Å and *R* _{2} is 0.74 Å, the equilibrium distance of H_{2}.

Contour plot of the 2A′ surface as a function of LiH distance (*R* _{3}) and HLiH bending angle (*ϕ*), while the other LiH distance (*R* _{1}) is fixed at 1.6 Å, the equilibrium bond length of a free LiH. The reference potential energy of 0 eV corresponds to a C_{2v} configuration in which the distance between Li and the center of H_{2} is 7.0 Å and *R* _{2} is 0.74 Å, the equilibrium distance of H_{2}.

Contour plot of the 1A′ surface as a function of LiH distance (*R* _{3}) and HLiH bending angle (*ϕ*), while the other LiH distance (*R* _{1}) is fixed at 1.6 Å. The reference potentail energy as 0 eV corresponds to a C configuration in which the distance between Li and the center of H_{2} is 7.0 Å and *R* _{2} is 0.74 Å, the equilibrium distance of H_{2}.

Contour plot of the 1A′ surface as a function of LiH distance (*R* _{3}) and HLiH bending angle (*ϕ*), while the other LiH distance (*R* _{1}) is fixed at 1.6 Å. The reference potentail energy as 0 eV corresponds to a C configuration in which the distance between Li and the center of H_{2} is 7.0 Å and *R* _{2} is 0.74 Å, the equilibrium distance of H_{2}.

Impact parameter dependence of the opacity functions for the Li(2^{2}P) plus H_{2}(*v* = 0) reaction at collision energy of 2.026 kcal/mol. The initial interatomic separation of Li–H_{2} is 10 Å.

Impact parameter dependence of the opacity functions for the Li(2^{2}P) plus H_{2}(*v* = 0) reaction at collision energy of 2.026 kcal/mol. The initial interatomic separation of Li–H_{2} is 10 Å.

Vibrational state distributions of LiH in the Li(2^{2}P) reactions with H_{2}(*v* = 0) at (a) collisional energy of 2.026 kcal/mol and (b) collisional energy of 14.85 kcal/mol, or (c) with H_{2}(*v* = 1) at collisional energy of 2.026 kcal/mol.

Vibrational state distributions of LiH in the Li(2^{2}P) reactions with H_{2}(*v* = 0) at (a) collisional energy of 2.026 kcal/mol and (b) collisional energy of 14.85 kcal/mol, or (c) with H_{2}(*v* = 1) at collisional energy of 2.026 kcal/mol.

Rotational state distributions of LiH in *v*′ = 0 level. H_{2} is in the quantum level of (a) (*v*, *j*) = (0, 1) with collisional energy at 2.026 kcal/mol, (b) (*v*, *j*) = (0, 1) with collisional energy at 14.85 kcal/mol, and (c) (*v*, *j*) = (1, 1) with collisional energy at 2.026 kcal/mol.

Rotational state distributions of LiH in *v*′ = 0 level. H_{2} is in the quantum level of (a) (*v*, *j*) = (0, 1) with collisional energy at 2.026 kcal/mol, (b) (*v*, *j*) = (0, 1) with collisional energy at 14.85 kcal/mol, and (c) (*v*, *j*) = (1, 1) with collisional energy at 2.026 kcal/mol.

Evolution of trajectories for LiH (*v*′ = 0, *j*′) produced in the H_{2}(*v* = 0, *j* = 1) reaction: (a) *j*′ = 4 and (b) *j*′ = 27, and (c) the HLiH bending angle dependence.

Evolution of trajectories for LiH (*v*′ = 0, *j*′) produced in the H_{2}(*v* = 0, *j* = 1) reaction: (a) *j*′ = 4 and (b) *j*′ = 27, and (c) the HLiH bending angle dependence.

Evolution of trajectories for LiH (*v*′ = 0, *j*′) produced in the H_{2}(*v* = 1, *j* = 1) reaction: (a) *j*′ = 4 and (b) *j*′ = 27, and (c) the HLiH bending angle dependence.

Evolution of trajectories for LiH (*v*′ = 0, *j*′) produced in the H_{2}(*v* = 1, *j* = 1) reaction: (a) *j*′ = 4 and (b) *j*′ = 27, and (c) the HLiH bending angle dependence.

(a) H–H separation spread and (b) Jacobi angle spread of the collision complex LiH_{2} in the reactions with H_{2}(*v* = 0, *j* = 1). The data are acquired when the trajectories just transit to the lower surface.

(a) H–H separation spread and (b) Jacobi angle spread of the collision complex LiH_{2} in the reactions with H_{2}(*v* = 0, *j* = 1). The data are acquired when the trajectories just transit to the lower surface.

(a) H–H separation spread and (b) Jacobi angle spread of the collision complex LiH_{2} in the reaction with H_{2}(*v* = 1, *j* = 1). The data are acquired when the reactive trajectories just transit to the lower surface.

(a) H–H separation spread and (b) Jacobi angle spread of the collision complex LiH_{2} in the reaction with H_{2}(*v* = 1, *j* = 1). The data are acquired when the reactive trajectories just transit to the lower surface.

## Tables

Parameters of two-body term potential fitting for the Li(2^{2}S, 2^{2}P) plus H_{2} reaction.

Parameters of two-body term potential fitting for the Li(2^{2}S, 2^{2}P) plus H_{2} reaction.

Parameters of three-body term potential fitting for the Li(2^{2}S, 2^{2}P) plus H_{2} reaction.

Parameters of three-body term potential fitting for the Li(2^{2}S, 2^{2}P) plus H_{2} reaction.

Dynamical parameters obtained in the QCT calculations.

Dynamical parameters obtained in the QCT calculations.

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