^{2}

*P*

_{1/2}) + H

_{2}(

*v*

_{ i }= 0, 1,

*j*

_{ i }= 0)

^{1}, Bin Jiang

^{1}, Daiqian Xie

^{1,a)}and Zhigang Sun

^{2,a)}

### Abstract

Quantum state-to-state dynamics for the quenching process Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 0, 1, *j* _{ i } = 0) → Br(^{2} *P* _{3/2}) + H_{2}(*v* _{ f }, *j* _{ f }) has been studied based on two-state model on the recent coupled potential energy surfaces. It was found that the quenching probabilities have some oscillatory structures due to the interference of reflected flux in the Br(^{2} *P* _{1/2}) + H_{2} and Br(^{2} *P* _{3/2}) + H_{2} channels by repulsive potential in the near-resonant electronic-to-vibrational energy transfer process. The final vibrational state resolved integral cross sections were found to be dominated by the quenching process Br(^{2} *P* _{1/2}) + H_{2}(*v*) → Br(^{2} *P* _{3/2}) + H_{2}(*v*+1) and the nonadiabaticreaction probabilities for Br(^{2} *P* _{1/2}) + H_{2}(*v* = 0, 1, *j* _{ i } = 0) are quite small, which are consistent with previous theoretical and experimental results. Our calculated total quenching rate constant for Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 0, *j* _{ i } = 0) at room temperature is in good agreement with the available experimental data.

The NJU team was supported by the National Natural Science Foundation of China (Grant Nos. 21133006 and 91021010), and by the Fundamental Research Funds for the Central Universities (1114020503). Z.S. was supported by the National Natural Science Foundation of China (21103187). Part of the calculations have been done on the IBM Blade cluster system in the High Performance Computing Center of Nanjing University.

I. INTRODUCTION

II. COMPUTATIONAL DETAILS

III. RESULTS AND DISCUSSIONS

A. Numerics

B. Probabilities

C. Opacity functions

D. ICSs

E. Total quenching rate constants

IV. CONCLUSIONS

### Key Topics

- Hydrogen reactions
- 18.0
- Non adiabatic reactions
- 14.0
- Reaction rate constants
- 13.0
- Angular momentum
- 6.0
- Chemical reaction cross sections
- 6.0

## Figures

Total (red dashed line) and vibrational state (*v* _{ f } = 0: pink dot-dashed line; *v* _{ f } = 1: dark blue line; *v* _{ f } = 2: light blue dashed line) resolved quenching probabilities as a function of the collision energy for Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 0, *j* _{ i } = 0) at several *J* values.

Total (red dashed line) and vibrational state (*v* _{ f } = 0: pink dot-dashed line; *v* _{ f } = 1: dark blue line; *v* _{ f } = 2: light blue dashed line) resolved quenching probabilities as a function of the collision energy for Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 0, *j* _{ i } = 0) at several *J* values.

Total (red dashed line) and vibrational state (*v* _{ f } = 0: pink dot-dashed line; *v* _{ f } = 1: light blue dashed line; *v* _{ f } = 2: dark blue line; *v* _{ f } = 3: maroon dot-dot-dashed line) resolved quenching probabilities as a function of the collision energy for Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 1, *j* _{ i } = 0) at several *J* values.

Total (red dashed line) and vibrational state (*v* _{ f } = 0: pink dot-dashed line; *v* _{ f } = 1: light blue dashed line; *v* _{ f } = 2: dark blue line; *v* _{ f } = 3: maroon dot-dot-dashed line) resolved quenching probabilities as a function of the collision energy for Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 1, *j* _{ i } = 0) at several *J* values.

Relative energies for the two spin-orbit corrected adiabatic potentials (the red solid and blue dashed lines are related to the and ^{2}Π_{1/2} states, respectively) and the asymptotic vibrational energy levels for the Br(^{2} *P* _{1/2}, ^{2} *P* _{3/2}) + H_{2}(*v* _{ i }, *j* _{ i } = 0) channel.

Relative energies for the two spin-orbit corrected adiabatic potentials (the red solid and blue dashed lines are related to the and ^{2}Π_{1/2} states, respectively) and the asymptotic vibrational energy levels for the Br(^{2} *P* _{1/2}, ^{2} *P* _{3/2}) + H_{2}(*v* _{ i }, *j* _{ i } = 0) channel.

The adiabatic vibrational potential energy curves as a function of *R* in the Jacobi coordinates of the Br + H_{2} channel. The dashed line indicates the lower adiabatic curves, the solid line indicates the upper adiabatic curves.

The adiabatic vibrational potential energy curves as a function of *R* in the Jacobi coordinates of the Br + H_{2} channel. The dashed line indicates the lower adiabatic curves, the solid line indicates the upper adiabatic curves.

Total quenching and reaction probabilities as a function of the collision energy for Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 0, *j* _{ i } = 0) at several *J* values.

Total quenching and reaction probabilities as a function of the collision energy for Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 0, *j* _{ i } = 0) at several *J* values.

Total quenching and reaction probabilities as a function of the collision energy for Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 1, *j* _{ i } = 0) at several *J* values.

Total quenching and reaction probabilities as a function of the collision energy for Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 1, *j* _{ i } = 0) at several *J* values.

(2*J* + 1) weighted opacity functions for the quenching processes of Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 0, *j* _{ i } = 0) (upper panel) and Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 1, *j* _{ i } = 0) (lower panel) at four collision energies (0.1 eV: red line; 0.4 eV: green long-dashed line; 0.7 eV: blue short-dashed line; 1.0 eV: pink dotted line).

(2*J* + 1) weighted opacity functions for the quenching processes of Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 0, *j* _{ i } = 0) (upper panel) and Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 1, *j* _{ i } = 0) (lower panel) at four collision energies (0.1 eV: red line; 0.4 eV: green long-dashed line; 0.7 eV: blue short-dashed line; 1.0 eV: pink dotted line).

Total and vibrational state resolved quenching ICSs as a function of the collision energy for Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 0, *j* _{ i } = 0) (upper panel, total ICS: red dashed line; *v* _{ f } = 0: pink dotted line; *v* _{ f } = 1: dark blue line; *v* _{ f } = 2: light blue dot-dashed line) and Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 1, *j* _{ i } = 0) (lower panel, total ICS: red dashed line; *v* _{ f } = 0: pink dotted line; *v* _{ f } = 1: light blue dot-dashed line; *v* _{ f } = 2: dark blue line; *v* _{ f } = 3: maroon dot-dot-dashed line). The notation “× 15” means that the ICSs were multiplied by a factor of 15.

Total and vibrational state resolved quenching ICSs as a function of the collision energy for Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 0, *j* _{ i } = 0) (upper panel, total ICS: red dashed line; *v* _{ f } = 0: pink dotted line; *v* _{ f } = 1: dark blue line; *v* _{ f } = 2: light blue dot-dashed line) and Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 1, *j* _{ i } = 0) (lower panel, total ICS: red dashed line; *v* _{ f } = 0: pink dotted line; *v* _{ f } = 1: light blue dot-dashed line; *v* _{ f } = 2: dark blue line; *v* _{ f } = 3: maroon dot-dot-dashed line). The notation “× 15” means that the ICSs were multiplied by a factor of 15.

Total quenching and reaction ICSs as a function of the collision energy for Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 0, *j* _{ i } = 0) (upper panel) and Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 1, *j* _{ i } = 0) (lower panel).

Total quenching and reaction ICSs as a function of the collision energy for Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 0, *j* _{ i } = 0) (upper panel) and Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 1, *j* _{ i } = 0) (lower panel).

Rotational state distribution for the quenching processes of Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 0, *j* _{ i } = 0) (a) and Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 1, *j* _{ i } = 0) (b) at four collision energies.

Rotational state distribution for the quenching processes of Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 0, *j* _{ i } = 0) (a) and Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 1, *j* _{ i } = 0) (b) at four collision energies.

Total quenching rate constants of Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 0, 1, *j* _{ i } = 0) (upper panel) and comparison between calculated and experimental quenching rate constants of Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 0, *j* _{ i } = 0) (lower panel) ranging from 100 to 600 K.

Total quenching rate constants of Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 0, 1, *j* _{ i } = 0) (upper panel) and comparison between calculated and experimental quenching rate constants of Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 0, *j* _{ i } = 0) (lower panel) ranging from 100 to 600 K.

## Tables

Numerical parameters used in the wave packet calculations for the quenching process. Atomic units are used unless stated otherwise.

Numerical parameters used in the wave packet calculations for the quenching process. Atomic units are used unless stated otherwise.

Numerical parameters used in the wave packet calculations for the reactive process, Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 1, *j* _{ i } = 0) → HBr + H. Atomic units are used unless stated otherwise.

Numerical parameters used in the wave packet calculations for the reactive process, Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 1, *j* _{ i } = 0) → HBr + H. Atomic units are used unless stated otherwise.

Calculated and available experimental quenching rate constants (10^{−12} cm^{3} molecule^{−1}s^{−1}) of Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 0,*j* _{ i } = 0) at 300 K.

Calculated and available experimental quenching rate constants (10^{−12} cm^{3} molecule^{−1}s^{−1}) of Br(^{2} *P* _{1/2}) + H_{2}(*v* _{ i } = 0,*j* _{ i } = 0) at 300 K.

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