Vibrational excitation and dissociation processes in high-temperature N<sub>2</sub>-O<sub>2</sub> state-to-state collisions based on neural network and dynamic simulation

GUO Changmin; ZHANG Hong; CHENG Xinlu

doi:10.7498/aps.74.20250533

Abstract

The scattering cross-sections and reaction rate coefficients are crucial parameters for elucidating the energy transfer mechanism of state-to-state collisions between molecular gases and also serve as a fundamental basis for modeling the non-equilibrium flow field. However, the database of kinetic processes related to nitrogen shock flows is still being developed. In this work, a detailed kinetic study of the N₂+ O₂ collision is carried out by combining the quasi-classical trajectory method (QCT) and neural network model (NN). Firstly, QCT is used to calculate 90 N₂(v) + O₂(w) processes with various initial vibrational states (v,w), and the contributions of all vibrational excitation and dissociation reaction channels are discussed. The following conclusions are drawn: 1) The contributions of the vibration-vibration (VV) energy exchange channel of O₂ and N₂ are similar, while the vibration-translational (VT) transition mainly occurs on O₂; 2) The total dissociation cross-section primarily results from the O₂ single-dissociation channel, followed by the exchange-dissociation channel, with relatively minor contributions from the N₂ single- and double-dissociation channels. Then, based on the QCT dataset, a high-performance NN model (R-value of 0.99) is trained to predict the total dissociation cross-section caused by N₂(v) + O₂(w) collisions. Compared with the method that only uses QCT, the method that jointly uses OCT and NN model can achieve an approximately 91.94% reduction in computational cost. Finally, to facilitate use in kinetic modeling, Arrhenius-type fits for the VV/VT rate coefficients are provided over the temperature range of 5000–30000 K, and an exponential form related to the translational energy E_t is used to fit the total dissociation cross-section.

Keywords:

state-to-state reaction rate coefficient /
vibration relaxation /
collision dissociation /
neural network model

Authors and contacts

1.
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China
2.
College of Physics, Sichuan University, Chengdu 610065, China

Corresponding author: CHENG Xinlu, chengxl@scu.edu.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2024YFF0508503).

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References

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Cited By

图 1 VV过程(1, 0) → (0, 1) (a) 和VT过程(1, 0) → (0, 0) (b)的速率系数作为平动温度的函数: 我们的计算结果(黑色实线)与已报道的理论数据^[25,39]对比

Figure 1. Rate coefficients for the VV process (1, 0) → (0, 1) (a) and VT process (1, 0) → (0, 0) (b) as a function of translational temperature: comparison between our calculated results (in solid black line) and reported theoretical data^[25,39].

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图 2 N₂(v) + O₂(10), N₂(v) + O₂(21)和N₂(v) + O₂(30)过程中VVN和VVO单量子跃迁截面随初始能级(v)和初始平动能(E_t)的等值线图

Figure 2. Contour map of VVN and VVO single-quantum transition cross sections with the initial energy level (v) and initial translational energy (E_t) of N₂(v) + O₂(10), N₂(v) + O₂(21) and N₂(v) + O₂(30) processes.

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图 3 N₂(v) + O₂(10), N₂(v) + O₂(21)和N₂(v) + O₂(30)过程中VTN和VTO单量子跃迁截面随N₂初始能级(v)和初始平动能(E_t)的等值线图

Figure 3. Contour map of VTN and VTO single-quantum transition cross sections with the initial energy level (v) and initial translational energy (E_t) of N₂(v) + O₂(10), N₂(v) + O₂(21) and N₂(v) + O₂(30) processes.

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图 4 不同N₂(v)-O₂(w)碰撞过程中单量子和多量子VVO和VTO速率系数的温度依赖性

Figure 4. Temperature dependence of single- and multi-quantum VVO and VTO rate coefficients during different N₂(v)-O₂(w) collisions.

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图 5 各个解离通道的反应截面随N₂初始振动能级(v)和初始平动能(E_t)的等值线图

Figure 5. Contour map of reaction cross sections of each dissociation channel with N₂ initial vibrational energy level (v) and initial translational energy (E_t).

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图 6 各个解离通道的反应截面随O₂初始振动能级(w)和初始平动能(E_t)的等值线图

Figure 6. Contour map of reaction cross sections of each dissociation channel with O₂ initial vibrational energy level (w) and initial translational energy (E_t).

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图 7 (a) NN-totaldiss模型预测值和QCT原始值对比; (b) NN预测值与原始QCT数据之间的误差直方图, 虚线表示误差为零

Figure 7. (a) Comparison of NN-totaldiss predicted data and the raw QCT data; (b) error histogram between the predicted values and the raw QCT data. The black dash line indicates zero error.

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图 8 QCT计算的(左)和NN-totaldiss模型预测的(右)总解离截面随初始平动能(E_t)以及O₂和N₂初始振动能级的等值线图

Figure 8. Contour map of QCT calculated (left) and NN-totaldiss predicted (right) total dissociation cross sections with initial translational energy (E_t) and the initial vibrational levels of O₂ and N₂.

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表 1 QCT数据集包含的N₂(v) + O₂(w)碰撞过程

Table 1. N₂(v) + O₂(w) collision processes contained in the QCT dataset.

Group	N₂(v)	O₂(w)	E_t (eV)
1	{0, 5, 10, 21, 30}	{0, 1, 3, 7, 10, 15, 21, 25, 30}	{0.2, 0.6, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
2	{0, 1, 3, 7, 10, 15, 21, 25, 30, 35}	{0, 5, 10, 21, 30}	{0.2, 0.6, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

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表 A1 VV/VT反应速率系数(单位: k/(cm³·s^–1))的Arrhenius拟合参数表(A, n, B). MSE是均方误差(单位: k/(cm³·s^–1)), 温度范围为5000—30000 K

Table A1. Arrhenius fitting parameters (A, n, B) for VV/VT reaction rate coefficient (unit: k/(cm³·s^–1)). MSE is the mean square error (unit: k/(cm³·s^–1)), and the temperature range is 5000–30000 K.

N₂(v) + O₂(w) → N₂(v') + O₂(w')	A	n	B	MSE
(0, 10) → (1, 9)	4.10 × 10^–10	–2.91 × 10^–1	4.81 × 10⁴	4.27 × 10^–26
(0, 10) → (0, 9)	2.44 × 10^–10	4.28 × 10^–2	2.01 × 10⁴	7.67 × 10^–22
(0, 10) → (0, 8)	3.33 × 10^–10	–6.70 × 10^–2	3.10 × 10⁴	3.04 × 10^–23
(0, 10) → (0, 7)	3.95 × 10^–10	–1.39 × 10^–1	3.96 × 10⁴	2.66 × 10^–24
(0, 21) → (1, 20)	4.24 × 10^–10	–4.58 × 10^–1	–4.53 × 10³	4.21 × 10^–23
(0, 21) → (0, 20)	3.50 × 10^–10	2.04 × 10^–1	2.78 × 10³	7.96 × 10^–21
(0, 21) → (0, 19)	2.51 × 10^–10	–3.01 × 10^–2	1.94 × 10⁴	2.32 × 10^–22
(0, 21) → (0, 18)	2.87 × 10^–10	–7.43 × 10^–2	2.46 × 10⁴	5.62 × 10^–23
(0, 30) → (1, 29)	3.01 × 10^–10	–3.75 × 10^–1	4.79 × 10⁴	6.99 × 10^–27
(0, 30) → (0, 29)	1.39 × 10^–10	9.46 × 10^–2	7.06 × 10³	6.44 × 10^–21
(0, 30) → (0, 28)	1.49 × 10^–10	2.78 × 10^–3	9.00 × 10³	9.18 × 10^–22
(0, 30) → (0, 27)	1.74 × 10^–10	–5.01 × 10^–2	1.14 × 10⁴	2.99 × 10^–22
(15, 10) → (16, 9)	2.31 × 10^–10	–9.11 × 10^–2	1.73 × 10⁴	8.85 × 10^–23
(15, 10) → (17, 8)	3.46 × 10^–10	–2.77 × 10^–1	3.64 × 10⁴	2.77 × 10^–25
(15, 10) → (18, 7)	3.94 × 10^–10	–3.69 × 10^–1	4.36 × 10⁴	1.97 × 10^–26
(15, 10) → (15, 9)	1.97 × 10^–10	5.51 × 10^–3	1.30 × 10⁴	8.14 × 10^–22
(15, 10) → (15, 8)	2.78 × 10^–10	–1.96 × 10^–1	2.58 × 10⁴	4.40 × 10^–24
(15, 10) → (15, 7)	3.17 × 10^–10	–3.04 × 10^–1	3.38 × 10⁴	2.16 × 10^–25
(15, 21) → (16, 20)	1.79 × 10^–10	–2.61 × 10^–2	1.56 × 10⁴	2.42 × 10^–22
(15, 21) → (17, 19)	2.69 × 10^–10	–3.02 × 10^–1	2.64 × 10⁴	5.21 × 10^–25
(15, 21) → (18, 18)	3.12 × 10^–10	–3.82 × 10^–1	3.60 × 10⁴	3.42 × 10^–26
(15, 21) → (15, 20)	1.96 × 10^–10	7.64 × 10^–2	1.35 × 10⁴	2.82 × 10^–21
(15, 21) → (15, 19)	2.46 × 10^–10	–1.03 × 10^–1	2.19 × 10⁴	3.80 × 10^–23
(15, 21) → (15, 18)	2.07 × 10^–10	–1.88 × 10^–1	2.49 × 10⁴	3.33 × 10^–24
(15, 30) → (16, 29)	9.24 × 10^–11	–8.39 × 10^–2	1.39 × 10³	3.39 × 10^–22
(15, 30) → (17, 28)	2.05 × 10^–10	–3.47 × 10^–1	2.70 × 10⁴	1.23 × 10^–25
(15, 30) → (18, 27)	3.20 × 10^–10	–4.66 × 10^–1	3.90 × 10⁴	4.67 × 10^–27
(15, 30) → (15, 29)	1.17 × 10^–10	1.13 × 10^–1	4.53 × 10³	1.04 × 10^–20
(15, 30) → (15, 28)	1.57 × 10^–10	–1.67 × 10^–2	1.10 × 10⁴	5.05 × 10^–22
(15, 30) → (15, 27)	5.12 × 10^–10	–2.19 × 10^–1	1.17 × 10⁴	1.06 × 10^–22
(35, 10) → (36, 9)	5.68 × 10^–10	–5.32 × 10^–2	3.17 × 10³	1.51 × 10^–20
(35, 10) → (37, 8)	1.30 × 10^–9	–2.97 × 10^–1	6.01 × 10³	4.83 × 10^–22
(35, 10) → (38, 7)	4.10 × 10^–10	–3.94 × 10^–1	6.35 × 10³	7.64 × 10^–24
(35, 10) → (35, 9)	2.01 × 10^–10	–6.83 × 10^–2	1.58 × 10⁴	1.33 × 10^–22
(35, 10) → (35, 8)	1.98 × 10^–10	–2.33 × 10^–1	1.85 × 10⁴	3.73 × 10^–24
(35, 10) → (35, 7)	1.88 × 10^–10	–3.31 × 10^–1	2.17 × 10⁴	3.19 × 10^–25
(35, 21) → (36, 20)	1.79 × 10^–10	–2.60 × 10^–2	1.56 × 10⁴	2.42 × 10^–22
(35, 21) → (37, 19)	2.69 × 10^–10	–3.02 × 10^–1	2.64 × 10⁴	5.21 × 10^–25
(35, 21) → (38, 18)	3.12 × 10^–10	–3.82 × 10^–1	3.60 × 10⁴	3.4 × 10^–26
(35, 21) → (35, 20)	1.96 × 10^–10	7.64 × 10^–2	1.35 × 10⁴	2.82 × 10^–21
(35, 21) → (35, 19)	2.46 × 10^–10	–1.03 × 10^–1	2.19 × 10⁴	3.80 × 10^–23
(35, 21) → (35, 18)	2.07 × 10^–10	–1.88 × 10^–1	2.49 × 10⁴	3.33 × 10^–24
(35, 30) → (36, 29)	5.99 × 10^–10	–8.87 × 10^–2	1.96 × 10³	1.15 × 10^–20
(35, 30) → (37, 28)	4.54 × 10^–10	–2.35 × 10^–1	3.14 × 10³	3.48 × 10^–22
(35, 30) → (38, 27)	9.69 × 10^–11	–2.38 × 10^–1	5.53 × 10³	9.00 × 10^–24
(35, 30) → (35, 29)	6.49 × 10^–11	1.25 × 10^–1	3.21 × 10³	5.24 × 10^–21
(35, 30) → (35, 28)	1.25 × 10^–10	–9.18 × 10^–2	1.26 × 10⁴	6.00 × 10^–23
(35, 30) → (35, 27)	1.61 × 10^–10	–2.35 × 10^–1	1.59 × 10⁴	3.84 × 10^–24

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表 A2 总解离截面(单位: Å²)的拟合参数表(a, b, c). 初始平动能E_t范围为0.2—10 eV, RMSE是均方根误差(单位: Å²)

Table A2. Fitting parameters (a, b, c) of total dissociation cross-section (unit: Å²). The range of initial translational energy E_t is 0.2–10 eV, and RMSE is root mean square error (unit: Å²).

N₂(v)	O₂(w)	a	b	c	RMSE
0	1	1.98 × 10¹	–1.02 × 10²	9.03 × 10⁰	1.82 × 10^–4
0	3	1.13 × 10¹	–5.82 × 10¹	5.11 × 10⁰	3.54 × 10^–4
0	5	8.29 × 10⁰	–4.30 × 10¹	3.87 × 10⁰	2.95 × 10^–3
0	7	6.43 × 10⁰	–3.35 × 10¹	3.14 × 10⁰	8.48 × 10^–3
0	10	–2.46 × 10²	3.52 × 10¹	–9.70 × 10^–1	5.70 × 10^–3
0	15	–9.18 × 10¹	1.06 × 10¹	2.57 × 10^–1	8.02 × 10^–3
0	21	–2.04 × 10¹	2.24 × 10^–1	8.60 × 10^–1	3.37 × 10^–2
0	25	–5.67 × 10⁰	–1.11 × 10⁰	1.01 × 10⁰	6.37 × 10^–2
0	30	–6.06 × 10^–1	–5.62 × 10^–1	1.10 × 10⁰	1.30 × 10^–1
1	21	–2.03 × 10¹	3.57 × 10^–1	8.50 × 10^–1	2.33 × 10^–2
1	30	–7.54 × 10^–1	–4.60 × 10^–1	1.09 × 10⁰	1.58 × 10^–1
3	15	–7.75 × 10¹	8.74 × 10⁰	3.16 × 10^–1	1.44 × 10^–2
3	21	–2.10 × 10¹	1.02 × 10⁰	7.94 × 10^–1	4.72 × 10^–2
3	30	–8.40 × 10^–1	–3.81 × 10^–1	1.09 × 10⁰	1.73 × 10^–1
5	30	–8.07 × 10^–1	–3.74 × 10^–1	1.09 × 10⁰	1.94 × 10^–1
5	0	8.27 × 10⁰	–4.28 × 10¹	3.65 × 10⁰	6.98 × 10^–3
5	1	8.21 × 10⁰	–4.25 × 10¹	3.75 × 10⁰	3.78 × 10^–3
5	3	7.21 × 10⁰	–3.75 × 10¹	3.44 × 10⁰	6.53 × 10^–3
5	7	–3.96 × 10²	6.61 × 10¹	–2.62 × 10⁰	1.60 × 10^–3
5	10	–2.83 × 10²	4.83 × 10¹	–1.81 × 10⁰	5.40 × 10^–3
5	15	–7.95 × 10¹	9.94 × 10⁰	2.43 × 10^–1	2.80 × 10^–2
5	21	–1.95 × 10¹	8.26 × 10^–1	8.08 × 10^–1	3.42 × 10^–2
5	25	–6.46 × 10⁰	–4.60 × 10^–1	9.66 × 10^–1	6.22 × 10^–2
7	15	–6.79 × 10¹	8.41 × 10⁰	2.93 × 10^–1	2.57 × 10^–2
7	21	–1.85 × 10¹	6.82 × 10^–1	8.22 × 10^–1	3.75 × 10^–2
7	30	–7.52 × 10¹	–3.87 × 10^–1	1.09 × 10⁰	2.02 × 10^–1
10	15	–6.21 × 10¹	7.99 × 10⁰	3.14 × 10^–1	3.16 × 10^–2
10	21	–1.75 × 10¹	7.87 × 10^–1	8.16 × 10^–1	4.21 × 10^–2
10	30	–6.64 × 10^–1	–4.20 × 10^–1	1.09 × 10⁰	2.00 × 10^–1
15	0	3.92 × 10⁰	–2.04 × 10¹	2.03 × 10⁰	1.68 × 10^–2
15	3	3.21 × 10⁰	–1.68 × 10¹	1.83 × 10⁰	4.68 × 10^–2
15	7	–1.97 × 10²	3.56 × 10¹	–1.29 × 10⁰	2.32 × 10^–2
15	10	–1.12 × 10²	1.78 × 10¹	–2.20 × 10^–1	3.96 × 10^–2
15	15	–4.74 × 10¹	5.30 × 10⁰	5.20 × 10^–1	3.20 × 10^–2
15	21	–1.20 × 10¹	–4.00 × 10^–1	9.19 × 10^–1	5.88 × 10^–2
15	25	–5.0 × 10⁰	–5.65 × 10^–1	9.88 × 10^–1	3.51 × 10^–2
15	30	–6.92 × 10^–1	–3.97 × 10^–1	1.09 × 10⁰	1.50 × 10^–1
18	21	–1.16 × 10¹	–2.55 × 10^–1	9.34 × 10^–1	5.33 × 10^–2
21	15	–3.44 × 10¹	4.04 × 10⁰	6.22 × 10^–1	4.97 × 10^–2
21	0	–7.70 × 10¹	5.01 × 10⁰	5.89 × 10^–1	1.06 × 10^–2
21	1	–7.61 × 10¹	5.57 × 10⁰	5.54 × 10^–1	7.48 × 10^–3
21	3	–8.50 × 10¹	9.82 × 10⁰	2.65 × 10^–1	1.68 × 10^–2
21	7	–6.54 × 10¹	7.75 × 10⁰	3.69 × 10^–1	2.71 × 10^–2
21	10	–4.66 × 10¹	4.61 × 10⁰	5.73 × 10^–1	1.65 × 10^–2
21	18	–1.81 × 10¹	8.87 × 10^–1	8.42 × 10^–1	6.70 × 10^–2
21	21	–1.09 × 10¹	8.07 × 10^–2	9.19 × 10^–1	5.56 × 10^–2
21	25	–3.91 × 10⁰	–8.38 × 10^–1	1.04 × 10⁰	6.94 × 10^–2
21	27	–2.07 × 10⁰	–7.80 × 10^–1	1.07 × 10⁰	6.97 × 10^–2
21	30	–4.61 × 10^–1	–5.58 × 10^–1	1.12 × 10⁰	1.79 × 10^–1
27	21	–6.79 × 10⁰	–4.70 × 10^–1	1.02 × 10⁰	8.37 × 10^–2
30	15	–9.22 × 10⁰	–3.68 × 10^–1	9.65 × 10^–1	1.25 × 10^–1
30	21	–4.34 × 10⁰	–9.02 × 10^–1	1.08 × 10⁰	1.40 × 10^–1
30	30	1.01 × 10^–1	–8.90 × 10^–1	1.23 × 10⁰	3.85 × 10^–1
35	21	–2.49 × 10⁰	–8.65 × 10^–1	1.13 × 10⁰	1.79 × 10^–1
35	5	–1.15 × 10¹	5.75 × 10^–1	8.62 × 10^–1	5.73 × 10^–2
35	10	–8.09 × 10⁰	–4.55 × 10^–2	9.44 × 10^–1	7.15 × 10^–2
35	30	1.06 × 10^–1	–8.47 × 10^–1	1.29 × 10⁰	5.14 × 10^–1

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Vibrational excitation and dissociation processes in high-temperature N₂-O₂ state-to-state collisions based on neural network and dynamic simulation

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Vibrational excitation and dissociation processes in high-temperature N2-O2 state-to-state collisions based on neural network and dynamic simulation

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Vibrational excitation and dissociation processes in high-temperature N₂-O₂ state-to-state collisions based on neural network and dynamic simulation