Quantum dynamics studies of the <inline-formula><tex-math id="M2">\begin{document}$\rm D+SiD^+ \to D_2+Si^ +$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20221155_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20221155_M2.png"/></alternatives></inline-formula> reaction

Zhao Wen-Li; Sun Feng-Wei; Zhang Hong; Wang Yong-Gang; Gao Feng; Meng Qing-Tian

doi:10.7498/aps.71.20221155

Abstract

The quantum dynamics calculations are carried out for the title reaction D +SiD⁺→D₂+Si⁺ to obtain the initial ($ \nu = 0{\text{ }},j = 0 $)reaction probability, integral cross section (ICS) and rate constant on the potential energy surface (PES) of Gao, Meng and Song. A total of 110 partial waves are calculated by using the Chebyshev wave packet method with full Coriolis coupling (CC) and centrifugal sudden (CS) approximation in a collision energy range from 1.0 × 10^–3to 1.0 eV. The calculated probability decreases with the collision energy increasing except for J≤40. The calculation results indicate that the CS approximation will overestimate or underestimate the reaction probability . The ICS decreases with the collision energy increasing and shows an oscillatory structure due to the$\rm{SiH_2^+} $well on the reaction path. The results show that the neglect of the Coriolis coupling leads to the overestimation of the cross section and the rate constant. Besides, the discrepancy between the integral cross sections from the CC and CS calculations decreases clearly with collision energy increasing. Comparison with the corresponding results of H+CH⁺ reaction indicates that isotope substitution reaction makes the cross section and the rate constant underestimated. The resulting integral reaction cross section displays less oscillatory structure, especially in the exact quantum calculation with the full Coriolis coupling effect taken into consideration. The kinetic isotope effect $(\kappa_{\rm H+SiH^+}(T)/\kappa_{\rm D+SiD^+}(T))$is found to decrease with temperature increasing. It can be seen that the reduced mass of reactant can exert a certain effect on dynamic behavior.

Keywords:

Authors and contacts

1.
School of Information Science and Engineering, Shandong Agricultural University, Taian 271018, China
2.
School of Physics and Electronics, Shandong Normal University, Jinan 250358, China

Corresponding author: Gao Feng, gaofeng@sdau.edu.cn ; Meng Qing-Tian, qtmeng@sdnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11674198 , 51971161) and Shandong Provincial Natural Science Foundation of China (Grant No. ZR2022MA087)

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References

[1]	Bender C F, Schaefer H F 1971 J. Mol. Spectrosc. 37 423 Google Scholar
[2]	Stoecklin T, Halvick P 2005 Phys. Chem. Chem. Phys. 7 2446 Google Scholar
[3]	Warmbier R, Schneider R 2011 Phys. Chem. Chem. Phys. 13 10285 Google Scholar
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图 1 ${\rm{Si{H}}}_2^+(\rm{X^2A_1}) $ 势能面(∠[H-Si-H] = 118.38º), 图中等势线间隔为0.2 eV, 红色实线为最小能量路径

Figure 1. The PES of ${\rm{Si{H}}}_2^+ $(X²A₁) for bending angle∠[H-Si-H] = 118.38º starting from–5.82 eV, the contour drawn with an increment of 0.2 eV, the solid red line is minimum energy path.

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图 2 最小能量路径(∠[D-Si-D]分别为30°, 60°, 90°, 120°, 180°)

Figure 2. The MEP of different approaching angles (∠[D-Si-D] = 30°, 60°, 90°, 120°, 180°)for the title reaction.

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图 3 $ {\text{D}} + {\text{Si}}{{\text{D}}^ + } \to {{\text{D}}_2} + {\text{S}}{{\text{i}}^ + } $反应不同分波 (J = 5, 20, 40, 60, 80, 100)的反应概率随碰撞能量的变化, 黑色实线对应CS概率, 红色虚线对应CC概率

Figure 3. The reaction probabilities of CC and CS calculations for $ {\text{D}} + {\text{Si}}{{\text{D}}^ + } \to {{\text{D}}_2} + {\text{S}}{{\text{i}}^ + } $ reaction at J = 5, 20, 40, 60, 80, and 100, The black soid line is for CS probability and the red dashed line is for CC probability.

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图 4 不同的角动量量子数下H+SiH⁺与D+SiD⁺的CC反应概率, 黑色实线对应H+SiH⁺反应, 红色虚线对应D+SiD⁺反应

Figure 4. The reaction probabilities of CC calculations for H +SiH⁺ and D +SiD⁺ reactions at J = 10, 20, 40, 60, 80, and 90. The black solid line is for H + SiH⁺ reaction and the red dashed line is for D +SiD⁺ reaction.

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图 5 H + SiH⁺与D + SiD⁺反应 ICS 随着碰撞能量的变化(1.0 ×10^–3—1.0 eV)

Figure 5. The ICSs of CS and CC calculations for H+ SiH⁺ and D +SiD⁺ reactions over collision energy of 3 1.0 ×10^–3—1.0 eV.

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图 6 H+ SiH⁺和$ {\text{D}} + {\text{Si}}{{\text{D}}^ + } $反应速率常数随温度的变化

Figure 6. Variation of reaction rate constant of H+ SiH⁺ and $ {\text{D}} + {\text{Si}}{{\text{D}}^ + } $with temperature.

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图 7 动力学同位素效应与温度的关系

Figure 7. Temperature dependence of kinetic isotope effect.

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表 1 波包计算中的数值参量(除特殊说明, 均采用原子单位 a.u.)

Table 1. Model parameters of wave packet calculation (The atomic unit is used in the calculation unlessotherwise stated).

坐标取值范围和基组数	吸收势	初始波包	光谱控制	流计算的位置	传播步数
$ R \in (0.2, \, 22) \; ({N_R} = 383) $ $ r \in (0.5, \, 16) \; ({N_r} = 255) $ $ \gamma \in (0, \, {180^ \circ }) \; ({N_\gamma } = 200) $	$ {R_d} = 18.0 \;\; {d_R} = 0.0005 $ $ {r_d} = 14.0 \;\; {d_r} = 0.001 $	$ {R_0} = 16.0 $ $ {E_0} = 0.15{\text{ eV}} $ $ \delta = 0.3 $	1.0	$ {r_f} = 13.8 $	50000

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[1]	Bender C F, Schaefer H F 1971 J. Mol. Spectrosc. 37 423 Google Scholar
[2]	Stoecklin T, Halvick P 2005 Phys. Chem. Chem. Phys. 7 2446 Google Scholar
[3]	Warmbier R, Schneider R 2011 Phys. Chem. Chem. Phys. 13 10285 Google Scholar
[4]	Herráez-Aguilar D, Jambrina P G, Menéndez M, Aldegunde J, Warmbier R, Aoiz F J 2014 Phys. Chem. Chem. Phys. 16 24800 Google Scholar
[5]	Li Y Q, Zhang P Y, Han K L 2015 J. Chem. Phys. 142 124302 Google Scholar
[6]	Guo J, Zhang A J, Zhou Y, Liu J Y, Jia J F, Wu H S 2017 Chem. Phys. Lett. 689 121 Google Scholar
[7]	Sundaram P, Manivannan V, Padmanaban R 2017 Phys. Chem. Chem. Phys. 19 20172 Google Scholar
[8]	Scheier P, Marsen B, Lonfat M, Schneider W D 2000 Surf. Sci. 458 113 Google Scholar
[9]	Maus M, Gantefor G, Eberhardt W 2000 Appl. Phys. A 70 535 Google Scholar
[10]	Kasap S, Capper P 2017 Springer Handbook of Electronic and Photonic Materials (Heidelberg: Springer) pp573–576
[11]	Zhang Y G, Dou G, Cui J, Yu Y 2018 J. Mol. Struct. 1165 318 Google Scholar
[12]	Bauer C, Hirst D M, Hall D I, Sarre P J, Rosmus P J. 1994 Chem. Sot. Faraday Trans. 90 517 Google Scholar
[13]	Vach H, Chaâbane N, Peslherbe G H 2002 Chem. Phys. Lett. 352 127 Google Scholar
[14]	Chaâbane N, Vach H, Cabarrocas P R I 2004 J. Phys. Chem. A 108 1818 Google Scholar
[15]	Gao F, Zhang L L, Zhao W L, Meng Q T, Song Y Z 2019 J. Chem. Phys. 150 224304 Google Scholar
[16]	Langhoff S R, Davidson E R 1974 Int. J. Quantum Chem. 8 61 Google Scholar
[17]	高峰 2020 博士学位论文 (济南: 山东师范大学) Gao F 2020 Ph. D. Dissertation (Jinan: Shandong Normal University) (in Chinese)
[18]	Zhao W L, Tan R S, Cao X C, Gao F, Meng Q T 2021 Chin. Phys. B 30 123403 Google Scholar
[19]	王茗馨, 王美山, 杨传路, 刘佳, 马晓光, 王立志 2015 64 043402 Google Scholar Wang M X, Wang M S, Yang C L, Liu J, Ma X G, Wang L Z 2015 Acta Phys. Sin. 64 043402 Google Scholar
[20]	夏文泽, 于永江, 杨传路 2012 61 223401 Google Scholar Xia W Z, Yu Y J, Yang C L 2012 Acta Phys. Sin 61 223401 Google Scholar
[21]	Guo L, Yang Y F, Fan X X, Ma F C, Li Y Q 2017 Commun. Theor. Phys. 67 549 Google Scholar
[22]	Zhang J Z H 1999 Theory and Application of Quantum Molecular Dynamics (Singapore: World Scientific) pp149–150
[23]	Lin S Y, Guo H 2003 J. Chem. Phys. 119 11602 Google Scholar
[24]	Mandelshtam V A, Taylor H S 1995 J. Chem. Phys. 102 7390 Google Scholar
[25]	Mandelshtam V A, Taylor H S 1995 J. Chem. Phys. 103 2903 Google Scholar
[26]	Tal-Ezer H, Kosloff R 1984 J. Chem. Phys. 81 3967 Google Scholar
[27]	Neuhauser D, Baer M, Judson R S, Kouri D J 1990 J. Chem. Phys. 93 312 Google Scholar
[28]	Althorpe S C 2001 J. Chem. Phys. 114 1601 Google Scholar
[29]	Zhai H C, Lin S Y 2015 Chem. Phys. 455 57 Google Scholar
[30]	Bowman J M 1991 J. Phys. Chem. 95 4960 Google Scholar
[31]	Gray S K, Goldfield, E M, Schatz G C, Balint-Kurti G G 1999 Phys. Chem. Chem. Phys. 1 1141 Google Scholar
[32]	Clary D C 1984 Mol. Phys. 53 3 Google Scholar
[33]	Chu T S, Han K L 2008 Phys. Chem. Chem. Phys. 10 2431 Google Scholar
[34]	De Fazio D, Castillo J F 1999 Phys. Chem. Chem. Phys. 1 1165 Google Scholar
[35]	Lu R F, Wang Y H, Deng K M, 2013 J. Comput. Chem. 34 1735 Google Scholar

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Quantum dynamics studies of the $\rm D+SiD^+ \to D_2+Si^ +$ reaction

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Corresponding author: Gao Feng, gaofeng@sdau.edu.cn ; Meng Qing-Tian, qtmeng@sdnu.edu.cn

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Quantum dynamics studies of the $\rm D+SiD^+ \to D_2+Si^ +$ reaction

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Authors and contacts

Corresponding author: Gao Feng, gaofeng@sdau.edu.cn ; Meng Qing-Tian, qtmeng@sdnu.edu.cn

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