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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 × 10–3 to 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:
- Chebyshev wave packet method /
- reaction probability /
- integral cross section /
- rate constant
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[3] Warmbier R, Schneider R 2011 Phys. Chem. Chem. Phys. 13 10285
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[4] Herráez-Aguilar D, Jambrina P G, Menéndez M, Aldegunde J, Warmbier R, Aoiz F J 2014 Phys. Chem. Chem. Phys. 16 24800
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[5] Li Y Q, Zhang P Y, Han K L 2015 J. Chem. Phys. 142 124302
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[7] Sundaram P, Manivannan V, Padmanaban R 2017 Phys. Chem. Chem. Phys. 19 20172
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[9] Maus M, Gantefor G, Eberhardt W 2000 Appl. Phys. A 70 535
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[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
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[12] Bauer C, Hirst D M, Hall D I, Sarre P J, Rosmus P J. 1994 Chem. Sot. Faraday Trans. 90 517
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[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
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[15] Gao F, Zhang L L, Zhao W L, Meng Q T, Song Y Z 2019 J. Chem. Phys. 150 224304
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[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)
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Google Scholar
[19] 王茗馨, 王美山, 杨传路, 刘佳, 马晓光, 王立志 2015 物理学报 64 043402
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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
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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
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[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
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[32] Clary D C 1984 Mol. Phys. 53 3
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Google Scholar
[34] De Fazio D, Castillo J F 1999 Phys. Chem. Chem. Phys. 1 1165
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[35] Lu R F, Wang Y H, Deng K M, 2013 J. Comput. Chem. 34 1735
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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.
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.
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.
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.
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.
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.
图 7 动力学同位素效应与温度的关系
Figure 7. Temperature dependence of kinetic isotope effect.
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 物理学报 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 物理学报 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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