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本文基于2022年报道的一个SiH2(11A′)势能面, 运用切比雪夫波包方法对$ \text{H}{(}^{2}\text{S})+\text{SiH}({\text{X}}^{2}\Pi ; \nu = 0, $$ j = 0)\to \text{Si}{(}^{1}\text{D})+{\text{H}}_{2}({\text{X}}^{1} \Sigma_{g}^{+}) $反应体系在$ 1.0 \times {10^{ - 3}} $—1.0 eV的碰撞能量范围内进行动力学研究. 分别应用忽略科里奥利耦合效应的耦合态近似和精确量子力学计算得到该反应的反应概率、积分散射截面和速率 常数. 计算发现在J 较大时, 科里奥利耦合效应显著提升该反应的反应概率, 忽略科里奥利耦合效应会使H + SiH 反应的积分散射截面和速率常数减小, 对于速率常数而言, 温度越高, 两种计算方法所得结果的差距越大. 精确的量子力学计算结果表明, H + SiH 反应的速率常数在300—1000 K之间几乎不随温度改变, 这与H + CH 反应非常相似, 但是在数值上, 前者比后者大1个数量级.Initial state-selected and energy-resolved reaction probabilities, integral cross sections(ICSs), and thermal rate constants of the $ \text{H}{(}^{2}\text{S})+S\text{iH}({\text{X}}^{2}\Pi; \nu = 0\text{ },j = 0)\to \text{Si}{(}^{1}\text{D})+{\text{H}}_{2}({\text{X}}^{1} \Sigma_{g}^{+}) $ reaction are calculated within the coupled state(CS) approximation and accurate calculation with full Coriolis coupling(CC) by a time-dependent wave packet propagation method (Chebyshev wave packet method). Therefore, a new ab initio global potential energy surface (PES) of the electronic ground state (11A′) of the system, which was recently reported by Li et al. [
Phys. Chem. Chem. Phys. 2022 24 7759 ], is employed. The contributions of all partial waves to the total angular momentum J = 80 for CS approximation and J = 90 for CC calculation are considered to obtain the converged ICSs in a collision energy range of 1.0 ×10–3－1.0 eV. The calculated probabilities and ICSs display a decreasing trend with the increase of the collision energy and show an oscillatory structure due to the SiH2 well on the reaction path. The neglect of CC effect will lead to underestimation of the ICS and the rate constant due to the formation of an SiH2 complex supported by the stationary points of the SiH2(11A′) PES. In addition, the results of the exact calculation including CC effect are compared with those calculated in the CS approximation. For the reaction probability, CC and CS calculations change with similar tends, shown by their observations at small total angular momentum J = 10, 20 and 30, and the CC results are larger than the CS results almost in the whole considered energy range at large total angular momentum J = 40, 50, 60 and 70. The gap between CS and CC probability get more pronounced with increasing of J, which reveals that Coriolis coupling effects become more and more important with J increasing for the title reaction. Moreover, the exact quantum-wave calculations show that the thermal rate constant between 300 K and 1000 K for the title reaction shows a similar temperature independent behavior to that for the H + CH reaction, but the value of the rate constant for the H + SiH reaction is an order of magnitude larger than that for the H + CH reaction.-
Keywords:
- reaction probability /
- integral cross section /
- rate constant
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图 1 $ {\text{Si}}{{\text{H}}_2} $等势线, 图中等势线间隔为0.2 eV (a)γ = 91.5°, 以雅可比坐标RH-SiH和RSi-H为横纵坐标; (b) γ = 90°, 以雅可比坐标RSi–HH和RHH为横纵坐标; (c) H-Si-H线性结构, 以RSi–H和RSi–H为横纵坐标; (d) Si-H-H线性结构, 以RH–H和RSi–H为横纵坐标; 4个图的势能线起始点分别是–6.713, –6.713, –4.008, –4.084 eV, 等高线增量为0.1 eV
Fig. 1. Equipotential contour plot for SiH2: (a) Contour plot for bond stretching as a function of the product Jacobi coordinates RH–SiH and RSi–H with the Jacobi angle γ = 91.5°; (b) as a function of the reactant Jacobi coordinates RSi—HH and RHH with the Jacobi angle γ = 90°; (c) linear H-Si-H geometry, using RSi–H and RSi–H as the horizontal and vertical coordinates; (d) linear Si-H-H geometry, using RH–H and RSi–H as the horizontal and vertical coordinates; the contour increments are 0.1 eV, and the four panels starting from –6.713, –6.713, –4.008, –4.084 eV.
图 2 最小能量路径, ∠[H-H-Si]分别为30°, 60°, 90°, 120°, 150°, 180°
Fig. 2. The MEP of different approaching angles, ∠[H-H-Si] = 30°, 60°, 90°, 120°, 150°, 180° for the title reaction.
图 3 $ \text{H}({}^{2}\text{S})+\text{SiH}({\text{X}}^{2}\Pi )(\nu = 0, j = 0) $反应不同总角动量量子数(J = 0, 10, 20, 30, 40, 50, 60, 70)对应的反应概率随着能量的变化
Fig. 3. The reaction probabilities of CC and CS calculations for $ \text{H}({}^{2}\text{S})+\text{SiH}({\text{X}}^{2}\Pi ) $ $ (\nu = 0, j = 0) $reaction at J = 5, 10, 20, 30, 40, 50, 70.
图 4 在不同能量Ec = 0.06, 0.50, 0.99 eV, 分波对于积分散射截面的贡献 (a) CS分波贡献; (b) CC分波贡献
Fig. 4. Partial wave contributions to the integral cross section at Ec = 0.06, 0.50, 0.99 eV: (a) CS; (b) CC.
图 5 在$ 1.0 \times {10^{ - 3}} $—1.0 eV的碰撞能量范围下, H+ SiH反应ICS随着碰撞能量的变化
Fig. 5. The ICSs of CS and CC calculations for H+ SiH reaction versus collision energy of $ 1.0 \times {10^{ - 3}} $–1.0 eV.
表 1 波包计算中的数值参量(采用原子单位a.u., 特殊情况另外注明)
Table 1. Model parameters of wave packet calculation (The atomic units are used in the calculation unless otherwise stated).
参量 H+SiH 散射坐标R的范围 (10–16, 22) 散射坐标R内格点数 383 内部坐标r的范围 (0.5, 16) 内部坐标r内格点数 255 角度γ范围 (90°, 180°) 角度格点数 200 阻尼起点Rd(rd) 18.0(14.0) 阻尼范围dR(dr) 0.0005(0.001) 初始波包的中心位置R0 16.0 初始波包的能量E0/eV 0.15 初始波包的宽度δ 0.3 光谱控制 0.1 流计算的位置rf 13.8 传播步数 100000 
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[1] Power D, Brint P, Spalding T 1984 J. Mol. Struct. 108 81
Google Scholar
[2] Kalemos A, Dunning Jr T H, Mavridis A 2004 Mol. Phys. 102 2597
Google Scholar
[3] Ball J R, Thomson C 1978 Int. J. Quantum Chem 14 39
Google Scholar
[4] Allen W D, Schaefer H F 1986 Chem. Phys. 108 243
Google Scholar
[5] Jasinski J M, Chu J O 1988 J. Chem. Phys. 88 1678
Google Scholar
[6] Herzberg G, Lagerqvist A, Mckenzie B J 1969 Can. J. Phys. 47 1889
Google Scholar
[7] Dubois I, Herzberg G, Verma R D 1967 J. Chem. Phys. 47 4262
Google Scholar
[8] Dubois I 1968 Can. J. Phys. 46 2485
Google Scholar
[9] Thoman Jr J, Steinfeld J 1986 Chem. Phys. Lett. 124 35
Google Scholar
[10] Ishikawa H, Kajimoto O 1991 I. Mol. Spectrosc. 150 610
Google Scholar
[11] Hirota E, Ishikawa H 1999 J. Chem. Phys. 110 4254
Google Scholar
[12] Yurchenko S N, Bunker P R, Kraemer W P, Jensen P 2004 Can. J. Chem. 82 694
Google Scholar
[13] Tokue I, Yamasaki K, Nanbu S 2005 J. Chem. Phys. 122 144307
Google Scholar
[14] Tokue I, Yamasaki K, Nanbu S 2006 J. Chem. Phys. 124 114308
Google Scholar
[15] Wu Y N, Zhang C F, Ma H T 2017 RSC Adv. 7 12074
Google Scholar
[16] Cao J W, Wu Y N, Ma H T, Shen Z T, Bian W S 2021 Phys. Chem. Chem. Phys. 23 6141
Google Scholar
[17] Wang H N, Lü Y L, Chen J X, Song Y Z, Zhang C Y, Li Y Q 2022 Phys. Chem. Chem. Phys. 24 7759
Google Scholar
[18] Skouteris D, Castillo J F, Manolopoulos D E 2000 Comput. Phys. Commun. 133 128
Google Scholar
[19] Bulut N, Castillo J F, Jambrina P G, Kłos J, Roncero O, Aoiz F J, Bañares L 2015 J. Phys. Chem. A 119 11951
Google Scholar
[20] Chu T S, Zhang Y, Han K L 2006 Int. Rev. Phys. Chem. 25 201
Google Scholar
[21] Lagana A, Lendvay G 2005 Theory of Chemical Reaction Dynamics (New York : Springer) p217
[22] Lin S Y, Guo H 2003 J. Chem. Phys. 119 11602
Google Scholar
[23] Lin S Y, Guo H 2004 J. Phys. Chem. A 108 2141
Google Scholar
[24] Gao F, Wang X L, Zhao W L, Song Y Z, Meng Q T 2018 Eur. Phys. J. D 72 224
Google Scholar
[25] Gao F, Zhang L L, Zhao W L, Meng Q T, Song Y Z 2019 J. Chem. Phys. 150 224304
Google Scholar
[26] Mandelshtam V A, Taylor H S 1995 J. Chem. Phys. 103 2903
Google Scholar
[27] Mandelshtam V A, Taylor H S 1995 J. Chem. Phys. 102 7390
Google Scholar
[28] Tal-Ezer H, Kosloff R 1984 J. Chem. Phys. 81 3967
Google Scholar
[29] Neuhauser D, Baer M, Judson R S, Kouri D J 1990 J. Chem. Phys. 93 312
Google Scholar
[30] Althorpe S C 2001 J. Chem. Phys. 114 1601
Google Scholar
[31] Zhai H C, Lin S Y 2015 Chem. Phys. 455 57
Google Scholar
[32] Zhang L L, Liu D, Yue D G, Song Y Z, Meng Q T 2020 J. Phys. B: At. , Mol. Opt. Phys. 53 095202
Google Scholar
[33] Harding L B, Guadagnini R, Schatz G C 1993 J. Phys. Chem. 97 5472
Google Scholar
[34] Peng Y, Jiang Z A, Chen J S 2017 J. Phys. Chem. A 121 2209
Google Scholar
[35] Peng Y, Zhang H 2022 J. Phys. Chem. A 126 1946
Google Scholar
[36] Buren B, Zhang J P, Li Y Q 2024 J. Phys. Chem. A 128 5115
Google Scholar
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