基于密度泛函理论的HCN与H<sub>2</sub>/H<sub>2</sub>O气相反应机理研究

孙明哲; 许建良; 侯秋实; 代正华; 王辅臣

doi:10.19906/j.cnki.JFCT.2024004

基于密度泛函理论的HCN与H₂/H₂O气相反应机理研究

doi: 10.19906/j.cnki.JFCT.2024004

孙明哲^1,,
许建良^1,,
侯秋实^2,,
代正华^{1, 3, ,},
王辅臣^1,

1.
华东理工大学资源与环境工程学院上海市煤气化工程技术研究中心, 上海 200237
2.
上海寰球工程有限公司, 上海 200032
3.
新疆大学化工学院, 新疆乌鲁木齐 830046

基金项目: 国家重点研发计划（2022YFB4101500），新疆自治区自然科学基金重点项目（2023D01D02）和上海市2021年科技创新行动计划课题（21DZ1209003）资助

详细信息

通讯作者:
Tel：+86 13817562292，E-mail：chinadai@ecust.edu.cn

中图分类号: O643
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出版历程
- 收稿日期: 2023-10-18
- 修回日期: 2023-12-28
- 录用日期: 2024-01-08
- 网络出版日期: 2024-03-27

Study on gas phase reaction mechanism of HCN and H₂/H₂O based on density functional theory

SUN Mingzhe^1
,,
XU Jianliang^1
,,
HOU Qiushi^2
,,
DAI Zhenghua^{1, 3
, ,},
WANG Fuchen^1
,

1.
School of Resources and Environmental Engineering, East China University of Science and Technology, Shanghai Coal Gasification Engineering Technology Research Center, Shanghai 200237, China
2.
Shanghai Huanqiu Engineering Co., Ltd, Shanghai 200032, China
3.
School of Chemical Engineering, Xinjiang University, Urumqi 830046, China

Funds: The project was supported by the National Key Research and Development Program of China ( 2022YFB4101500), Natural Science Foundation of Xinjiang Uygur Autonomous Region of China (2023D01D02), and Shanghai 2021 Science and Technology Innovation Action Plan Project (21DZ1209003).

摘要

摘要: 含HCN的废弃物在气化炉内的高温转化是其绿色处理的方法之一，其中，HCN与H₂/H₂O的反应是其在气化炉内的主要转化过程。本工作基于密度泛函理论，采用Gaussian及其配套软件对HCN与H₂/H₂O的反应机理进行了研究。通过分子成键、断键角度提出HCN与H₂/H₂O的各两种反应路径，结合能垒和热力学分析确定了相对最优路径，并计算了相对最优反应路径的速率常数。结果表明，HCN与H₂反应相对最优路径为：三个H₂分子在C≡N上分三步进行加成得到产物CH₄+NH₃；HCN与H₂O反应相对最优路径为：H₂O分子进攻C原子，O原子和C原子的H先后转移至N原子得到产物CO+NH₃。两条相对最优路径在1473 K以上有明显反应速率，分别为9.57×10⁻⁴和1.71 mol/(L·s)。研究结果为高温下HCN与H₂/H₂O反应的工艺和设备开发提供了理论数据支撑。
- HCN /
- 气相反应 /
- 密度泛函理论 /
- 热力学 /
- 动力学
Abstract: HCN is a highly toxic substance that can enter the human body through the skin and respiratory system, and in severe cases, cause death. HCN can achieve partial conversion under high-temperature gasification conditions, mainly by reacting with H₂ and H₂O. In order to further explore the micro reaction mechanism of HCN with H₂ and H₂O during gasification, and to investigate the effects of temperature and pressure changes on the reaction, this paper uses quantum chemical simulation methods to study the reaction path, reaction thermodynamics, and kinetics of the above reactions, and quantitatively analyzes the changes in thermodynamic parameters and reaction rate constants with temperature, fitting the Arrhenius equation related to the reaction. Calculate the distribution of Fukui functions for various reactants and intermediates in the reaction process of HCN with H₂ and H₂O using Multiwfn, and speculate on possible reaction pathways. The transition state search and single point energy calculation of the reaction process between HCN and H₂ and H₂O were carried out using Gaussian & Gaussian View. Similarly, using the wave function program Multiwfn to calculate the Mayer bond order. The analysis of the bond order curve during the reaction process can reveal the changes in the strength of chemical bonds and the situation of bond formation and breaking. Use the Shermo program to calculate the thermodynamic parameters of each stagnation point at different temperatures, including enthalpy, entropy, Gibbs free energy, and partition function. Finally, the KiSThelP program was used to calculate the reaction rate constants for each step of the reaction based on classical transition state theory at different temperatures. The results show that the relatively optimal path for the reaction between HCN and H₂ is as follows: three H₂ molecules are added in three steps on C≡N to obtain the product CH₄+NH₃; The relatively optimal path for the reaction between HCN and H₂O is as follows: H₂O molecules attack C atoms, and the H of O and C atoms are transferred to N atoms to obtain the product CO+NH₃. The first step of reaction between HCN and H₂ is R1→IM1 which is below 534 K with ΔG<0. After exceeding this temperature, ΔG>0 becomes a reverse spontaneous reaction. It can be considered that an increase in temperature is not conducive to the electrophilic addition reaction of the first H₂ on C≡N. The second step is IM1→IM2, with ΔG below 1103 K less than 0 and above greater than 0, indicates that the spontaneity of the second step H₂ addition reaction is inhibited as the temperature gradually increases. The third step is IM2→P1. Within the set temperature range, its ΔG is always less than 0, and the reaction can always proceed spontaneously. The ΔG of the first step reaction R2→IM5 in Path 3 is only less than 0 at room temperature, indicating that this step is difficult to occur spontaneously at high temperatures. Path 3 second step reaction IM5→IM6 ΔG is always less than 0 within the set temperature range. The third step of the reaction is IM6→P2, and the temperature of ΔG below 958 K is greater than 0, making it difficult to occur spontaneously. The research results on changes in pressure and free energy show that pressure can increase the upper temperature limit for spontaneous reaction.The reaction rates of HCN with H₂ and HCN with H₂O are relatively fast at high temperatures. The rate determining steps for Path 1 and Path 3 at high temperatures are R1 → IM1, R2 → IM5, respectively. The rate constants for the two reaction steps above 1473 K are 9.57×10⁻⁴ and 1.71 mol/(L·s), respectively. The pre-exponential factors for these two reactions were calculated to be 4.45×10⁹ and 4.68×10⁸ s⁻¹, and the activation energies were 357.62 and 239.30 kJ/mol, respectively.
- HCN /
- gas phase reaction /
- DFT /
- thermodynamics /
- kinetics

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图 1 HCN与H₂反应路径示意图

Figure 1 Reaction paths of HCN and H₂

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图 2 HCN与H₂反应过程中的Mayer键级-键长曲线（a）−（e）及不同路径的势能（f）

Figure 2 Mayer Bond order-bond length curve during the reaction between HCN and H₂ (a)−(e) and potential energy graphs for different pathways (f)

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图 3 HCN与H₂O反应路径示意图

Figure 3 Reaction paths of HCN and H₂O

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图 4 HCN与H₂O反应过程中的Mayer键级-键长曲线（a）−（e）及不同路径的势能（f）

Figure 4 Mayer Bond order-bond length curve during the reaction between HCN and H₂O (a)−(e) and potential energy graphs for different pathways (f)

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图 5 HCN与H₂、H₂O的各步反应的吉布斯自由能变△G随温度的变化

Figure 5 △G of HCN with H₂ and H₂O at different reaction steps as a function of temperature

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图 6 HCN与H₂/H₂O总反应在常压与7 MPa下的自由能随温度的变化

Figure 6 Temperature dependent free energy of the total reaction between HCN and H₂/H₂O at atmospheric pressure and 7 MPa

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表 1 HCN与H₂反应过程中优化后分子的Fukui函数等值面及各原子位点亲电反应CFF值

Table 1 Optimized Fukui function isosurfaces of molecules and CFF values of electrophilic reactions at various atomic sites during the HCN and H₂ reaction process

Species & Fukui function isosurface	Atomic number	$ {f}_{A}^{-} $
HCN	HCN-H HCN-C HCN-N	0.02536 0.38361 0.59106
IM1	IM1-C1 IM1-H2 IM1-N3 IM1-H4 IM1-H5	0.15909 0.05071 0.63940 0.07323 0.07745
IM2	IM2-C1 IM2-H2 IM2-N3 IM2-H4 IM2-H5 IM2-H6 IM2-H7	0.10057 0.01700 0.68701 0.05376 0.01703 0.05376 0.07087
IM3	IM3-C1 IM3-H2 IM3-N3 IM3-H4 IM3-H5	0.75997 0.08608 0.08908 0.04195 0.02294
:C; :N; :H; IM: intermediate.

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表 2 HCN与H₂反应路径中的反应物、重要的过渡态、中间体和产物的优化几何结构

Table 2 Optimized geometric structures of reactants, important transition states, intermediates, and products in the reaction pathway between HCN and H₂

Species	Structure parameter
Species	Bond length/Å	Bond angle/(°)	Dihedral angel/(°)
H₂	R(1,2) 0.7442
HCN	R(2,1) 1.0668 R(1,3) 1.1491	A(2,1,3) 180.0000
TS1	R(1,3) 1.0928 R(1,5) 1.5135 R(3,4) 1.3986 R(5,4) 1.1139 R(1,2) 1.0928	A(2,1,3) 144.6852 A(3,1,5) 116.0948 A(4,3,1) 55.5995 A(1,5,4) 53.2891	D(1,3,4,5) 0.0005 D(2,1,5,4) 179.9998
IM1	R(1,3) 1.2658 R(1,5) 1.0972 R(3,4) 1.0273 R(1,2) 1.0921	A(2,1,5) 115.9175 A(2,1,3) 118.7672 A(4,3,1) 110.5457	D(5,1,3,4) 0.0001 D(2,1,3,4) −180.0012
TS2	R(1,7) 1.5447 R(3,6) 1.4571 R(1,3) 1.3869 R(7,6) 1.0871	A(5,1,3) 123.5767 A(7,1,3) 110.5757 A(6,3,1) 52.7742 A(7,6,3) 142.4171	D(7,1,3,6) −1.4737 D(7,1,3,4) 88.6393 D(2,1,3,4) −168.0049 D(6,3,1,5) −110.7991
IM2	R(1,7) 1.1015 R(3,6) 1.0150 R(1,3) 1.4661 R(3,4) 1.0150	A(7,1,3) 115.5229 A(4,3,6) 106.2779 A(5,1,3) 109.2559 A(4,3,1) 110.0534	D(7,1,3,6) −58.4100 D(7,1,3,4) 58.3957 D(2,1,3,4) −179.9826 D(6,3,1,5) 179.9200
TS3	R(1,9) 2.0063 R(3,8) 1.0370 R(1,3) 2.0039 R(1,5) 1.0886 R(3,6) 1.0275	A(9,1,3) 68.9162 A(8,3,1) 89.2010 A(9,8,3) 120.3781 A(7,1,5) 113.7174 A(8,3,4) 107.7419	D(9,1,3,8) 14.9600 D(9,1,3,6) 138.9165 D(8,3,1,7) −53.7533 D(7,1,3,6) 69.3032 D(5,1,3,4) 84.2266
TS4	R(1,2) 1.1021 R(1,3) 1.3035 R(3,4) 1.2204 R(3,5) 1.2196 R(4,5) 1.0095	A(2,1,3) 117.8227 A(1,3,4) 109.7895 A(1,3,5) 109.8708 A(4,3,5) 48.8790	D(2,1,3,4) −21.0180 D(2,1,3,5) 26.1657
IM3	R(1,2) 1.1101 R(1,3) 1.3109 R(3,4) 1.0224 R(3,5) 1.0137	A(2,1,3) 105.8954 A(1.3,4) 126.8288 A(1,3,5) 119.4255 A(4,3,5) 110.3356	D(2,1,3,4) −0.0485 D(2,1,3,5) −179.9298
TS5	R(1,6) 1.2521 R(1,7) 1.8189 R(6,7) 0.9709 R(1,3) 1.3417	A(6,1,7) 30.2755 A(6,1,3) 120.3818 A(7,1,3) 110.7730 A(5,3,4) 115.1700	D(6,1,3,4) −110.0514 D(7,1,3,5) 87.9517 D(2,1,3,5) −176.3768 D(2,1,3,4) 17.5926
P1	R(1,7) 1.0919 R(3,4) 1.0150	A(4,3,6) 107.2535 A(2,1,5) 109.0833

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表 3 HCN与H₂O反应过程中优化后分子的Fukui函数等值面及各原子位点亲电反应CFF值

Table 3 Optimized Fukui function isosurfaces of molecules and CFF values of electrophilic reactions at various atomic sites during the HCN and H₂O reaction process

Species & Fukui function isosurface	Atomic number	$ {f}_{A}^{-} $
HCN	HCN-H HCN-C HCN-N	0.02536 0.38361 0.59106
IM5	IM5-O1 IM5-H2 IM5-H3 IM5-C4 IM5-H5 IM5-N6	0.18270 0.05485 0.01658 0.14178 0..02315 0..58080
IM6	IM6-O1 IM6-H2 IM6-H3 IM6-C4 IM6-H5 IM6-N6	0.57988 0.02032 0.02041 0.10906 0.05605 0.21426
IM7	IM7-O1 IM7-H2 IM7-H3 IM7-C4 IM7-H5 IM7-N6	0.15798 0.03530 0.02008 0.66425 0.01201 0.11044
:O; :C; :N; :H; IM: intermediate.

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表 4 HCN与H₂O反应路径中的反应物、重要的过渡态、中间体和产物的优化几何结构

Table 4 Optimized geometric structures of reactants, important transition states, intermediates, and products in the reaction pathway between HCN and H₂O

Species	Structure parameter
Species	Bond length/Å	Bond angle/(°)	Dihedral angel/(°)
>H₂O	R(1,2) 0.9619 R(1,3) 0.9619	A(2,1,3) 105.0645
HCN	R(2,1) 1.0668 R(1,3) 1.1491	A(2,1,3) 180.0000
TS8	R(4,1) 1.7315 R(5,2) 1.3527 R(1,2) 1.2767 R(4,6) 1.2022	A(5,4,6) 149.9711 A(3,1,2) 113.1294 A(5,4,1) 108.3661 A(4,6,2) 75.8243	D(3,1,4,6) 106.5879 D(5,4,1,2) 178.6648 D(1,4,6,2) −1.4199
IM5	R(3,1) 0.9638 R(1,4) 1.3656 R(4,6) 1.2569 R(6,2) 1.0226 R(5,4) 1.0910	A(3,1,4) 110.2408 A(5,4,6) 120.5837 A(4,6,2) 111.2873 A(1,4,6) 124.5519	D(3,1,4,6) −179.9530 D(5,4,6,2) 179.9971 D(3,1,4,5) 0.0067 D(1,4,6,2) −0.0454
TS9	R(3,6) 1.3419 R(1,4) 1.2799 R(6,4) 1.3009 R(1,3) 1.3343	A(1,4,5) 122.7112 A(1,4,6) 108.9032 A(3,6,2) 161.0386 A(3,6,4) 73.4046 A(2,6,4) 125.5567	D(5,4,6,3) −179.9966 D(2,6,4,1) 179.9304 D(3,1,4,6) 0.0146
IM6	R(3,6) 1.0084 R(1,4) 1.2094 R(6,4) 1.3608 R(2,6) 1.0058 R(4,5) 1.1078	A(1,4,6) 125.0723 A(5,4,6) 111.9086 A(2,6,3) 119.3349 A(3,6,4) 119.0869	D(5,4,6,2) 0.0109 D(1,4,6,3) −0.0085
TS10	R(4,6) 1.8572 R(1,4) 1.1567 R(5,6) 1.4147 R(2,6) 1.0179 R(3,6) 1.0188	A(1,4,6) 122.1969 A(4,6,3) 123.6470 A(2,6,3) 111.6923 A(5,6,2) 110.1399 A(5,6,3) 136.9573	D(2,6,4,1) −110.6570 D(5,4,6,3) −124.9287 D(1,4,6,3) 31.9173 D(2,6,4,5) 92.4970
P4	R(1,4) 1.1278 R(6,5) 1.0151 R(6,3) 1.0154 R(6,2) 1.0154	A(5,6,3) 107.0866 A(5,6,2) 106.8252 A(2,6,3) 107.0106
TS11	R(3,1) 0.9637 R(4,6) 1.3231 R(4,1) 1.3483 R(6,2) 1.0402 R(6,5) 1.2844	A(3,1,4) 107.9583 A(1,4,6) 115.9444 A(5,6,2) 131.5169 A(4,6,2) 113.6095 A(5,6,4) 58.3649	D(3,1,4,6) 179.9985 D(3,1,4,5) −108.0773 D(2,6,4,1) 5.83156 D(2,6,4,5) −125.4769
IM7	R(5,6) 1.0052 R(2,6) 1.0197 R(6,4) 1.3276 R(4,1) 1.3535 R(1,3) 0.9602	A(5,6,2) 118.1916 A(5,6,4) 119.0565 A(2,6,4) 122.7519 A(6,4,1) 107.0787 A(4,1,3) 106.4910	D(6,4,1,3) 179.9516 D(5,6,4,1) 179.9516 D(2,6,4,1) −0.0131
TS12	R(1,4) 1.2555 R(4,6) 1.6007 R(6,3) 1.3443 R(6,5) 1.0205 R(6,2) 1.0205	A(1,4,6) 94.9820 A(3,6,4) 69.2820 A(4,6,5) 112.7127 A(2,6,5) 108.0600 A(2,6,3) 123.4042	D(2,6,3,1) −104.1762 D(5,6,4,1) −118.6872 D(1,3,6,4) 0.0111

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表 5 HCN与H₂/H₂O热力学可行反应的焓变△H

Table 5 △H of thermodynamically feasible reactions between HCN and H₂/H₂O

Reaction	△H/(kJ·mol⁻¹)	T/K
R1→IM1	−57.83→−68.03→−65.18	298→1198→1998
IM1→IM2	−136.31→−141.34→−135.06	298→948→1998
IM2→P1	−84→−72.93	298→1998
HCN+3H₂→CH₄+NH₃	−278.15→−290.05→−273.18	298→948→1998
R2→IM5	−766.76→−769.23→−756	298→598→1998
IM5→IM6	−69.16→−68.94→−69.36	298→548→1998
IM6→P2	52.29→54.08→44.51	298→598→1998
HCN+H₂O→NH₃+CO	−783.63→−784.19→−780.86	298→748→1998

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表 6 HCN与H₂/H₂O热力学可行反应的熵变△S

Table 6 △S of thermodynamically feasible reactions between HCN and H₂/H₂O

Reaction	△S/(J·mol⁻¹·K⁻¹)	T/K
R1→IM1	−104.37→−124.84→123.16	298→1198→1998
IM1→IM2	−117.06→−128.18→124.18	298→948→1998
IM2→P1	−19.06→−8.06	298→1998
HCN+3H₂→CH₄+NH₃	−240.49→−266.16→−255.4	298→948→1998
R2→IM5	−136.74→−143.44→−133.73	298→648→1998
IM5→IM6	4.84→5.49→5.05	298→548→1998
IM6→P2	52.47→57.25→49.9	298→598→1998
HCN+H₂O→NH₃+CO	−79.42→−80.94→−78.78	298→748→1998

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表 7 HCN与H₂/H₂O各步反应速率常数

Table 7 Reaction rate constant of HCN and H₂/H₂O in Each Step

Reaction	k/(s⁻¹·M⁻¹)
Reaction	298 K	673 K	1073 K	1473 K	1873 K
R(HCN+3H₂)→IM1	1.03×10⁻⁵³	6.05×10⁻¹⁹	1.42×10⁻⁸	9.57×10⁻⁴	6.45×10⁻¹
IM1→IM2	4.31×10⁻⁴⁸	4.93×10⁻¹⁷	1.02×10⁻⁷	2.37×10⁻³	8.89×10⁻¹
IM2→P1	4.08×10⁻⁵⁶	9.26×10⁻²⁰	9.38×10⁻⁹	1.32×10⁻³	1.37
R(HCN+H₂O)→IM5	6.67×10⁻³⁴	7.17×10⁻¹¹	7.06×10⁻⁴	1.71	1.70×10²
IM5→IM6	1.45×10⁻¹¹	2.77×10²	2.60×10⁶	1.82×10⁸	2.16×10⁹
IM6→P4	3.24×10⁻⁴⁴	4.24×10⁻¹²	1.90×10⁻²	5.40×10²	2.00×10⁵

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表 8 HCN与H₂/H₂O各步反应的两参数阿伦尼乌斯方程

Table 8 The two parameter Arrhenius Equation for the reaction of HCN with H₂/H₂O in each step

Reaction	A/s⁻¹	E_a /( kJ·mol⁻¹)	Arrhenius equation	R²
R(HCN+3H₂)→IM1	4.45×10⁹	357.62	k=4.46×10⁹ e^{−43 011.61/T}	0.99997
IM1→IM2	5.09×10⁸	320.28	k=5.09×10⁸ e^{−38 520.66/T}	0.99994
IM2→P1	2.48×10¹⁰	375.89	k=2.48×10¹⁰ e^{−45 208.97/T}	0.99991
R(HCN+H₂O)→IM5	4.68×10⁸	239.30	k=4.68×10⁸ e^{−28781.05/T}	0.99977
IM5→IM6	1.25×10¹³	136.68	k=1.25×10¹³ e^−16679.3/T	0.99997
IM6→P4	2.67×10¹⁴	330.70	k=2.67×10¹⁴ e^{−39773.89/T}	0.99997

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