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N型甲烷水合物结构和电子性质的密度泛函理论计算

罗强 杨恒 郭平 赵建飞

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N型甲烷水合物结构和电子性质的密度泛函理论计算

罗强, 杨恒, 郭平, 赵建飞

Density functional theory calculation of structure and electronic properties in N-methane hydrate

Luo Qiang, Yang Heng, Guo Ping, Zhao Jian-Fei
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  • 基于密度泛函理论的第一性原理方法, 在广义梯度近似下考虑Grimme色散修正, 预测并研究N型甲烷水合物结构和电子性质, 得到如下结论: 1) N型甲烷水合物的水笼子整体结构为截角八面体(4668), 由8个正六边形和6个正方形构成, 其中六边形的平均边长和正方形的平均边长约为2.723Å, 对称群为$IM\bar 3M$, 具有简单和严格的周期性稳定结构; 2) N型甲烷水合物晶格参数为7.700Å, 密度为0.903 g/cm3, 大于I型、II型及H型水合物密度; 3) 计算并得到了N型甲烷水合物XRD衍射图, 其与I型甲烷水合物结构较为接近, 前者水笼子大, 甲烷分子与水笼子相互作用力为范德瓦耳斯力; 4) N型甲烷水合物密度为形成能为–0.247 eV, 易于形成, 电子态密度及分波态密度也均表明了甲烷与N型水笼子相互作用微弱, 靠分子力作用; 5) N型甲烷水合物为绝缘体材料, 能隙大于5 eV.
    As a clean and efficient unconventional energy source, natural gas hydrate has been highly valued and vigorously developed by many countries in recent years. In order to solve the problem that the existing hydrate structure symmetry is not high, which leads the theoretical research to be restricted, it is imperative to explore a new type of methane hydrate structure with high symmetry. Using the first-principles method which is based on the density functional theory (DFT), the structure and electronic properties of N-methane hydrate are calculated in the generalized gradient approximation (GGA) for Grimme dispersion correction. The obtained results are shown below. 1) The water cage structure of N-methane hydrate is a truncated octahedron (4668), which is composed of 8 regular hexagons and 6 squares, and the average length of the hexagons and the average length of the squares are both 2.723 Å. The average bond length of water molecules is optimized to be 1.056 Å, and the average bond angle of water molecules is 107.738°. The average bond length of methane molecules is 1.0973 Å. The average distance from methane molecules to water molecules is 4.2831 Å that is longer than the distance in the I- methane hydrate. So N-methane hydrate can accommodate larger volumes of gas molecules. The symmetric group is ${\rm{IM}}\bar 3{\rm{M}}$ for N-methane hydrate, which has a simple and strict periodic stable structure. 2) The lattice parameter of N-methane hydrate is 7.70 Å, and the density is 0.903 g/cm3, which is greater than I-, II- and H-type hydrate density. 3) The x-ray diffraction(XRD) pattern of N-methane hydrateis calculated and is close to that of of I-methane hydrate, while the water cage of N-methane hydrate is larger. 4) The interaction between methane molecules and the water cage is van der Waals force, and the formation energy of N- methane hydrate is –0.247 eV, which indicates that the N-methane hydrate is easy to form. Both the density of states and partial density of states indicate that the interaction between methane and water cage is weak, and it relies on molecular force. 5) In addition, N-methane hydrate is an insulator material with the energy gap greater than 5 eV.
      通信作者: 罗强, luoqiang@swpu.edu.cn ; 郭平, guopingswpi@vip.sina.com
    • 基金项目: 国家自然科学基金(批准号: 51875091, 61701455)和四川省科技计划(批准号: 2018JY0174)资助的课题.
      Corresponding author: Luo Qiang, luoqiang@swpu.edu.cn ; Guo Ping, guopingswpi@vip.sina.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos.51875091,61701455) and the Science and Technology Project of Sichuan Province, China (Grant No.2018JY0174).
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    Max M, Lowrie A 1996 J. Petrol. Geol. 19 41Google Scholar

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    Collett T S 2002 AAPG Bull. 86 1971

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    Kvamme B, Kuznetsova T, Sapate A, Qorbani K 2016 J. Nat. Gas Sci. Eng. 35 1594Google Scholar

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    Khlebnikov V, Antonov S, Mishin A, Bakulin D, Khamidullina I, Liang M, Vinokurov V, Gushchin P A 2016 Nat. Gas Ind. 36 40Google Scholar

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    Castellani B, Rossetti G, Tupsakhare S, Rossi F, Nicolini A, Castaldi M 2016 J. Petrol. Sci. Eng. 147 515Google Scholar

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    Michael K, Roland B, Edward B, Lewis R N 2004 J. Am. Chem. Soc. 126 9407Google Scholar

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    Xu C G, Cai J, Lin F H, Chen Z Y, Li X S 2015 Energy 79 111Google Scholar

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    Naeiji P, Varaminian F, Rahmati M 2017 J. Nat. Gas Sci. Eng. 44 122Google Scholar

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    朱金龙, 赵予生, 靳常青 2019 物理学报 68 018203

    Zhu J L, Zhao Y S, Jin C Q 2019 Acta Phys. Sin. 68 018203

    [15]

    Choudhary N, Kushwaha O S, Bhattacharjee G, Chakrabarty S, Kumara R 2017 Energt Procedia 105 5026Google Scholar

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    Alavi S, Ohmura R 2016 J. Chem. Phys. 145 154708Google Scholar

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    Huang Y, Yuan L, Su Y, Zhao J 2015 Mol. Simul. 41 1086Google Scholar

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    Nguyen A H, Molinero V 2014 J. Chem. Phys. 140 3440

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    Yagasaki T, Matsumoto M, Andoh Y, Okazaki S, Tanaka H 2014 J. Phys. Chem. B 118 11797

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    Druart M L, Michel L, Van D H 2014 Fluid Phase Equilib. 381 108Google Scholar

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    耿春宇, 丁丽颖, 韩清珍, 温浩 2008 物理化学学报 24 595Google Scholar

    Geng C Y, Ding L Y, Han Q Z, Wen H 2008 Acta Phys. Chim. Sin. 24 595Google Scholar

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    Lasich M, Ramjugernath D 2016 Philos. Mag. 96 15Google Scholar

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    Zong X, Cheng G, Qiu N, Huang Q, He J, Du S, Li Y 2017 Chem. Lett. 46 1141Google Scholar

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    Liu Y, Ojamäe L 2014 J. Phys. Chem. A 118 51

    [25]

    Zhang X, Qiu N, Huang Q, Zha X, He J, Li Y, Du S 2017 J. Mol. Struct. 1153 292

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    Waldron C J, English N J 2017 J. Chem. Phys. 147 024506Google Scholar

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    Zquierdo-Ruiz F, Otero-de-la-Roza A, Contreras-García J, Menéndez B, Recio J M 2015 High Pressure Res. 35 49Google Scholar

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    Liu C, Zhang Z, Guo G J 2016 RSC Adv. 6 106443Google Scholar

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    Tang L, Shi R, Su Y, Zhao J 2015 J. Phys. Chem. A 119 10971Google Scholar

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    郑朝阳, 赵纪军 2012 物理化学学报 28 1809Google Scholar

    Zheng C Y, Zhao J J 2012 Acta Phys. Chim. Sin. 28 1809Google Scholar

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    Huang Y, Zhu C, Wang L, Cao X, Su Y, Jiang X, Meng S, Zhao J, Zeng X C 2016 Sci. Adv. 2 e1501010Google Scholar

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    曹潇潇 2016 博士学位论文(大连: 大连理工大学)

    Cao X X 2016 Ph. D. Dissertation (Dalian: Dalian University of Technology University) (in Chinese)

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    曹潇潇, 苏艳, 赵纪军, 刘昌岭, 周潘旺 2014 物理化学学报 30 1437Google Scholar

    Cao X X, Su Y, Zhao J J, Liu C L, Zhou D W 2014 Acta Phys. Chim. Sin. 30 1437Google Scholar

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    Nityananda R, Hohenberg P, Kohn W 2017 Resonance 22 809Google Scholar

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    Kohn W, Sham L J 1965 Phys. Rev. 140 1133Google Scholar

    [36]

    Huang Y Y, Zhu C Q, Wang L 2017 Chem. Phys. Lett. 2017 186Google Scholar

    [37]

    Blöchl E 1994 Phys. Rev. B 50 17953Google Scholar

    [38]

    Kresse G, Joubert D 1999 Phys. Rev. B 59 1758

    [39]

    罗强, 唐斌, 张智, 冉曾令 2013 物理学报 62 077101Google Scholar

    Luo Q, Tang B, Zhang Z, Ran Z L 2013 Acta Phys. Sin. 62 077101Google Scholar

    [40]

    Wang Z H, Li Y, Meng W J, Guo P, Luo Q, Ran Z L 2017 Appl. Ecol. Environ. Res. 15 861Google Scholar

    [41]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [42]

    Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188Google Scholar

    [43]

    Broyden C G 1970 J. Inst. Math. Applic. 6 76Google Scholar

    [44]

    Fletcher R 1970 Comput. J. 13 317Google Scholar

    [45]

    Goldfarb D 1970 Math. Comput. 24 23Google Scholar

    [46]

    Shanno D F 1970 Math. Comput. 24 647Google Scholar

    [47]

    Guo P, Qiu Y L, Li L L, Luo Q, Zhao J F, Pan Y K 2018 Chin. Phys. B 27 276

    [48]

    丁家祥, 史伶俐, 申小冬, 梁德青 2017 化工学报 68 4802

    Ding J X, Shi L L, Sheng X D, Liang D Q 2017 J. Chem. Ind. Eng. 68 4802

  • 图 1  模型示意图 (a) N型甲烷水合物骨架模型; (b) 优化后的结构

    Fig. 1.  Model diagram: (a) N-methane hydrate skeleton model; (b) optimized structure of N-methane hydrate.

    图 2  N型甲烷水合物结构X射线衍射图

    Fig. 2.  X-ray diffraction of N- methane hydrate structure.

    图 3  甲烷分子态密度和分波态密度

    Fig. 3.  Density of states and partial density of states in methane molecules.

    图 4  水笼子的态密度及分波态密度

    Fig. 4.  Density of state and partial density of state in water cage.

    图 5  能带结构

    Fig. 5.  Energy band structures.

    表 1  平均晶格参数

    Table 1.  Average lattice parameters.

    晶格参数GGA原始值I型甲烷水合物[47]
    六边形边长/Å2.72312.68042.7152
    四边形边长/Å2.72332.7656/
    水分子键长/Å1.00560.9940.993
    水分子键角/(°)107.738109.406106.629
    甲烷分子键长/Å1.09731.11781.0917
    甲烷分子键角/(°)109.471109.454109.471
    甲烷分子到水分子距离/Å4.28314.2783.78115
    氢键键长/Å1.72931.70251.7128
    下载: 导出CSV

    表 2  GGA近似下的形成能

    Table 2.  Formation energy of GGA approximation

    能量GGAI型甲烷水合物[47]
    Eform/eV–0.247–0.581
    Etotal/eV–6074.782–21186.729
    Ecage/eV–5634.720–20976.902
    ECH4/eV–219.784–209.246
    下载: 导出CSV
  • [1]

    Holder G, Kamath V, Godbole S 1984 Annu. Rev. Energy 9 427

    [2]

    Max M, Lowrie A 1996 J. Petrol. Geol. 19 41Google Scholar

    [3]

    Collett T S 2002 AAPG Bull. 86 1971

    [4]

    Kvamme B, Kuznetsova T, Sapate A, Qorbani K 2016 J. Nat. Gas Sci. Eng. 35 1594Google Scholar

    [5]

    Zhao J, Chen X, Song Y, Zhu Z, Yang L, Tian Y, Wang J, Yang M, Zhang Y 2014 Energy Procedia 61 75Google Scholar

    [6]

    Khlebnikov V, Antonov S, Mishin A, Bakulin D, Khamidullina I, 梁萌, Vinokurov V, Gushchin P A 2016 天然气工业 36 40Google Scholar

    Khlebnikov V, Antonov S, Mishin A, Bakulin D, Khamidullina I, Liang M, Vinokurov V, Gushchin P A 2016 Nat. Gas Ind. 36 40Google Scholar

    [7]

    Lim D, Ro H, Seo Y, Seo Y, Lee J, Kim S, Lee J , Lee H 2017 J. Chem. Thermodyn. 106 16Google Scholar

    [8]

    Partoon B, Nashed O, Kassim Z, Sabil K, Sangwai J, Lal B 2016 Process Eng. 148 1220

    [9]

    Zhang L X, Yang L, Wang J Q, Zhao J F, Dong H S, Yang M J, Liu Y, Song Y C 2017 Chem. Eng. J. 308 40Google Scholar

    [10]

    Castellani B, Rossetti G, Tupsakhare S, Rossi F, Nicolini A, Castaldi M 2016 J. Petrol. Sci. Eng. 147 515Google Scholar

    [11]

    Michael K, Roland B, Edward B, Lewis R N 2004 J. Am. Chem. Soc. 126 9407Google Scholar

    [12]

    Xu C G, Cai J, Lin F H, Chen Z Y, Li X S 2015 Energy 79 111Google Scholar

    [13]

    Naeiji P, Varaminian F, Rahmati M 2017 J. Nat. Gas Sci. Eng. 44 122Google Scholar

    [14]

    朱金龙, 赵予生, 靳常青 2019 物理学报 68 018203

    Zhu J L, Zhao Y S, Jin C Q 2019 Acta Phys. Sin. 68 018203

    [15]

    Choudhary N, Kushwaha O S, Bhattacharjee G, Chakrabarty S, Kumara R 2017 Energt Procedia 105 5026Google Scholar

    [16]

    Alavi S, Ohmura R 2016 J. Chem. Phys. 145 154708Google Scholar

    [17]

    Huang Y, Yuan L, Su Y, Zhao J 2015 Mol. Simul. 41 1086Google Scholar

    [18]

    Nguyen A H, Molinero V 2014 J. Chem. Phys. 140 3440

    [19]

    Yagasaki T, Matsumoto M, Andoh Y, Okazaki S, Tanaka H 2014 J. Phys. Chem. B 118 11797

    [20]

    Druart M L, Michel L, Van D H 2014 Fluid Phase Equilib. 381 108Google Scholar

    [21]

    耿春宇, 丁丽颖, 韩清珍, 温浩 2008 物理化学学报 24 595Google Scholar

    Geng C Y, Ding L Y, Han Q Z, Wen H 2008 Acta Phys. Chim. Sin. 24 595Google Scholar

    [22]

    Lasich M, Ramjugernath D 2016 Philos. Mag. 96 15Google Scholar

    [23]

    Zong X, Cheng G, Qiu N, Huang Q, He J, Du S, Li Y 2017 Chem. Lett. 46 1141Google Scholar

    [24]

    Liu Y, Ojamäe L 2014 J. Phys. Chem. A 118 51

    [25]

    Zhang X, Qiu N, Huang Q, Zha X, He J, Li Y, Du S 2017 J. Mol. Struct. 1153 292

    [26]

    Waldron C J, English N J 2017 J. Chem. Phys. 147 024506Google Scholar

    [27]

    Zquierdo-Ruiz F, Otero-de-la-Roza A, Contreras-García J, Menéndez B, Recio J M 2015 High Pressure Res. 35 49Google Scholar

    [28]

    Liu C, Zhang Z, Guo G J 2016 RSC Adv. 6 106443Google Scholar

    [29]

    Tang L, Shi R, Su Y, Zhao J 2015 J. Phys. Chem. A 119 10971Google Scholar

    [30]

    郑朝阳, 赵纪军 2012 物理化学学报 28 1809Google Scholar

    Zheng C Y, Zhao J J 2012 Acta Phys. Chim. Sin. 28 1809Google Scholar

    [31]

    Huang Y, Zhu C, Wang L, Cao X, Su Y, Jiang X, Meng S, Zhao J, Zeng X C 2016 Sci. Adv. 2 e1501010Google Scholar

    [32]

    曹潇潇 2016 博士学位论文(大连: 大连理工大学)

    Cao X X 2016 Ph. D. Dissertation (Dalian: Dalian University of Technology University) (in Chinese)

    [33]

    曹潇潇, 苏艳, 赵纪军, 刘昌岭, 周潘旺 2014 物理化学学报 30 1437Google Scholar

    Cao X X, Su Y, Zhao J J, Liu C L, Zhou D W 2014 Acta Phys. Chim. Sin. 30 1437Google Scholar

    [34]

    Nityananda R, Hohenberg P, Kohn W 2017 Resonance 22 809Google Scholar

    [35]

    Kohn W, Sham L J 1965 Phys. Rev. 140 1133Google Scholar

    [36]

    Huang Y Y, Zhu C Q, Wang L 2017 Chem. Phys. Lett. 2017 186Google Scholar

    [37]

    Blöchl E 1994 Phys. Rev. B 50 17953Google Scholar

    [38]

    Kresse G, Joubert D 1999 Phys. Rev. B 59 1758

    [39]

    罗强, 唐斌, 张智, 冉曾令 2013 物理学报 62 077101Google Scholar

    Luo Q, Tang B, Zhang Z, Ran Z L 2013 Acta Phys. Sin. 62 077101Google Scholar

    [40]

    Wang Z H, Li Y, Meng W J, Guo P, Luo Q, Ran Z L 2017 Appl. Ecol. Environ. Res. 15 861Google Scholar

    [41]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [42]

    Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188Google Scholar

    [43]

    Broyden C G 1970 J. Inst. Math. Applic. 6 76Google Scholar

    [44]

    Fletcher R 1970 Comput. J. 13 317Google Scholar

    [45]

    Goldfarb D 1970 Math. Comput. 24 23Google Scholar

    [46]

    Shanno D F 1970 Math. Comput. 24 647Google Scholar

    [47]

    Guo P, Qiu Y L, Li L L, Luo Q, Zhao J F, Pan Y K 2018 Chin. Phys. B 27 276

    [48]

    丁家祥, 史伶俐, 申小冬, 梁德青 2017 化工学报 68 4802

    Ding J X, Shi L L, Sheng X D, Liang D Q 2017 J. Chem. Ind. Eng. 68 4802

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出版历程
  • 收稿日期:  2018-12-19
  • 修回日期:  2019-05-14
  • 上网日期:  2019-08-01
  • 刊出日期:  2019-08-20

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