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基于路径积分分子动力学与热力学积分方法的高压氢自由能计算

陈基 冯页新 李新征 王恩哥

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基于路径积分分子动力学与热力学积分方法的高压氢自由能计算

陈基, 冯页新, 李新征, 王恩哥

A fully quantum description of the free-energy in high pressure hydrogen

Chen Ji, Feng Ye-Xin, Li Xin-Zheng, Wang En-Ge
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  • 在相图研究中, 严格计算一个真实系统在特定温度、压强下的自由能是近年来该领域理论方法发展的前沿. 自Mermin提出有限温度密度泛函理论后, 在电子结构层面, 弱关联系统中人们就其在对自由能贡献的描述已相对完善, 但在原子核运动的描述上, 热运动与量子运动的非简谐项却总被忽视. 本文将路径积分分子动力学与热力学积分结合, 对300 GPa下氢晶体Cmca 结构中原子核热涨落与量子涨落对自由能的影响进行了分析. 发现在100 K核量子涨落非简谐项的贡献约为15 meV每原子, 远大于不同结构间静态焓的差别. 该研究提醒人们简谐近似在核量子效应描述中可能存在的不准确性(即使在低温下). 同时, 我们采取的方法 也为人们进行自由能的准确计算提供了一个简单有效的手段.
    Hydrogen is the lightest and most abundant element in the universe. Ever since Wigner and Huntington's prediction that pressure induced metallization might happen in solid hydrogen, understanding the hydrogen phase diagram has become one of the greatest challenges in condensed matter and high pressure physics. The light mass of hydrogen means that the nuclear quantum effects could be important in describing this phase diagram under high pressures. Numerical evaluations of their contributions to the structural, vibrational, and energetic properties, however, are difficult and up to now most of the theoretical simulations still remain classical. This is particularly true for the energetic properties. When the free-energies of different phases are compared in determining the ground state structure of the system at a given pressure and temperature, most of the theoretical simulations remain classical. When nuclear quantum effects must be taken into account, one often resorts to the harmonic approximation. In the very rare case, the anharmonic contributions from the nuclear statistical effects are considered by using a combination of the thermodynamic integration and the at initio molecular dynamics methods, which helps to include the classical nuclear anharmonic effects. Quantum nuclear anharmonic effects, however, are completely untouched. Here, using a self-developed combination of the thermodynamic integration and the at initio path-integral molecular dynamics methods, we calculated the free-energies of the high pressure hydrogen at 100 K from 200 GPa to 300 GPa. The harmonic lattice was taken as the reference and the Cmca phase of the solid hydrogen was chosen. When the bead number of the path-integral (P) equals one, our approach reaches the so-called classical limit. Upon increasing P until the results are converged, our approach reaches the limit when both classical and quantum nuclear anharmonic effects are included. Therefore, by comparing the free-energy of the harmonic lattice and the thermodynamic integration results at P equals one, we isolate the classical nuclear anharmonic effects. By comparing the thermodynamic integration results at P equals one and with those when they are converged with respect to P, we isolate the quantum nuclear anharmonic effects in a very clean manner. Our calculations show that the classical nuclear anharmonic contributions to the free-energy are negligible at this low temperature. Those contributions from the quantum nuclear anharmonic effects, however, are as large as ~15 meV per atom. This value also increases with pressure. This study presents an algorithm to quantitatively calculate the quantum contribution of the nuclear motion to free-energy beyond the often used harmonic approximation. The large numbers we got obtained also indicate that such quantum nuclear anharmonic effects are important in describing the phase diagram of hydrogen, at/above the pressures studied.
      通信作者: 李新征, xzli@pku.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11422431, 11275008, 11274012, 91021007)和中国博士后科学基金(批准号: 2014M550005)资助的课题.
      Corresponding author: Li Xin-Zheng, xzli@pku.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11422431, 11275008, 11274012, 91021007), and the National Postdoc Research Foundation of China (Grant No. 2014M550005).
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    Xu G, Ming W, Yao Y, Dai X, Zhang S C, Fang Z 2008 EPL 82 67002

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    Lee P A, Nagaosa N, Wen X G 2006 Rev. Mod. Phys. 78 17

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    Pickard C J, Needs R J 2007 Nat. Phys. 3 473

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    Frenkel D, Lekkerkerker H N W, Stroobants A 1988 Nature 332 822

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    Meijer E J, Frenkel D 1991 J. Chem. Phys. 94 2269

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    Alfé D, Gillan M J, Price G D 1999 Nature 401 462

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    Alfé D, Price G D, Gillan M J 2001 Phys. Rev. B 64 045123

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    Wigner E, Huntington H B 1935 J. Chem. Phys. 3 764

    [13]

    Babaev E, Sudbo A, Ashcroft N W 2004 Nature 431 666

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    Bonev S A, Schwegler E, Ogitsu T, Galli G 2004 Nature 431 669

    [15]

    Deemyad S, Silvera I F 2008 Phys. Rev. Lett. 100 155701

    [16]

    Li X Z, Walker B, Probert M I J, Pickard C J, Needs R J, Michaelides A 2013 J. Phys.: Condens. Matter 25 085402

    [17]

    Chen J, Li X Z, Zhang Q F, Probert M I J, Pickard C J, Needs R J, Michaelides A, Wang E G 2013 Nat. Commun. 4 2064

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    Mao H K, Hemley R J 1994 Rev. Mod. Phys. 66 671

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    McMahon J M, Morales M A, Pierleoni C, Ceperley D M 2012 Rev. Mod. Phys. 84 1607

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    Zha C S, Liu Z X, Hemley R J 2012 Phys. Rev. Lett. 108 146402

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    Perez A, von Lilienfeld O A 2011 J. Chem. Theory Comput. 7 2358

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    Habershon S, Manolopoulos D E 2011 J. Chem. Phys. 135 224111

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    Feng Y X, Chen J, Alfè D, Li X Z, Wang E G 2015 J. Chem. Phys. 142 064506

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    Alfé D 2009 Comput. Phys. Commun. 180 2622

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

  • [1]

    Mermin N D 1985 Phys. Rev. A 137 1441

    [2]

    Gillan M J 1989 J. Phys.: Condens. Matter 1 689

    [3]

    Wentzcovitch R M, Martins J L, Allen P B 1992 Phys. Rev. B 45 11372

    [4]

    Xu G, Ming W, Yao Y, Dai X, Zhang S C, Fang Z 2008 EPL 82 67002

    [5]

    Lee P A, Nagaosa N, Wen X G 2006 Rev. Mod. Phys. 78 17

    [6]

    Pickard C J, Needs R J 2007 Nat. Phys. 3 473

    [7]

    Li X Z, Wang E G 2014 Computer Simulations of Molecules and Condensed Matters: From Electronic Structures to Molecular Dynamics (Beijing: Peking University Press) pp134-140

    [8]

    Frenkel D, Lekkerkerker H N W, Stroobants A 1988 Nature 332 822

    [9]

    Meijer E J, Frenkel D 1991 J. Chem. Phys. 94 2269

    [10]

    Alfé D, Gillan M J, Price G D 1999 Nature 401 462

    [11]

    Alfé D, Price G D, Gillan M J 2001 Phys. Rev. B 64 045123

    [12]

    Wigner E, Huntington H B 1935 J. Chem. Phys. 3 764

    [13]

    Babaev E, Sudbo A, Ashcroft N W 2004 Nature 431 666

    [14]

    Bonev S A, Schwegler E, Ogitsu T, Galli G 2004 Nature 431 669

    [15]

    Deemyad S, Silvera I F 2008 Phys. Rev. Lett. 100 155701

    [16]

    Li X Z, Walker B, Probert M I J, Pickard C J, Needs R J, Michaelides A 2013 J. Phys.: Condens. Matter 25 085402

    [17]

    Chen J, Li X Z, Zhang Q F, Probert M I J, Pickard C J, Needs R J, Michaelides A, Wang E G 2013 Nat. Commun. 4 2064

    [18]

    Mao H K, Hemley R J 1994 Rev. Mod. Phys. 66 671

    [19]

    McMahon J M, Morales M A, Pierleoni C, Ceperley D M 2012 Rev. Mod. Phys. 84 1607

    [20]

    Zha C S, Liu Z X, Hemley R J 2012 Phys. Rev. Lett. 108 146402

    [21]

    Liu H Y, Zhu L, Cui W W, Ma Y M 2012 J. Chem. Phys. 137 074501

    [22]

    Perez A, von Lilienfeld O A 2011 J. Chem. Theory Comput. 7 2358

    [23]

    Habershon S, Manolopoulos D E 2011 J. Chem. Phys. 135 224111

    [24]

    Kresse G, Furthmller J 1996 Phys. Rev. B 54 11169

    [25]

    Feng Y X, Chen J, Alfè D, Li X Z, Wang E G 2015 J. Chem. Phys. 142 064506

    [26]

    Alfé D 2009 Comput. Phys. Commun. 180 2622

    [27]

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

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出版历程
  • 收稿日期:  2015-05-15
  • 修回日期:  2015-06-29
  • 刊出日期:  2015-09-05

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