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共振价键波函数在高压液氢量子蒙卡模拟中的适用性研究

李名锐 周刚 初哲 戴湘晖 吴海军 范如玉

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共振价键波函数在高压液氢量子蒙卡模拟中的适用性研究

李名锐, 周刚, 初哲, 戴湘晖, 吴海军, 范如玉

Applicability of resonating valence bond wave function with quantum Monte Carlo method for modeling high pressure liquid hydrogen

Li Ming-Rui, Zhou Gang, Chu Zhe, Dai Xiang-Hui, Wu Hai-Jun, Fan Ru-Yu
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  • 在共振价键理论基础上, 选取高压液氢电子主要占据轨道的线性组合作为基组, 构建由Jastrow项和反对称孪生函数乘积项 (AGP) 组成的波函数. 考虑电子关联作用的共振价键 (RVB) 波函数得出的能量值低于LDA能量值; 当满足rs1.75或T 15000 K时引入backflow项以改善波函数结点面, 改善后的能量值下降约1 mHa/atom, 能量方差值变小. 将构建的RVB波函数与电子-离子耦合的蒙特卡罗法 (CEIMC) 相结合, 计算结果与实验及其他ab-initio结果相符合, 获得的液氘单次冲击Hugoniot曲线基本通过所有加载类型实验误差棒, 液氘在50.3 GPa处具有最大压缩率4.48, 在100120 GPa内未发现压缩率有急剧增大的现象. 构建的RVB 波函数能够适用于较宽密度与温度范围内(1.0 rs2.2, 2800 K T60000 K)液氢的模拟, 与CEIMC法相结合可提高液氢冲击特性的模拟精度.
    Based on the resonating valence bond theory, the linear combinations of the main orbits occupied by liquid hydrogen electrons are selected as the basis sets to construct the Jastrow antisymmetrized geminal product. The resonating valence bond (RVB) wave function which takes into consideration electron correlation effects provides lower energy than the local density approximation (LDA) function. In order to improve the nodal accuracy of the variational trial wave function, the backflow correlations are suggested to be employed whenever rs1.75 or T 15000 K, the improved wave function has about 1 mHa/atom decrease in local energy with respect to the one without backflow effects at the VMC level, and has a lower variance simultaneity. After combining the coupled electron-ion Monte Carlo (CEIMC) method with the RVB wave function, the simulation results we have obtained are in good agreement with the experimental and other ab-initio ones; the deuterium principal Hugoniot curve passing through the error bars of various existing experiments conducted via different high-pressure technologies has a maximum compression of 4.48 at about 50.3GPa, but the phenomenon of apparent increase in compression ratio along the Hugoniot between 100120 GPa has not been found. The RVB wave function discussed in this paper when adopted the CEIMC method is not only quite suitable for the simulation of liquid hydrogen within a wide range of density and temperature (1.0 rs2.2, 2800 K T60000 K), but also can give some more applicable thermodynamic properties of hydrogen under shock loading.
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    Kwon Y, Ceperley D M, Martin R M 1994 Phys. Rev. B 50 1684

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    Holzmann M, Ceperley D M, Pierleoni C, Esler K 2003 Phys. Rev. E 68 046707

    [52]

    Silvera I, Goldman V 1978 J. Chem. Phys. 69 4209

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    [54]

    Dewing M D 2000 Ph.D. Dissertation (USA: University of Illinois at Urbana-Champaign)

    [55]

    Lin C, Zong F H, Ceperley D M 2001 Phys. Rev. E 64 016702

    [56]

    Holmes N C, Ross M, Nellis W J 1995 Phys. Rev. B 52 15835

    [57]

    Nellis W J, Mitchell A C, Theil M, Devine G. J, Trainor R J, Brown N 1983 J. Chem. Phys. 79 1480

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    Lenosky T J, Kress J D, Collins L A 1997 Phys. Rev. B 56 5164

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    Magro W R, Ceperley D M, Pierleoni C, Bernu B 1996 Phys. Rev. Lett. 76 1240

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  • [1]

    Nellis W J, Ross M, Holmes N C 1995 Science 269 1249

    [2]

    Van Horn H M 1991 Science 252 384

    [3]

    Silvera I 2010 PNAS 107 12743

    [4]

    Weir S T, Mitchell A C, Nellis W J 1996 Phy. Rev. Lett. 76 1860

    [5]

    Da Silva L B, Celliers P, Collins G W, Budil K S, Holmes N C, Barbee T W, Hammel B A, Kilkenny J D, Wallace R J, Ross M, Cauble R, Ng A, Chiu G 1997 Phys. Rev. Let. 78 483

    [6]

    Collins G W, Da Silva L B, Celliers P, Gold D M, Foord M E, Wallace R J, Ng A, Weber S V, Budil K S, Cauble R 1998 Science 281 1178

    [7]

    Collins G W, Celliers P, Da Silva L B, Cauble R, Gold D, Foord M, Budil K S, Stewart R, Holmes N C, Ross M 1998 Phys. Plasmas 5 1864

    [8]

    Hicks D, Boehly T, Celliers P, Eggert J, Moon S, Meyerhofer D, Collins G 2009 Phys. Rev. B 79 014112

    [9]

    Knudson M D, Hanson D L, Bailey J E, Hall C A, Asay J R, Anderson W W 2001 Phys. Rev. Lett. 87 225501

    [10]

    Knudson M D, Hanson D L, Bailey J E, Hall C A, Asay J R, Deeney C 2004 Phys. Rev. B 69 144209

    [11]

    Belov S I, Boriskov G V, Bykov A I, Ilkaev R I, Lukyanov N B, Matveev A Y, Mikhailova O L, Selemir V D, Simakov G V, Trunin R F, Trusov I P, Urlin V D, Fortov V E, Shuikin A N 2002 JETP Lett. 76 433

    [12]

    Boriskov G V, Bykov A I, Ilkaev R I, Selemir V D, Simakov G V, Trunin R F, Urlin V D, Fortov V E, Shuikin A N 2003 Dokl. Phys. 48 553

    [13]

    Boriskov G V, Bykov A I, Ilkaev R I, Selemir V D, Simakov G V, Trunin R F, Urlin V D, Shuikin A N, Nellis W J 2005 Phys. Rev. B 71 092104

    [14]

    Grishechkin S K, Gruzdev S K, Gryaznov V K, Zhernokletov M V, Ilkaev R I, Iosilevskii I L, Kashintseva G N, Kirshanov S I, Manachkin S F, Mintsev V B, Mikhailov A L, Mezhevov A B, Mochalov M A, Fortov V E, Khrustalev V V, Shuikin A N, Yukhimchuk A A 2004 JETP Lett. 80 398

    [15]

    Kerley G I 1972 Phys. Earth planet. Interiors 6 78

    [16]

    Ross M 1998 Phys. Rev. B 58 669

    [17]

    Saumon D, Chabrier G 1992 Phys. Rev. A 46 2084

    [18]

    Chen Q F, Cai L C, Jing F Q, Chen D Q 1999 Acta. Phys. Sin. 48 0485 (in Chinese) [陈其峰, 蔡灵仓, 经福谦, 陈栋泉 1999 物理学报 48 0485] Gu Y J, Zheng J, Chen Z Y, Chen Q F, Cai L C 2010 Acta. Phys. Sin. 59 4508 (in Chinese) [顾云军, 郑军, 陈志云, 陈其峰, 蔡灵仓 2010 物理学报 59 4508]

    [19]

    Rogers F J 2001 Contrib. Plasma Phys. 41 179

    [20]

    Car R, Parrinello M 1985 Phys. Rev. Lett. 55 2471

    [21]

    Scandolo S 2003 PNAS 100 3051

    [22]

    Lenosky T J, Bickham S R, Kress J D, Collins L A 2000 Phys. Rev. B 61 1

    [23]

    Collins L A, Bickham S R, Kress J D, Mazevet S, Lenosky T J, Troullier N J, Windl W 2001 Phys. Rev. B 63 184110

    [24]

    Desjarlais M P 2003 Phys. Rev. B 68 064204

    [25]

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

    [26]

    Bonev S A, Militzer B, Galli G 2004 Phys. Rev. B 69 014101

    [27]

    Vorberger J, Tamblyn I, Militzer B, Bonev S A 2007 Phys. Rev. B 75 024206

    [28]

    Holst B, Redmer R, Desjarlais M P 2008 Phys. Rev. B 77 184201

    [29]

    Johnson K A, Ashcroft N W 2000 Nature 403 632

    [30]

    Militzer B, Ceperley D M 2000 Phys. Rev. Lett. 85 1890

    [31]

    Dewing M, Ceperley D M, Pierleoni C 2002 Lect. Notes Phys. 605 473

    [32]

    Pierleoni C, Ceperley D M 2006 Lect. Notes Phys. 703 641

    [33]

    Ceperley D M, Dewing M 1999 J. Chem. Phys. 110 9812

    [34]

    Lin F, Morales M A, Delaney K T, Pierleoni C, Martin R M, Ceperley D M 2009 Phys. Rev. Lett. 103 256401

    [35]

    Morales M A, Pierleoni C, Ceperley D 2010 Phys. Rev. E 81 021202

    [36]

    Delaney K T, Pierleoni C, Ceperley D M 2006 Phys. Rev. Lett. 97 235702

    [37]

    Saumon D, Chabrier G 1989 Phys. Rev. Lett. 62 2397

    [38]

    Gaudoin R, Nekovee M, Foulkes W M, Needs R J, Rajagopal G 2001 Phys. Rev. B 63 115115

    [39]

    Pierleoni C, Delaney K T, Morales M A, Ceperley D M, Holzmann M 2008 Comput. Phys. Commun. 179 89

    [40]

    Pauling L 1960 Nature of the chemical bond (3rd Edn.) (New York: Cornell University Press)p204

    [41]

    Ling Y L 1984 Evolution of chemical bond theory (1st Edn.) (beijing: Science Press) p127 (in Chinese) [凌永乐 1984 化学键理论的演进 (第一版) (北京: 科学出版社) 第127页]

    [42]

    Attaccalite C, Sorella S 2008 Phys. Rev. Lett. 100 114501

    [43]

    Attaccalite C 2005 Ph.D. Dissertation (Trieste: International School for Advanced Studies)

    [44]

    Casula M, Attaccalite C, Sorella S 2004 J. Chem. Phys. 121 7110

    [45]

    Ceperley D M 1978 Phys. Rev. B 18 3126

    [46]

    Fahy S, Wang X W, Louie S G 1990 Phys. Rev. B 42 3503

    [47]

    Feynman R P, Cohen M 1956 Phys. Rev. 102 1189

    [48]

    Schmidt K E, Lee M A, Kalos M H, Chester G V 1981 Phys. Rev. Lett. 47 807

    [49]

    Moskowitz J W, Schmidt K E 1992 J. Chem. Phys. 97 3382

    [50]

    Kwon Y, Ceperley D M, Martin R M 1994 Phys. Rev. B 50 1684

    [51]

    Holzmann M, Ceperley D M, Pierleoni C, Esler K 2003 Phys. Rev. E 68 046707

    [52]

    Silvera I, Goldman V 1978 J. Chem. Phys. 69 4209

    [53]

    Kolos W, Wolniewicz L 1965 J. Chem. Phys. 43 2429

    [54]

    Dewing M D 2000 Ph.D. Dissertation (USA: University of Illinois at Urbana-Champaign)

    [55]

    Lin C, Zong F H, Ceperley D M 2001 Phys. Rev. E 64 016702

    [56]

    Holmes N C, Ross M, Nellis W J 1995 Phys. Rev. B 52 15835

    [57]

    Nellis W J, Mitchell A C, Theil M, Devine G. J, Trainor R J, Brown N 1983 J. Chem. Phys. 79 1480

    [58]

    Lenosky T J, Kress J D, Collins L A 1997 Phys. Rev. B 56 5164

    [59]

    Magro W R, Ceperley D M, Pierleoni C, Bernu B 1996 Phys. Rev. Lett. 76 1240

    [60]

    Knudson M D, Desjarlais M P 2009 Phys. Rev. Lett. 103 225501

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出版历程
  • 收稿日期:  2013-03-10
  • 修回日期:  2013-05-02
  • 刊出日期:  2013-08-05

共振价键波函数在高压液氢量子蒙卡模拟中的适用性研究

  • 1. 清华大学工程物理系, 北京 100084;
  • 2. 西北核技术研究所, 西安 710024

摘要: 在共振价键理论基础上, 选取高压液氢电子主要占据轨道的线性组合作为基组, 构建由Jastrow项和反对称孪生函数乘积项 (AGP) 组成的波函数. 考虑电子关联作用的共振价键 (RVB) 波函数得出的能量值低于LDA能量值; 当满足rs1.75或T 15000 K时引入backflow项以改善波函数结点面, 改善后的能量值下降约1 mHa/atom, 能量方差值变小. 将构建的RVB波函数与电子-离子耦合的蒙特卡罗法 (CEIMC) 相结合, 计算结果与实验及其他ab-initio结果相符合, 获得的液氘单次冲击Hugoniot曲线基本通过所有加载类型实验误差棒, 液氘在50.3 GPa处具有最大压缩率4.48, 在100120 GPa内未发现压缩率有急剧增大的现象. 构建的RVB 波函数能够适用于较宽密度与温度范围内(1.0 rs2.2, 2800 K T60000 K)液氢的模拟, 与CEIMC法相结合可提高液氢冲击特性的模拟精度.

English Abstract

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