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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

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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  • 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.
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    [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

  • [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

  • 引用本文:
    Citation:
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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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