| [1] |
Marx D, Tuckerman M E, Hutter J and Parrinello M 1999 Nature 397 601
|
| [2] |
Marrone J A and Car R 2008 Phys. Rev. Lett. 101 017801
|
| [3] |
Fanourgakis G S, Schenter G K and Xantheas S S 2006 J. Chem. Phys. 125 141102
|
| [4] |
Habershon T E, Markland S and Manolopoulos D E 2009 J. Chem. Phys. 131 024501
|
| [5] |
Chen B, Ivanov I, Klein M L and Parrinello M 2003 Phys. Rev. Lett. 91 215503
|
| [6] |
Li X Z, Probert M I J, Alavi A and Michaelides A 2010 Phys. Rev. Lett. 104 066102
|
| [7] |
Li X Z, Walker B and Michaelides A 2011 Proc. Natl. Acad. Sci. USA 108 6369
|
| [8] |
Matsushita E and Matsubara T 1982 Prog. Theor. Phys. 67 1
|
| [9] |
Ubbelohde A R and Gallagher K J 1955 Acta. Crystallogr. 8 71
|
| [10] |
Marrone J A, Lin L and Car R 2009 J. Chem. Phys. 130 204511
|
| [11] |
Burnham C J, Anick D J, Mankoo P K and Reiter G F 2008 J. Chem. Phys. 128 154519
|
| [12] |
Meng X Z 2015 Nat. Phys. 11 235
|
| [13] |
Zhang D H, Collins M A and Lee S Y 2000 Science 290 961
|
| [14] |
Liu K 2001 Annu. Rev. Phys. Chem. 52 139
|
| [15] |
Collins M A 2002 Theo. Chem. Acc. 108 313
|
| [16] |
Althorpe S C and Clary D C 2003 Annu. Rev. Phys. Chem. 54 593
|
| [17] |
Qiu M H 2006 Science 311 1440
|
| [18] |
Feynman R P 1949 Phys. Rev. 76 769
|
| [19] |
Feynman R P 1953 Phys. Rev. 90 1116
|
| [20] |
Feynman R P 1953 Phys. Rev. 91 1291
|
| [21] |
Feynman R P 1953 Phys. Rev. 91 1301
|
| [22] |
Feynman R P and Hibbs A R 1965 Quantum Mechanics and Path Integrals (New York: McGraw-Hill Inc.)
|
| [23] |
Chandler D and Wolynes P G 1981 J. Chem. Phys. 74 4078
|
| [24] |
Parrinello M and Rahman A 1984 J. Chem. Phys. 80 860
|
| [25] |
Berne B J and Thirumalai D 1986 Annu. Rev. Phys. Chem. 37 401
|
| [26] |
Pollock E L and Ceperley D M 1984 Phys. Rev. B 30 2555
|
| [27] |
Ceperley D M and Pollock E L 1986 Phys. Rev. Lett. 56 351
|
| [28] |
Pollock E L and Ceperley D M 1987 Phys. Rev. B 36 8343
|
| [29] |
Ceperley D M 1995 Rev. Mod. Phys. 67 279
|
| [30] |
Tuckerman M E, Marx D, Klein M L and Parrinello M 1996 J. Chem. Phys. 104 5579
|
| [31] |
Marx D and Parrinello M 1996 J. Chem. Phys. 104 4077
|
| [32] |
Morales M A, Pierleoni C, Schwegler E and Ceperley D M 2010 Proc. Natl. Acad. Sci. USA 107 12799
|
| [33] |
Li X Z 2013 J. Phys.: Condens. Matter 25 085402
|
| [34] |
Chen J 2013 Nat. Commun. 4 2064
|
| [35] |
Morales M A, McMahon J M, Pierleoni C and Ceperley D M 2013 Phys. Rev. Lett. 110 065702
|
| [36] |
Morales M A, McMahon J M, Pierleoni C and Ceperley D M 2013 Phys. Rev. B 87 184107
|
| [37] |
Davidson E R M, Klimes J, Alf'e D and Michaelides A 2014 ACS Nano 8 9905
|
| [38] |
Tachikawa M and Shiga M 2005 J. Am. Chem. Soc. 127 11908
|
| [39] |
Kaczmarek A, Shiga M and Marx D 2009 J. Phys. Chem. A 113 1985
|
| [40] |
Tozzini V 2005 Curr. Opin. Struct. Biol. 15 144
|
| [41] |
Bartels C and Karplus M 1998 J. Phys. Chem. B 102 865
|
| [42] |
Sugita Y and Okamoto Y 1999 Chem. Phys. Lett. 314 141
|
| [43] |
Laio A and Parrinello M 2002 Proc. Natl. Acad. Sci. USA 99 12562
|
| [44] |
Gao Y Q, Yang L J, Fan Y B and Shao Q 2008 Int. Rev. Phys. Chem. 27 201
|
| [45] |
Pérez A and von Lilienfeld O A 2011 J. Chem. Theory Comput. 7 2358
|
| [46] |
Habershon S and Manolopoulos D E 2011 J. Chem. Phys. 135 224111
|
| [47] |
Li X Z and Wang E G 2014 Computer Simulations of Molecules and Condensed Matters: From Electronic Structures to Molecular Dynamics (Beijing: Peking University Press)
|
| [48] |
Stroobants A, Lekkerkerker H N W and Frenkel D 1987 Phys. Rev. A 36 2929
|
| [49] |
Frenkel D, Lekkerkerker H N W and Stroobants A 1988 Nature 332 822
|
| [50] |
Meijer E J, Frenkel D, LeSar R A and Ladd A J C 1990 J. Chem. Phys. 92 7570
|
| [51] |
Meijer E J and Frenkel D 1991 J. Chem. Phys. 94 2269
|
| [52] |
Eldridge M D, Madden P A and Frenkel D 1993 Nature 365 35
|
| [53] |
Perdew J P, Burke K and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
|
| [54] |
Clark S J 2005 Z. Kristallogr 220 567
|
| [55] |
Tuckerman M E, Berne B J, Martyna G J and Klein M L 1993 J. Chem. Phys. 99 2796
|
| [56] |
Feng Y X, Chen J, Alfé D, Li X Z, Wang E G, et al. 2015 J. Chem. Phys. 142 064506
|
| [57] |
Feng Y X et al. to be submitted
|
| [58] |
Andersen H C 1980 J. Chem. Phys. 72 2384
|
| [59] |
Raugei S and Klein M L 2003 J. Am. Chem. Soc. 125 8992
|
| [60] |
Gregory J K and Clary D C 1996 J. Phys. Chem. 100 18014
|
| [61] |
Clary D C, Benoit D M and van Mourik T 2000 Acc. Chem. Res. 33 441
|
| [62] |
Wendler K, Thar J, Zahn S and Kirchner B 2010 J. Phys. Chem. A 114 9529
|
| [63] |
Xantheas S S and Dunning T H 1993 J. Chem. Phys. 99 8774
|
| [64] |
Cubero E, Orozco M, Hobza P and Luque F J 1999 J. Phys. Chem. A 103 6394
|
| [65] |
Swalina C, Wang Q, Chakraborty A and Hammes-Schiffer S 2007 J. Phys. Chem. A 111 2206
|