1 Beck M H, J？ckle A, Worth G A, et al. The multiconfiguration time-dependent Hartree (MCTDH) method: A highly efficient algorithm for propagating wavepackets. Phys Rep, 2000, 324: 1-105
[2]
2 Althorpe S C, Clary D C. Quantum scattering calculations on chemical reactions. Annu Rev Phys Chem, 2003, 54: 493-529
[3]
3 Zhang D H, Collins M A, Lee S Y. First-principles theory for the H+H2O, D2O reactions. Science, 2000, 290: 961-963
[4]
4 Collins M A. Molecular potential-energy surfaces for chemical reaction dynamics. Theor Chem Acc, 2002, 108: 313-324
[5]
5 Marx D, Parrinello M. Structural quantum effects and three-centre two-electron bonding in CH5+. Nature, 1995, 375: 216-218
[6]
6 Marx D, Parrinello M. The effect of quantum and thermal fluctuations on the structure of the floppy molecule C2H3+. Science, 1996, 271: 179-181
[7]
7 Tuckerman M E, Marx D, Klein M L, et al. On the quantum nature of the shared proton in hydrogen bonds. Science, 1997, 275: 817-820
[8]
8 Benoit M, Marx D, Parrinello M. Tunnelling and zero-point motion in high-pressure ice. Nature, 1998, 392: 258-261
[9]
9 Marx D, Tuckerman M E, Hutter J, et al. The nature of the hydrated excess proton in water. Nature, 1999, 397: 601-604
11 Tuckerman M E, Marx D, Parrinello M. The nature and transport mechanism of hydrated hydroxide ions in aqueous solution. Nature, 2002, 417: 925-929
[12]
12 Wang Y, Ma Y. Perspective: Crystal structure prediction at high pressures. J Chem Phys, 2014, 140: 040901
[13]
13 Pamuk B, Soler J M, Ramírez R, et al. Anomalous nuclear quantum effects in ice. Phys Rev Lett, 2012, 108: 193003
[14]
14 Nagata Y, Pool R E, Backus E H G, et al. Nuclear quantum effects affect bond orientation of water at the water-vapor interface. Phys Rev Lett, 2012, 109: 226101
[15]
15 Ceriotti M, Cuny J, Parrinello M, et al. Nuclear quantum effects and hydrogen bond fluctuations in water. Proc Natl Acad Sci USA, 2013, 110: 15591-15596
[16]
16 Drechsel-Grau C, Marx D. Quantum simulation of collective proton tunneling in hexagonal ice crystals. Phys Rev Lett, 2014, 112: 148302
[17]
17 Wang Y, Babin V, Bowman J M, et al. The water hexamer: Cage, prism, or both. full dimensional quantum simulations say both. J Am Chem Soc, 2012, 134: 11116-11119
[18]
18 Li X Z, Probert M I J, Alavi A, et al. Quantum nature of the proton in water-hydroxyl overlayers on metal surfaces. Phys Rev Lett, 2010, 104: 066102
[19]
19 Li X Z, Walker B, Michaelides A. Quantum nature of the hydrogen bond. Proc Natl Acad Sci USA, 2011, 108: 6369-6373
[20]
20 Guillaume C L, Gregoryanz E, Degtyareva O, et al. Cold melting and solid structures of dense lithium. Nat Phys, 2011, 7: 211-214
[21]
21 Chen J, Li X Z, Zhang Q, et al. Quantum simulation of low-temperature metallic liquid hydrogen. Nat Commun, 2013, 4: 2064
[22]
22 Li X Z, Walker B, Probert M I J, et al. Classical and quantum ordering of protons in cold solid hydrogen under megabar pressures. J Phys Condens Matter, 2013, 25: 085402
[23]
23 Alfè D, Gillan M J, Price G D. Complementary approaches to the ab initio calculation of melting properties. J Chem Phys, 2002, 116: 6170-6177
[24]
24 Cao J, Voth G A. The formulation of quantum statistical mechanics based on the Feynman path centroid density. IV. Algorithms for centroid molecular dynamics. J Chem Phys, 1994, 101: 6168-6183
[25]
25 Hernández E R, Rodriguez-Prieto A, Bergara A, et al. First-principles simulations of lithium melting: Stability of the bcc phase close to melting. Phys Rev Lett, 2010, 104: 185701
[26]
26 Feng Y, Chen J, Alfe D, et al. Nuclear quantum effects on the high pressure melting of dense lithium. J Chem Phys, 2015, 142: 064506
[27]
27 Morales J J, Singer K. Path integral simulation of the free energy of (Lennard-Jones) neon. Mol Phys, 1991, 73: 873-880
[28]
28 Habershon S, Manolopoulos D E. Thermodynamic integration from classical to quantum mechanics. J Chem Phys, 2011, 135: 224111
[29]
29 Wigner E, Huntington H B. On the possibility of a metallic modification of hydrogen. J Chem Phys, 1935, 3: 764-770
[30]
30 Loubeyre P, Occelli F, LeToullec R. Optical studies of solid hydrogen to 320 GPa and evidence for black hydrogen. Nature, 2002, 416: 613-617
[31]
31 Eremets M I, Troyan I A. Conductive dense hydrogen. Nat Mater, 2011, 10: 927-931
[32]
32 Zha C S, Liu Z, Hemley R J. Synchrotron infrared measurements of dense hydrogen to 360 GPa. Phys Rev Lett, 2012, 108: 146402
[33]
33 Bonev S A, Schwegler E, Ogitsu T, et al. A quantum fluid of metallic hydrogen suggested by first-principles calculations. Nature, 2004, 431: 669-672
[34]
34 Deemyad S, Silvera I F. Melting line of hydrogen at high pressures. Phys Rev Lett, 2008, 100: 155701
[35]
35 Babaev E, Sudb？ A, Ashcroft N W. A superconductor to superfluid phase transition in liquid metallic hydrogen. Nature, 2004, 431: 666-668
[36]
36 McMahon J M, Ceperley D M. High-temperature superconductivity in atomic metallic hydrogen. Phys Rev B, 2011, 84: 144515
[37]
37 Ashcroft N W. Metallic hydrogen: A high-temperature superconductor? Phys Rev Lett, 1968, 21: 1748
[38]
38 McMahon J M, Morales M A, Pierleoni C, et al. The properties of hydrogen and helium under extreme conditions. Rev Mod Phys, 2012, 84: 1607-1653
[39]
39 Loubeyre P, LeToullec R, Hausermann D, et al. X-ray diffraction and equation of state of hydrogen at megabar pressures. Nature, 1996, 383: 702-704
[40]
40 Eremets M I, Troyan I A. Conductive dense hydrogen. Nat Mater, 2011, 10: 927-931
[41]
41 Howie R T, Guillaume C L, Scheler T, et al. Mixed molecular and atomic phase of dense hydrogen. Phys Rev Lett, 2012, 108: 125501
[42]
42 Liu H, Ma Y. Proton or deuteron transfer in phase IV of solid hydrogen and deuterium. Phys Rev Lett, 2013, 110: 025903
[43]
43 Marqués M, McMahon M I, Gregoryanz E, et al. Crystal structures of dense lithium: A meal-semiconductor-metal transition. Phys Rev Lett, 2011, 106: 095502
[44]
44 Shimizu K, Ishikawa H, Takao D, et al. Superconductivity in compressed lithium at 20 K. Nature, 2002, 419: 597-599
[45]
45 Lazicki A, Fei Y, Hemley R J. High-pressure differential thermal analysis measurements of the melting curve of lithium. Solid State Commun, 2010, 150: 625-627
[46]
46 Schaeffer A M J, Talmadge W B, Temple S R, et al. High pressure melting of lithium. Phys Rev Lett, 2012, 109: 185702
[47]
47 Li B, Ding Y, Yang W, et al. Calcium with the b-tin structure at high pressure and low temperature. Proc Natl Acad Sci USA, 2012, 109: 16459-16462
[48]
48 Yabuuchi T, Matsuoka T, Nakamoto Y, et al. Superconductivity of Ca exceeding 25 K at megabar pressures. J Phys Soc Jpn, 2006, 75: 083703
[49]
49 Teweldeberhan A M, Dubois J L, Bonev S A. High-pressure phases of calcium: Density-functional theory and diffusion quantum Monte Carlo approach. Phys Rev Lett, 2010, 105: 235503
[50]
50 Errea I, Rousseau B, Bergara A. Anharmonic stabilization of the high-pressure simple cubic phase of calcium. Phys Rev Lett, 2011, 106: 165501
[51]
51 Liu H, Cui W, Ma Y. Hybrid functional study rationalizes the simple cubic phase of calcium at high pressures. J Chem Phys, 2012, 137: 184502
[52]
52 Di Gennaro M, Saha S K, Verstraete M J. Role of dynamical instability in the ab initio phase diagram of calcium. Phys Rev Lett, 2013, 111: 025503
