The coupled electron-ion monte carlo method

Lecture Notes in Physics

Volumn 703, Issue , 2006, Pages 641-683

  Pierleoni, Carlo ^a   Ceperley, David M ^b  

^a UNIVERSITY OF L'AQUILA   (Italy)

^b University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33947200137     PISSN: 00758450     EISSN: None     Source Type: Book Series    
DOI: 10.1007/3-540-35273-2_18     Document Type: Article

References (70)

1. R. Car and M. Parrinello (1985) Unified Approach for Molecular Dynamics and Density-Functional Theory. Phys. Rev. Letts. 55, p. 2471
2. M. Bernasconi, G. L. Chiarotti, P. Focher, S. Scandolo, E. Tosatti, and M. Parrinello (1995) First-principle-constant pressure molecular dynamics. J. Phys. Chem. Solids 56, p. 501
3. A. Alavi, J. Kohanoff, M. Parrinello, and D. Frenkel (1994) Ab Initio Molecular Dynamics with Excited Electrons. Phys. Rev. Letts. 73, pp. 2599-2602
4. D. Marx and M. Parrinello (1996) Ab initio path integral molecular dynamics: Basic ideas. J. Chem. Phys. 104, p. 4077
5. R. M. Martin (2004) Electronic Structure. Basic Theory and Practical Methods. Cambridge University Press, Cambridge
6. M. W. C. Foulkes, L. Mitas, R. J. Needs, and G. Rajagopal (2001) Quantum Monte Carlo simulations of solids. Rev. Mod. Phys. 73, p. 33
7. E. G. Maksimov and Y. I. Silov (1999) Hydrogen at high pressure. Physics-Uspekhi 42, p. 1121
8. M. Stadele and R. M. Martin (2000) Metallization of Molecular Hydrogen: Predictions from Exact-Exchange Calculations. Phys. Rev. Lett. 84, pp. 6070-6073
9. K. A. Johnson and N. W. Ashcroft (2000) Structure and bandgap closure in dense hydrogen. Nature 403, p. 632
10. D. Alfé, M. Gillan, M. D. Towler, and R. J. Needs (2004) Efficient localized basis set for quantum Monte Carlo calculations on condensed matter. Phys. Rev. B 70, p. 161101
11. B. L. Hammond, W. A. Lester Jr., and P. J. Reynolds (1994) Monte Carlo methods in Ab Initio Quantum Chemistry. World Scientific Singapore
12. R. M. Panoff and J. Carlson (1989) Fermion Monte Carlo algorithms and liquid 3He. Phys. Rev. Letts. 62, p. 1130
13. Y. Kwon, D. M. Ceperley, and R. M. Martin (1994) Quantum Monte Carlo calculation of the Fermi-liquid parameters in the two-dimensional electron gas. Phys. Rev. B 50, pp. 1684-1694
14. M. Holzmann, D. M. Ceperley, C. Pierleoni, and K. Esler (2003) Backflow correlations for the electron gas and metallic hydrogen. Phys. Rev. E 68, p. 046707[1-15]
15. M. Dewing and D. M. Ceperley (2002) Methods in Coupled Electron-Ion Monte Carlo. In Recent Advances in Quantum Monte Carlo Methods II (Ed. S. Rothstein), World Scientific
16. D. M. Ceperley, M. Dewing, and C. Pierleoni (2002) The Coupled Electronic-Ionic Monte Carlo Simulation Method. Lecture Notes in Physics 605, pp. 473-499, Springer-Verlag; physics/0207006
17. C. Pierleoni, D. M. Ceperley, and M. Holzmann (2004) Coupled Electron-Ion Monte Carlo Calculations of Dense Metallic Hydrogen. Phys. Rev. Lett. 93, 146402[1-4]
18. S. Baroni and S. Moroni (1999) Reptation Quantum Monte Carlo: A Method for Unbiased Ground-State Averages and Imaginary-Time Correlations. Phys. Rev. Letts. 82, pp. 4745-4748
19. S. Baroni, S. Moroni Reptation quantum Monte Carlo in "Quantum Monte Carlo Methods in Physics and Chemistry", eds. M. P. Nightingale and C. J. Umrigar (Kluwer, 1999), p. 313
20. D. M. Ceperley (1995) Path integrals in the theory of condensed helium. Rev. Mod. Phys. 67, pp. 279-355
21. A. Sarsa, K. E. Schmidt, and W. R. Magro (2000) A path integral ground state method. J. Chem. Phys. 113, p. 1366
22. R. P. Feynman (1998) Statistical Mechanics: A set of lectures. Westview Press
23. K. Huang (1988) Statistical Mechanics, John Wiley
24. S. Zhang and H. Krakauer (2003) Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants. Phys. Rev. Lett. 90, p. 136401
25. R. W. Hall (2005) Simulation of electronic and geometric degrees of freedom using a kink-based path integral formulation: Application to molecular systems. J. Chem. Phys. 122, p. 164112[1-8]
26. A. J. W. Thom and A. Alavi (2005) A combinatorial approach to the electron correlation problem. J. Chem. Phys. in print
27. D. M. Ceperley (1996) Path integral Monte Carlo methods for fermions. In Monte Carlo and Molecular Dynamics of Condensed Matter Systems, ed. by K. Binder and G. Ciccotti, Editrice Compositori, Bologna, Italy
28. D. M. Ceperley (1991) Fermion Nodes. J. Stat. Phys. 63, p. 1237
29. D. Bressanini, D. M. Ceperley, and P. Reynolds (2001) What do we know about wave function nodes?. In Recent Advances in Quantum Monte Carlo Methods II, ed. S. Rothstein, World Scientfic
30. G. Ortiz, D. M. Ceperley, and R. M. Martin (1993) New stochastic method for systems with broken time-reversal symmetry: 2D fermions in a magnetic field. Phys. Rev. Lett. 71, p. 2777
31. C. Lin, F. H. Zong, and D. M. Ceperley (2001) Twist-averaged boundary conditions in continuum quantum Monte Carlo algorithms. Phys. Rev. E 64, 016702[1-12]
32. G. Ortiz and D. M. Ceperley (1995) Core Structure of a Vortex in Superfluid 4He. Phys. Rev. Lett. 75, p. 4642
33. V. D. Natoli (1994) A Quantum Monte Carlo study of the high pressure phases of solid hydrogen, Ph.D. Theses, University of Illinois at Urbana-Champaign.
34. D. M. Ceperley and B. J. Alder (1987) Ground state of solid hydrogen at high pressures. Phys. Rev. B 36, p. 2092
35. X. W. Wang, J. Zhu, S. G. Louie, and S. Fahy (1990) Magnetic structure and equation of state of bcc solid hydrogen: A variational quantum Monte Carlo study. Phys. Rev. Lett. 65, p. 2414
36. V. Natoli, R. M. Martin, and D. M. Ceperley (1993) Crystal structure of atomic hydrogen. Phys. Rev. Lett. 70, p. 1952
37. V. Natoli, R. M. Martin, and D. M. Ceperley (1995) Crystal Structure of Molecular Hydrogen at High Pressure. Phys. Rev. Lett. 74, p. 1601
38. C. Pierleoni and D. M. Ceperley (2005) Computational methods in Coupled Electron-Ion Monte Carlo. Chem. Phys. Chem. 6, p. 1872
39. D. Ceperley (1986) The Statistical Error of Green's Function Monte Carlo, in Proceedings of the Metropolis Symposium on. The Frontiers of Quantum Monte Carlo. J. Stat. Phys. 43, p. 815
40. D. M. Ceperley and M. H. Kalos (1979) Monte Carlo Methods in Statistical Physics, ed. K. Binder, Springer-Verlag.
41. D. M. Ceperley, G. V. Chester, and M. H. Kalos (1977) Monte Carlo simulation of a many-fermion study. Phys. Rev. B 16, p. 3081
42. D. M. Ceperley and B. J. Alder (1984) Quantum Monte Carlo for molecules: Green's function and nodal release. J. Chem. Phys. 81, p. 5833
43. C. Pierleoni, K. Delaney, and D. M. Ceperley, to be published
44. D. Frenkel and B. Smit (2002) Understanding Molecular Simulations: From Algorithms to Applications, 2nd Ed., Academic Press, San Diego
45. S. Moroni, private communication
46. D. M. Ceperley and M. Dewing (1999) The penalty method for random walks with uncertain energies. J. Chem. Phys. 110, p. 9812
47. I. F. Silvera and V. V. Goldman (1978) The isotropic intermolecular potential for H2 and D2 in the solid and gas phases. J. Chem. Phys. 69, p. 4209
48. W. Kolos and L. Wolniewicz (1964) Accurate Computation of Vibronic Energies and of Some Expectation Values for H2, D2, and T2. J. Chem. Phys. 41, p. 3674
49. E. Babaev, A. Sudbo, and N. W. Ashcroft (2004) A superconductor to superfluid phase transition in liquid metallic hydrogen. Nature 431, p. 666
50. I. F. Silvera (1980) The solid molecular hydrogens in the condensed phase: Fundamentals and static properties. Rev. Mod. Phys. 52, p. 393
51. C. Pierleoni, D. M. Ceperley, B. Bernu, and W. R. Magro (1994) Equation of State of the Hydrogen Plasma by Path Integral Monte Carlo Simulation. Phys. Rev. Lett. 73, p. 2145
52. W. R. Magro, D. M. Ceperley, C. Pierleoni and B. Bernu (1996) Molecular Dissociation in Hot, Dense Hydrogen. Phys. Rev. Lett. 76, p. 1240
53. B. Militzer and D. M. Ceperley (2000) Path Integral Monte Carlo Calculation of the Deuterium Hugoniot. Phys. Rev. Lett. 85, p. 1890
54. B. Militzer and D. M. Ceperley (2001) Path integral Monte Carlo simulation of the low-density hydrogen plasma. Phys. Rev. E 63, p. 066404
55. D. Hohl, V. Natoli, D. M. Ceperley, and R. M. Martin (1993) Molecular dynamics in dense hydrogen. Phys. Rev. Lett. 71, p. 541
56. J. Kohanoff and J. P. Hansen (1995) Ab Initio Molecular Dynamics of Metallic Hydrogen at High Densities. Phys. Rev. Lett. 74, pp. 626-629
57. ibid. (1996) Statistical properties of the dense hydrogen plasma: An ab initio molecular dynamics investigation. Phys. Rev. E 54, pp. 768-781
58. J. Kohanoff, S. Scandolo, G. L. Chiarotti, and E. Tosatti (1997) Solid Molecular Hydrogen: The Broken Symmetry Phase. Phys. Rev. Lett. 78, p. 2783
59. S. Scandolo (2003) Liquid-liquid phase transition in compressed hydrogen from first-principles simulations. PNAS 100, p. 3051
60. S. A. Bonev, E. Schwegler, T. Ogitsu, and G. Galli (2004) A quantum fluid of metallic hydrogen suggested by first-principles calculations. Nature 431, p. 669
61. S. T. Weir, A. C. Mitchell, and W. J. Nellis (1996) Metallization of Fluid Molecular Hydrogen at 140 GPa (1.4 Mbar). Phys. Rev. Lett. 76, p. 1860
62. T. Guillot, G. Chabrier, P. Morel, and D. Gautier (1994) Nonadiabatic models of Jupiter and Saturn. Icarus 112, p. 354
63. T. Guillot, P. Morel (1995) Coupled Electron Ion Monte Carlo Calculations of Atomic Hydrogen. Astron. & Astrophys. Suppl. 109, p. 109
64. M. Holzmann, C. Pierleoni, and D. M. Ceperley (2005) Coupled Electron Ion Monte Carlo Calculations of Atomic Hydrogen. Comput. Physics Commun. 169, p. 421
65. N. C. Holmes, M. Ross, and W. J. Nellis (1995) Temperature measurements and dissociation of shock-compressed liquid deuterium and hydrogen. Phys. Rev. B 52, p. 15835
66. J. C. Grossman, L. Mitas (2005) Efficient Quantum Monte Carlo Energies for Molecular Dynamics Simulations. Phys. Rev. Lett. 94, p. 056403
67. F. Krajewski and M. Parrinello (2005) Stochastic linear scaling for metals and nonmetals. Phys. Rev. B 71, p. 233105
68. F. Krajewski, M. Parrinello, Linear scaling electronic structure calculations and accurate sampling with noisy forces. cond-mat/0508420
69. C. Attaccalite (2005) RVB phase of hydrogen at high pressure:tOwards the first ab-initio Molecular Dynamics by Quantum Monte Carlo, Ph.D. theses, SISSATrieste.
70. K. Delaney, C. Pierleoni and D.M. Ceperley (2006) Quantum Monte Carlo Simulation of the High-Pressure Molecular-Atomic Transition in Fluid Hydrogen. dond-mat/0603750, submitted to Phys. Rev. Letts.,