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The Coupled Electron-Ion Monte Carlo Method

  • C. Pierleoni
  • D.M. Ceperley
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 703)

Abstract

Twenty years ago Car and Parrinello introduced an efficient method to perform Molecular Dynamics simulation for classical nuclei with forces computed on the “fly” by a Density Functional Theory (DFT) based electronic calculation [1]. Because the method allowed study of the statistical mechanics of classical nuclei with many-body electronic interactions, it opened the way for the use of simulation methods for realistic systems with an accuracy well beyond the limits of available effective force fields. In the last twenty years, the number of applications of the Car-Parrinello ab-initio molecular dynamics has ranged from simple covalent bonded solids, to high pressure physics, material science and biological systems. There have also been extensions of the original algorithm to simulate systems at constant temperature and constant pressure [2], finite temperature effects for the electrons [3], and quantum nuclei [4].

Keywords

Trial Function Twist Angle Random Phase Approximation Nodal Surface Quantum Monte Carlo 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    R. Car and M. Parrinello (1985) Unified Approach for Molecular Dynamics and Density-Functional Theory. Phys. Rev. Letts. 55, p. 2471CrossRefADSGoogle Scholar
  2. 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. 501CrossRefADSGoogle Scholar
  3. 3.
    A. Alavi, J. Kohanoff, M. Parrinello, and D. Frenkel (1994) Ab Initio Molecular Dynamics with Excited Electrons. Phys. Rev. Letts. 73, pp. 2599–2602CrossRefADSGoogle Scholar
  4. 4.
    D. Marx and M. Parrinello (1996) Ab initio path integral molecular dynamics: Basic ideas. J. Chem. Phys. 104, p. 4077CrossRefADSGoogle Scholar
  5. 5.
    R. M. Martin (2004) Electronic Structure. Basic Theory and Practical Methods. Cambridge University Press, CambridgezbMATHGoogle Scholar
  6. 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. 33CrossRefADSGoogle Scholar
  7. 7.
    E. G. Maksimov and Y. I. Silov (1999) Hydrogen at high pressure. Physics- Uspekhi 42, p. 1121CrossRefADSGoogle Scholar
  8. 8.
    M. Stadele and R. M. Martin (2000) Metallization of Molecular Hydrogen: Predictions from Exact-Exchange Calculations. Phys. Rev. Lett. 84, pp. 6070–6073CrossRefADSGoogle Scholar
  9. 9.
    K. A. Johnson and N. W. Ashcroft (2000) Structure and bandgap closure in dense hydrogen. Nature 403, p. 632CrossRefADSGoogle Scholar
  10. 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. 161101CrossRefADSGoogle Scholar
  11. 11.
    B. L. Hammond, W. A. Lester Jr., and P. J. Reynolds (1994) Monte Carlo methods in Ab Initio Quantum Chemistry. World Scientific SingaporeCrossRefGoogle Scholar
  12. 12.
    R. M. Panoff and J. Carlson (1989) Fermion Monte Carlo algorithms and liquid 3He. Phys. Rev. Letts. 62, p. 1130CrossRefADSGoogle Scholar
  13. 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. 1684–1694CrossRefADSGoogle Scholar
  14. 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]Google Scholar
  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 ScientificGoogle Scholar
  16. 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/0207006Google Scholar
  17. 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]Google Scholar
  18. 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; 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. 313Google Scholar
  19. 19.
    D. M. Ceperley (1995) Path integrals in the theory of condensed helium. Rev. Mod. Phys. 67, pp. 279–355CrossRefADSGoogle Scholar
  20. 20.
    A. Sarsa, K. E. Schmidt, and W. R. Magro (2000) A path integral ground state method. J. Chem. Phys. 113, p. 1366CrossRefADSGoogle Scholar
  21. 21.
    R. P. Feynman (1998) Statistical Mechanics: a set of lectures. Westview PressGoogle Scholar
  22. 22.
    K. Huang (1988) Statistical Mechanics, John WileyGoogle Scholar
  23. 23.
    S. Zhang and H. Krakauer (2003) Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants. Phys. Rev. Lett. 90, p. 136401CrossRefADSGoogle Scholar
  24. 24.
    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]Google Scholar
  25. 25.
    A. J. W. Thom and A. Alavi (2005) A combinatorial approach to the electron correlation problem. J. Chem. Phys. in printGoogle Scholar
  26. 26.
    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, ItalyGoogle Scholar
  27. 27.
    D. M. Ceperley (1991) Fermion Nodes. J. Stat. Phys. 63, p. 1237CrossRefADSGoogle Scholar
  28. 28.
    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 ScientficGoogle Scholar
  29. 29.
    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. 2777CrossRefADSGoogle Scholar
  30. 30.
    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]Google Scholar
  31. 31.
    G. Ortiz and D. M. Ceperley (1995) Core Structure of a Vortex in Superfluid 4He. Phys. Rev. Lett. 75, p. 4642CrossRefADSGoogle Scholar
  32. 32.
    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.Google Scholar
  33. 33.
    D. M. Ceperley and B. J. Alder (1987) Ground state of solid hydrogen at high pressures. Phys. Rev. B 36, p. 2092CrossRefADSGoogle Scholar
  34. 34.
    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. 2414CrossRefADSGoogle Scholar
  35. 35.
    V. Natoli, R. M. Martin, and D. M. Ceperley (1993) Crystal structure of atomic hydrogen. Phys. Rev. Lett. 70, p. 1952CrossRefADSGoogle Scholar
  36. 36.
    V. Natoli, R. M. Martin, and D. M. Ceperley (1995) Crystal Structure of Molecular Hydrogen at High Pressure. Phys. Rev. Lett. 74, p. 1601CrossRefADSGoogle Scholar
  37. 37.
    C. Pierleoni and D. M. Ceperley (2005) Computational methods in Coupled Electron-Ion Monte Carlo. Chem. Phys. Chem. 6, p. 1872Google Scholar
  38. 38.
    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. 815Google Scholar
  39. 39.
    D. M. Ceperley and M. H. Kalos (1979) Monte Carlo Methods in Statistical Physics, ed. K. Binder, Springer-Verlag.Google Scholar
  40. 40.
    D. M. Ceperley, G. V. Chester, and M. H. Kalos (1977) Monte Carlo simulation of a many-fermion study. Phys. Rev. B 16, p. 3081CrossRefADSGoogle Scholar
  41. 41.
    D. M. Ceperley and B. J. Alder (1984) Quantum Monte Carlo for molecules: Green’s function and nodal release. J. Chem. Phys. 81, p. 5833CrossRefADSGoogle Scholar
  42. 42.
    C. Pierleoni, K. Delaney, and D. M. Ceperley, to be publishedGoogle Scholar
  43. 43.
    D. Frenkel and B. Smit (2002) Understanding Molecular Simulations: From Algorithms to Applications, 2nd Ed., Academic Press, San DiegoGoogle Scholar
  44. 44.
    S. Moroni, private communicationGoogle Scholar
  45. 45.
    D. M. Ceperley and M. Dewing (1999) The penalty method for random walks with uncertain energies. J. Chem. Phys. 110, p. 9812CrossRefADSGoogle Scholar
  46. 46.
    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. 4209CrossRefADSGoogle Scholar
  47. 47.
    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. 3674CrossRefADSGoogle Scholar
  48. 48.
    E. Babaev, A. Sudbo, and N. W. Ashcroft (2004) A superconductor to superfiuid phase transition in liquid metallic hydrogen. Nature 431, p. 666CrossRefADSGoogle Scholar
  49. 49.
    I. F. Silvera (1980) The solid molecular hydrogens in the condensed phase: Fundamentals and static properties. Rev. Mod. Phys. 52, p. 393CrossRefADSGoogle Scholar
  50. 50.
    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; W. R. Magro, D. M. Ceperley, C. Pierleoni and B. Bernu (1996) Molecular Dissociation in Hot, Dense Hydrogen. Phys. Rev. Lett. 76, p. 1240Google Scholar
  51. 51.
    B. Militzer and D. M. Ceperley (2000) Path Integral Monte Carlo Calculation of the Deuterium Hugoniot. Phys. Rev. Lett. 85, p. 1890CrossRefADSGoogle Scholar
  52. 52.
    B. Militzer and D. M. Ceperley (2001) Path integral Monte Carlo simulation of the low-density hydrogen plasma. Phys. Rev. E 63, p. 066404CrossRefADSGoogle Scholar
  53. 53.
    D. Hohl, V. Natoli, D. M. Ceperley, and R. M. Martin (1993) Molecular dynamics in dense hydrogen. Phys. Rev. Lett. 71, p. 541Google Scholar
  54. 54.
    J. Kohanoff and J. P. Hansen (1995) Ab Initio Molecular Dynamics of Metallic Hydrogen at High Densities. Phys. Rev. Lett. 74, pp. 626–629; ibid. (1996) Statistical properties of the dense hydrogen plasma: An ab initio molecular dynamics investigation. Phys. Rev. E 54, pp. 768–781Google Scholar
  55. 55.
    J. Kohanoff, S. Scandolo, G. L. Chiarotti, and E. Tosatti (1997) Solid Molecular Hydrogen: The Broken Symmetry Phase. Phys. Rev. Lett. 78, p. 2783CrossRefADSGoogle Scholar
  56. 56.
    S. Scandolo (2003) Liquid-liquid phase transition in compressed hydrogen from first-principles simulations. PNAS 100, p. 3051CrossRefADSGoogle Scholar
  57. 57.
    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. 669CrossRefADSGoogle Scholar
  58. 58.
    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. 1860CrossRefADSGoogle Scholar
  59. 59.
    T. Guillot, G. Chabrier, P. Morel, and D. Gautier (1994) Nonadiabatic models of Jupiter and Saturn. Icarus 112, p. 354; T. Guillot, P. Morel (1995) Coupled Electron Ion Monte Carlo Calculations of Atomic Hydrogen. Astron. & Astrophys. Suppl. 109, p. 109Google Scholar
  60. 60.
    M. Holzmann, C. Pierleoni, and D. M. Ceperley (2005) Coupled Electron Ion Monte Carlo Calculations of Atomic Hydrogen. Comput. Physics Commun. 169, p. 421CrossRefADSGoogle Scholar
  61. 61.
    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. 15835CrossRefADSGoogle Scholar
  62. 62.
    J. C. Grossman, L. Mitas (2005) Efficient Quantum Monte Carlo Energies for Molecular Dynamics Simulations. Phys. Rev. Lett. 94, p. 056403CrossRefADSGoogle Scholar
  63. 63.
    F. Krajewski and M. Parrinello (2005) Stochastic linear scaling for metals and nonmetals. Phys. Rev. B 71, p. 233105; F. Krajewski, M. Parrinello, Linear scaling electronic structure calculations and accurate sampling with noisy forces. cond-mat/0508420Google Scholar
  64. 64.
    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.Google Scholar
  65. 65.
    K. Delaney, C. Pierleoni and D.M. Ceperley (2006) Quantum Monte Carlo Simulation of the High-Pressure Molecular-Atomic Transition in Fluid Hydrogen. cond-mat/0603750, submitted to Phys. Rev. Letts.Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • C. Pierleoni
    • 1
  • D.M. Ceperley
    • 2
  1. 1.Department of PhysicsUniversity of L’Aquila, Polo di CoppitoItaly
  2. 2.Department of Physics and NCSAUniversity of Illinois at Urbana-ChampaignUrbanaU.S.A.

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