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Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology Volume 1 pp 641–683Cite as

The Coupled Electron-Ion Monte Carlo Method

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Part of the book series: Lecture Notes in Physics ((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].

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References

  1. R. Car and M. Parrinello (1985) Unified Approach for Molecular Dynamics and Density-Functional Theory. Phys. Rev. Letts. 55, p. 2471

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  4. D. Marx and M. Parrinello (1996) Ab initio path integral molecular dynamics: Basic ideas. J. Chem. Phys. 104, p. 4077

    Article  ADS  Google Scholar 

  5. R. M. Martin (2004) Electronic Structure. Basic Theory and Practical Methods. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  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

    Article  ADS  Google Scholar 

  7. E. G. Maksimov and Y. I. Silov (1999) Hydrogen at high pressure. Physics- Uspekhi 42, p. 1121

    Article  ADS  Google Scholar 

  8. M. Stadele and R. M. Martin (2000) Metallization of Molecular Hydrogen: Predictions from Exact-Exchange Calculations. Phys. Rev. Lett. 84, pp. 6070–6073

    Article  ADS  Google Scholar 

  9. K. A. Johnson and N. W. Ashcroft (2000) Structure and bandgap closure in dense hydrogen. Nature 403, p. 632

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  11. B. L. Hammond, W. A. Lester Jr., and P. J. Reynolds (1994) Monte Carlo methods in Ab Initio Quantum Chemistry. World Scientific Singapore

    Book  Google Scholar 

  12. R. M. Panoff and J. Carlson (1989) Fermion Monte Carlo algorithms and liquid 3He. Phys. Rev. Letts. 62, p. 1130

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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. 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

    Google Scholar 

  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

    Google Scholar 

  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. 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. 313

    Google Scholar 

  19. D. M. Ceperley (1995) Path integrals in the theory of condensed helium. Rev. Mod. Phys. 67, pp. 279–355

    Article  ADS  Google Scholar 

  20. A. Sarsa, K. E. Schmidt, and W. R. Magro (2000) A path integral ground state method. J. Chem. Phys. 113, p. 1366

    Article  ADS  Google Scholar 

  21. R. P. Feynman (1998) Statistical Mechanics: a set of lectures. Westview Press

    Google Scholar 

  22. K. Huang (1988) Statistical Mechanics, John Wiley

    Google Scholar 

  23. S. Zhang and H. Krakauer (2003) Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants. Phys. Rev. Lett. 90, p. 136401

    Article  ADS  Google Scholar 

  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. A. J. W. Thom and A. Alavi (2005) A combinatorial approach to the electron correlation problem. J. Chem. Phys. in print

    Google Scholar 

  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, Italy

    Google Scholar 

  27. D. M. Ceperley (1991) Fermion Nodes. J. Stat. Phys. 63, p. 1237

    Article  ADS  Google Scholar 

  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 Scientfic

    Google Scholar 

  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. 2777

    Article  ADS  Google Scholar 

  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. G. Ortiz and D. M. Ceperley (1995) Core Structure of a Vortex in Superfluid 4He. Phys. Rev. Lett. 75, p. 4642

    Article  ADS  Google Scholar 

  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. D. M. Ceperley and B. J. Alder (1987) Ground state of solid hydrogen at high pressures. Phys. Rev. B 36, p. 2092

    Article  ADS  Google Scholar 

  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. 2414

    Article  ADS  Google Scholar 

  35. V. Natoli, R. M. Martin, and D. M. Ceperley (1993) Crystal structure of atomic hydrogen. Phys. Rev. Lett. 70, p. 1952

    Article  ADS  Google Scholar 

  36. V. Natoli, R. M. Martin, and D. M. Ceperley (1995) Crystal Structure of Molecular Hydrogen at High Pressure. Phys. Rev. Lett. 74, p. 1601

    Article  ADS  Google Scholar 

  37. C. Pierleoni and D. M. Ceperley (2005) Computational methods in Coupled Electron-Ion Monte Carlo. Chem. Phys. Chem. 6, p. 1872

    Google Scholar 

  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. 815

    Google Scholar 

  39. D. M. Ceperley and M. H. Kalos (1979) Monte Carlo Methods in Statistical Physics, ed. K. Binder, Springer-Verlag.

    Google Scholar 

  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. 3081

    Article  ADS  Google Scholar 

  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. 5833

    Article  ADS  Google Scholar 

  42. C. Pierleoni, K. Delaney, and D. M. Ceperley, to be published

    Google Scholar 

  43. D. Frenkel and B. Smit (2002) Understanding Molecular Simulations: From Algorithms to Applications, 2nd Ed., Academic Press, San Diego

    Google Scholar 

  44. S. Moroni, private communication

    Google Scholar 

  45. D. M. Ceperley and M. Dewing (1999) The penalty method for random walks with uncertain energies. J. Chem. Phys. 110, p. 9812

    Article  ADS  Google Scholar 

  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. 4209

    Article  ADS  Google Scholar 

  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. 3674

    Article  ADS  Google Scholar 

  48. E. Babaev, A. Sudbo, and N. W. Ashcroft (2004) A superconductor to superfiuid phase transition in liquid metallic hydrogen. Nature 431, p. 666

    Article  ADS  Google Scholar 

  49. I. F. Silvera (1980) The solid molecular hydrogens in the condensed phase: Fundamentals and static properties. Rev. Mod. Phys. 52, p. 393

    Article  ADS  Google Scholar 

  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. 1240

    Google Scholar 

  51. B. Militzer and D. M. Ceperley (2000) Path Integral Monte Carlo Calculation of the Deuterium Hugoniot. Phys. Rev. Lett. 85, p. 1890

    Article  ADS  Google Scholar 

  52. B. Militzer and D. M. Ceperley (2001) Path integral Monte Carlo simulation of the low-density hydrogen plasma. Phys. Rev. E 63, p. 066404

    Article  ADS  Google Scholar 

  53. D. Hohl, V. Natoli, D. M. Ceperley, and R. M. Martin (1993) Molecular dynamics in dense hydrogen. Phys. Rev. Lett. 71, p. 541

    Google Scholar 

  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. 768–781

    Google Scholar 

  55. J. Kohanoff, S. Scandolo, G. L. Chiarotti, and E. Tosatti (1997) Solid Molecular Hydrogen: The Broken Symmetry Phase. Phys. Rev. Lett. 78, p. 2783

    Article  ADS  Google Scholar 

  56. S. Scandolo (2003) Liquid-liquid phase transition in compressed hydrogen from first-principles simulations. PNAS 100, p. 3051

    Article  ADS  Google Scholar 

  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. 669

    Article  ADS  Google Scholar 

  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. 1860

    Article  ADS  Google Scholar 

  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. 109

    Google Scholar 

  60. M. Holzmann, C. Pierleoni, and D. M. Ceperley (2005) Coupled Electron Ion Monte Carlo Calculations of Atomic Hydrogen. Comput. Physics Commun. 169, p. 421

    Article  ADS  Google Scholar 

  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. 15835

    Article  ADS  Google Scholar 

  62. J. C. Grossman, L. Mitas (2005) Efficient Quantum Monte Carlo Energies for Molecular Dynamics Simulations. Phys. Rev. Lett. 94, p. 056403

    Article  ADS  Google Scholar 

  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/0508420

    Google Scholar 

  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. 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 

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Authors and Affiliations

  1. Department of Physics, University of L’Aquila, Polo di Coppito, Via Vetoio, L’Aquila, 67010, Italy

    C. Pierleoni

  2. Department of Physics and NCSA, University of Illinois at Urbana-Champaign, 61801, Urbana, IL, U.S.A.

    D.M. Ceperley

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  1. C. Pierleoni
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Editors and Affiliations

  1. Dipartimento di Fisica, Università di Modena e Reggio Emilia, Via Campi, 213/A, 41100, Modena, Italy

    Mauro Ferrario Professor

  2. Dipartimento di Fisica, INFN, Università di Roma La Sapienza, Piazzale Aldo Moro 2, 00185, Roma, Italy

    Giovanni Ciccotti Professor

  3. Institut für Physik, Universität Mainz, Staudinger Weg 7, 55128, Mainz, Germany

    Kurt Binder Professor

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Pierleoni, C., Ceperley, D. (2006). The Coupled Electron-Ion Monte Carlo Method. In: Ferrario, M., Ciccotti, G., Binder, K. (eds) Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology Volume 1. Lecture Notes in Physics, vol 703. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-35273-2_18

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