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].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. Car and M. Parrinello (1985) Unified Approach for Molecular Dynamics and Density-Functional Theory. Phys. Rev. Letts. 55, p. 2471
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
A. Alavi, J. Kohanoff, M. Parrinello, and D. Frenkel (1994) Ab Initio Molecular Dynamics with Excited Electrons. Phys. Rev. Letts. 73, pp. 2599–2602
D. Marx and M. Parrinello (1996) Ab initio path integral molecular dynamics: Basic ideas. J. Chem. Phys. 104, p. 4077
R. M. Martin (2004) Electronic Structure. Basic Theory and Practical Methods. Cambridge University Press, Cambridge
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
E. G. Maksimov and Y. I. Silov (1999) Hydrogen at high pressure. Physics- Uspekhi 42, p. 1121
M. Stadele and R. M. Martin (2000) Metallization of Molecular Hydrogen: Predictions from Exact-Exchange Calculations. Phys. Rev. Lett. 84, pp. 6070–6073
K. A. Johnson and N. W. Ashcroft (2000) Structure and bandgap closure in dense hydrogen. Nature 403, p. 632
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
B. L. Hammond, W. A. Lester Jr., and P. J. Reynolds (1994) Monte Carlo methods in Ab Initio Quantum Chemistry. World Scientific Singapore
R. M. Panoff and J. Carlson (1989) Fermion Monte Carlo algorithms and liquid 3He. Phys. Rev. Letts. 62, p. 1130
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
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]
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
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
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]
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
D. M. Ceperley (1995) Path integrals in the theory of condensed helium. Rev. Mod. Phys. 67, pp. 279–355
A. Sarsa, K. E. Schmidt, and W. R. Magro (2000) A path integral ground state method. J. Chem. Phys. 113, p. 1366
R. P. Feynman (1998) Statistical Mechanics: a set of lectures. Westview Press
K. Huang (1988) Statistical Mechanics, John Wiley
S. Zhang and H. Krakauer (2003) Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants. Phys. Rev. Lett. 90, p. 136401
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]
A. J. W. Thom and A. Alavi (2005) A combinatorial approach to the electron correlation problem. J. Chem. Phys. in print
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
D. M. Ceperley (1991) Fermion Nodes. J. Stat. Phys. 63, p. 1237
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
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
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]
G. Ortiz and D. M. Ceperley (1995) Core Structure of a Vortex in Superfluid 4He. Phys. Rev. Lett. 75, p. 4642
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.
D. M. Ceperley and B. J. Alder (1987) Ground state of solid hydrogen at high pressures. Phys. Rev. B 36, p. 2092
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
V. Natoli, R. M. Martin, and D. M. Ceperley (1993) Crystal structure of atomic hydrogen. Phys. Rev. Lett. 70, p. 1952
V. Natoli, R. M. Martin, and D. M. Ceperley (1995) Crystal Structure of Molecular Hydrogen at High Pressure. Phys. Rev. Lett. 74, p. 1601
C. Pierleoni and D. M. Ceperley (2005) Computational methods in Coupled Electron-Ion Monte Carlo. Chem. Phys. Chem. 6, p. 1872
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
D. M. Ceperley and M. H. Kalos (1979) Monte Carlo Methods in Statistical Physics, ed. K. Binder, Springer-Verlag.
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
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
C. Pierleoni, K. Delaney, and D. M. Ceperley, to be published
D. Frenkel and B. Smit (2002) Understanding Molecular Simulations: From Algorithms to Applications, 2nd Ed., Academic Press, San Diego
S. Moroni, private communication
D. M. Ceperley and M. Dewing (1999) The penalty method for random walks with uncertain energies. J. Chem. Phys. 110, p. 9812
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
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
E. Babaev, A. Sudbo, and N. W. Ashcroft (2004) A superconductor to superfiuid phase transition in liquid metallic hydrogen. Nature 431, p. 666
I. F. Silvera (1980) The solid molecular hydrogens in the condensed phase: Fundamentals and static properties. Rev. Mod. Phys. 52, p. 393
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
B. Militzer and D. M. Ceperley (2000) Path Integral Monte Carlo Calculation of the Deuterium Hugoniot. Phys. Rev. Lett. 85, p. 1890
B. Militzer and D. M. Ceperley (2001) Path integral Monte Carlo simulation of the low-density hydrogen plasma. Phys. Rev. E 63, p. 066404
D. Hohl, V. Natoli, D. M. Ceperley, and R. M. Martin (1993) Molecular dynamics in dense hydrogen. Phys. Rev. Lett. 71, p. 541
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
J. Kohanoff, S. Scandolo, G. L. Chiarotti, and E. Tosatti (1997) Solid Molecular Hydrogen: The Broken Symmetry Phase. Phys. Rev. Lett. 78, p. 2783
S. Scandolo (2003) Liquid-liquid phase transition in compressed hydrogen from first-principles simulations. PNAS 100, p. 3051
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
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
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
M. Holzmann, C. Pierleoni, and D. M. Ceperley (2005) Coupled Electron Ion Monte Carlo Calculations of Atomic Hydrogen. Comput. Physics Commun. 169, p. 421
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
J. C. Grossman, L. Mitas (2005) Efficient Quantum Monte Carlo Energies for Molecular Dynamics Simulations. Phys. Rev. Lett. 94, p. 056403
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
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.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/3-540-35273-2_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35270-9
Online ISBN: 978-3-540-35273-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)