The Application of Quantum Monte Carlo to Problems in Electronic Structure

  • D. M. Ceperley
Part of the NATO ASI Series book series (NSSE, volume 205)


A overall view of the quantum Monte Carlo methods which have been applied to the calculation of electronic properties of condensed matter systems is given. The dependance of statistical and systematic errors on trial functions and computer time is discussed. Generic problems and opportunities are identified.


Trial Function Quantum Monte Carlo Diffusion Monte Carlo Variational Monte Carlo Exact Wave Function 
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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  1. 1.
    Kalos. M H., Levesque, D. and Verlet, L., Phys. Rev. A9,2178 (1974).ADSGoogle Scholar
  2. 2.
    McMillan, W. L., Phys. Rev. A 138, 442 (1965).ADSCrossRefGoogle Scholar
  3. 3.
    Bijl, A. Physcia 7,869 (1940)ADSCrossRefGoogle Scholar
  4. 3a.
    R. Jastrow, Phys. Rev. 98, 1479 (1955).ADSzbMATHCrossRefGoogle Scholar
  5. 4.
    Ceperley, D.M., and Kalos, M.H., “Quantum Many-Body Problems,” in Monte Carlo Methods in Statistical Physics, ed. K. Binder, Springer-Verlag, 1979.Google Scholar
  6. 5.
    Ceperley, D., Chester, G.V., and Kalos, M.H., Phys. Rev. B, 16, 3081 (1977).ADSCrossRefGoogle Scholar
  7. 6.
    Umrigar, C. J., Wilson, K. G., and Wilkins, J. W., Phys. Rev. Letts. 60,1719 (1988).ADSCrossRefGoogle Scholar
  8. 7.
    Schmidt, K. E. and Moskowitz, J. W., J. Chem. Phys. 93, 4172 (1990).ADSCrossRefGoogle Scholar
  9. 8.
    Ceperley, D., Phys. Rev. B, 18, 3126 (1978).ADSCrossRefGoogle Scholar
  10. 9.
    Ceperley, D.M., and Alder, B.J., Phys. Rev. Letts., 45, 566 (1980).ADSCrossRefGoogle Scholar
  11. 10.
    Reynolds, P.J., Ceperley, D.M., Alder, B.J., and Lester Jr., W.A., J. Chem. Phys., 77, 5593 (1982)ADSCrossRefGoogle Scholar
  12. 11.
    Ceperley, D., J. Comp. Phys., 51, 404 (1983).ADSzbMATHCrossRefGoogle Scholar
  13. 11a.
    Ceperley, D.M., and Alder, B.J., J. Chem. Phys., 81, 5833 (1984).ADSCrossRefGoogle Scholar
  14. 12.
    Schmidt, K. E. and Kalos, M. H. in Applications of the Monte Carlo Method in Statistical Physics. Ed. K. Binder (Springer-Verlag, 1984).Google Scholar
  15. 13.
    Anderson, J. B. , J. Chem. Phys. 65, 4121 (1976).ADSCrossRefGoogle Scholar
  16. 14.
    Stratonovitch, R. L., Dokl. Akad. Nauk. SSSR 115,1097(1957).MathSciNetGoogle Scholar
  17. 14a.
    Hubbard, J., Phys. Rev. Letts. 3, 77 (1959).ADSCrossRefGoogle Scholar
  18. 15.
    White, S. R., Wilkins, J. W., and Wilson, K.G., Phys. Rev. Letts. 56, 5024 (1988).ADSGoogle Scholar
  19. 16.
    Ceperley, D.M, and Pollock, E.L., Phys. Rev. Letts., 56, 351 (1986).ADSCrossRefGoogle Scholar
  20. 16a.
    Ceperlev, D. M., and Pollock, E. L., “Path-Integral Computation Techniques for Superfluid 4He”, Proceedings of Elba Conference on Monte Carlo Methods for Physics. 1990.Google Scholar
  21. 16b.
    Schmidt, K. E., and Ceperley, D. M., “Monte Carlo Techniques for Quantum Fluids, Solids and Droplets”, in Monte Carlo Methods Vol 3, ed. K. Binder, Springer-Verlag, 1991.Google Scholar
  22. 17.
    Ceperley, D. M., “Fermion Nodes”, in press J. Stat. Phys. (1991).Google Scholar
  23. 18.
    Ceperley, D., J. of Stat. Phys., 43, 815 (1986).ADSCrossRefGoogle Scholar
  24. 19.
    Fahy, S., Wang, X. W., and Louie, S. G., Phys. Rev. Letts. 61,1631 (1988)ADSCrossRefGoogle Scholar
  25. 19a.
    Fahy, S., Wang, X. W., and Louie, S. G.; Phys. Rev. B42, 3503 (1990).ADSGoogle Scholar
  26. 20.
    Bachelet, G.B., Ceperley, D.M., and Chiochetti, M., Phys. Rev. Letts., 62, 2088 (1989).ADSCrossRefGoogle Scholar
  27. 21.
    Hurley, M. M. and Christiansen, P. A., J. Chem. Phys. 86, 1069 (1987),ADSCrossRefGoogle Scholar
  28. 21a.
    Hammond, B. L., Reynolds, P. J. and Lester, W. A. J. Chem. Phys. 87,1130 (1987).ADSCrossRefGoogle Scholar
  29. 22.
    Mitas, L., Shirley E. L., and Ceperley, D. M., “Nonlocal Pseudopotentials and Diffusion Monte Carlo” submitted to J. Chem. Phys. (1991)Google Scholar
  30. 23.
    Shirley, E., Martin, R. M., Bachelet G. B., and Ceperley, D. M., Phys. Rev. B 42, 5057(1990).ADSGoogle Scholar
  31. 24.
    Li, X.-P., Ceperley, D. M., and Martin,R. M., “Calculation of the Equation of State of Solid Si by Green’s Function Monte Carlo”, submitted Phys. Rev. Letts. 1990.Google Scholar
  32. 25.
    Ceperley, D.M., and Alder, B.J., Phys. Rev. B., 36, 2092 (1987).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • D. M. Ceperley
    • 1
  1. 1.National Center for Supercomputing Applications, Department of Physics and the Beckman InstituteUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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