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Molecular physics and chemistry applications of quantum Monte Carlo

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  • Part 5. Atomic Molecular and Nuclear Physics
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Abstract

We discuss recent work with the diffusion quantum Monte Carlo (QMC) method in its application to molecular systems. The formal correspondence of the imaginary-time Schrödinger equation to a diffusion equation allows one to calculate quantum mechanical expectation values as Monte Carlo averages over an ensemble of random walks. We report work on atomic and molecular total energies, as well as properties including electron affinities, binding energies, reaction barriers, and moments of the electronic charge distribution. A brief discussion is given on how standard QMC must be modified for calculating properties. Calculated energies and properties are presented for a number of molecular systems, including He, F, F−, H2, N, and N2. Recent progress in extending the basic QMC approach to the calculation of “analytic” (as opposed to finite-difference) derivatives of the energy is presented, together with an H2 potential-energy curve obtained using analytic derivatives.

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References

  1. P. J. Reynolds, D. M. Ceperley, B. J. Alder, and W. A. Lester, Jr.,J. Chem. Phys. 77:5593 (1982).

    Article  ADS  Google Scholar 

  2. J. W. Moskowitz, K. E. Schmidt, M. A. Lee, and M. H. Kalos,J. Chem. Phys. 77:349 (1982).

    Article  ADS  Google Scholar 

  3. P. J. Reynolds, R. N. Barnett, and W. A. Lester, Jr.,Int. J. Quant. Chem. Symp. 18:709 (1984); F. Mentch and J. Anderson,J. Chem. Phys. 80:2675 (1984); R. N. Barnett, P. J. Reynolds, and W. A. Lester, Jr.,J. Chem. Phys. 82:2700 (1985).

    Article  Google Scholar 

  4. D. M. Ceperley and B. J. Alder,J. Chem. Phys. 81:5833 (1984).

    Article  ADS  Google Scholar 

  5. P. J. Reynolds, M. Dupuis, and W. A. Lester, Jr.,J. Chem. Phys. 82:1983 (1985).

    Article  ADS  Google Scholar 

  6. See also the article by K. E. Schmidt in this issue.

  7. M. H. Kalos,Phys. Rev. 128:1791 (1962);J. Comp. Phys. 1:257 (1967); M. H. Kalos, D. Levesque, and L. Verlet,Phys. Rev. A 9:2178 (1974); D.M. Ceperley inRecent Progress in Many-Body Theories, J. G. Zabolitzky, M. de Llano, M. Fortes, and J. W. Clark, eds. (Springer-Verlag, Berlin, 1981).

    Article  ADS  MathSciNet  Google Scholar 

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

    Google Scholar 

  9. J. M. Hammersley and D. C. Handscomb,Monte Carlo Methods (Methuen, London, 1964).

    MATH  Google Scholar 

  10. D. M. Ceperley and B. J. Alder,Phys. Rev. Lett. 45:566 (1980).

    Article  ADS  Google Scholar 

  11. P. Pulay, inModern Theoretical Chemistry, vol. 4, p. 153, H. F. Schaefer III, ed. (Plenum, New York, 1977); M. Dupuis and H. F. King,J. Chem. Phys. 68:3998 (1978).

    Google Scholar 

  12. P. Saxe, Y. Yamaguchi, and H. F. Schaefer III,J. Chem. Phys. 77:5647 (1982).

    Article  ADS  Google Scholar 

  13. B. Holmer and D. M. Ceperley, private communication; B. Wells, P. J. Reynolds, and W. A. Lester, Jr., unpublished; B. H. Wells,Chem. Phys. Lett. 115:89 (1985).

  14. P. J. Reynolds, R. N. Harnett, B. L. Hammond, R. M. Grimes, and W. A. Lester, Jr.,Int. J. Quant. Chem. 29:589 (1986).

    Article  Google Scholar 

  15. W. Kolos and L. Wolniewicz,J. Chem. Phys. 43:2429 (1965).

    Article  ADS  Google Scholar 

  16. M. H. Kalos,Phys. Rev. A 2:250 (1970).

    Article  ADS  Google Scholar 

  17. R. N. Barnett, P. J. Reynolds, and W. A. Lester, Jr., “Molecular Properties by Quantum Monte Carlo,” in preparation.

  18. Z. Ritter and R. Pauncz,J. Chem. Phys. 32:1820 (1960).

    Article  ADS  Google Scholar 

  19. C. E. Moore, Natl. Bur. Standards Circ. No. 467:I (1949).

    Google Scholar 

  20. W. Kolos and C. C. J. Roothaan,Rev. Mod. Phys. 32:219 (1960).

    Article  ADS  MathSciNet  Google Scholar 

  21. B. Liu,J. Chem. Phys. 58:1925 (1973).

    Article  ADS  Google Scholar 

  22. E. Clementi and C. Roetti,At. Data Nucl. Data Tables 14:177 (1974).

    Article  ADS  Google Scholar 

  23. P. E. M. Siegbahn,Int. J. Quant. Chem. 23:1869 (1983).

    Article  Google Scholar 

  24. A. Veillard and E. Clementi,J. Chem. Phys. 49:2415 (1968).

    Article  ADS  Google Scholar 

  25. P. A. Christiansen and E. A. McCullough, Jr.,J. Chem. Phys. 67:1877 (1977).

    Article  ADS  Google Scholar 

  26. F. Grimaldi,J. Chem. Phys. 43:S59 (1965).

    Article  ADS  Google Scholar 

  27. F. Sasaki and M. Yoshimine,Phys. Rev. A 9:17, 26 (1974).

    Article  ADS  Google Scholar 

  28. E. Clementi and A. D. McLean,Phys. Rev. 133A:419 (1964).

    Article  ADS  Google Scholar 

  29. S. Fraga, J. Karwowski, K. M. S. Saxena,Handbook of Atomic Data (Elsevier, Amsterdam, 1976).

    Google Scholar 

  30. B. H. Botch and T. H. Dunning, Jr.,J. Chem. Phys. 76:6046 (1982).

    Article  ADS  Google Scholar 

  31. R. N. Barnett, P. J. Reynolds, and W. A. Lester, Jr.,J. Chem. Phys. 84 (to appear, 1986).

  32. H. Hotop and W. C. Lineberger,J. Phys. Chem. Ref. Data 4:539 (1975).

    Article  ADS  Google Scholar 

  33. A. Lofthus and P. H. Krupenie,J. Phys. Chem. Ref. Data 6:113 (1977).

    Article  ADS  Google Scholar 

  34. B. Liu,J. Chem. Phys. 80:581 (1984).

    Article  ADS  Google Scholar 

  35. D. Feller, L. E. McMurchie, W. T. Borden, and E. R. Davidson,J. Chem. Phys. 77:6134 (1982); P. Saxe, H. F. Schaefer III, and N. C. Handy,J. Phys. Chem. 85:745 (1981).

    Article  ADS  Google Scholar 

  36. H.-J. Werner and E.-A. Reinsch,J. Chem. Phys. 76:3144 (1982).

    Article  ADS  Google Scholar 

  37. A. R. W. McKellar, P. R. Bunker, T. J. Sears, K. M. Evenson, R. J. Saykally, and S. R. Langhoff,J. Chem. Phys. 79:5251 (1983).

    Article  ADS  Google Scholar 

  38. A. D. McLean and M. Yoshimine,J. Chem. Phys. 45:3676 (1966).

    Article  ADS  Google Scholar 

  39. F. P. Billingsley II and M. Krauss,J. Chem. Phys. 60:2767 (1974).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Materials and Molecular Research Division, Lawrence Berkeley Laboratory, University of California, 94720, Berkeley, California, USA

    P. J. Reynolds

  2. Department of Chemistry, University of California, 94720, Berkeley, California

    R. N. Barnett, B. L. Hammond & W. A. Lester Jr.

Authors
  1. P. J. Reynolds
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  2. R. N. Barnett
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  3. B. L. Hammond
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  4. W. A. Lester Jr.
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Additional information

This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the U. S. Department of Energy under contract number DE-AC03-76SF00098.

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Reynolds, P.J., Barnett, R.N., Hammond, B.L. et al. Molecular physics and chemistry applications of quantum Monte Carlo. J Stat Phys 43, 1017–1026 (1986). https://doi.org/10.1007/BF02628327

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