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Applications of Simulated Annealing in Electronic Structure Studies of Metallic Clusters

  • Mark R. Pederson
  • Michael J. Mehl
  • Barry M. Klein
  • Joseph G. Harrison

Abstract

With the advent of the density functional formalism1, improved numerical schemes, and the steady increase in computational power, researchers are now confidently studying a wide variety of technologically important materials properties which in some cases are not amenable to laboratory observation. In this paper, we survey an all-electron, full potential computational algorithm which employs a compact basis set of Gaussian type function for such studies. In Sec. II, the computationally intensive steps of this problem and recent work-toward reducing the computational complexity, are briefly reviewed2,3. By incorporating a simulated annealing algorithm we are able to simultaneously vary both the linear and nonlinear “electronic coordinates” and, when necessary, bypass the direct diagonalization step. With this formulation, the computational cost increases linearly with the number of atoms in the regime of tens to hundreds of non-identical atoms3,4. This method enables the accurate evaluation of Hellmann-Feynman (HF) forces. In Sec. III through V we present static and dynamic simulations on a variety of lithium clusters ranging in size from two to twenty seven atoms. By way of these examples, we explicitly show how to predict vacancy formation energies, defect induced lattice relaxation, cohesive energies and vibrational phenomena in many-atom systems. In addition, by carrying out calculations on successively larger crystal fragments, we are able to simulate crystal growth and observe the transition from atomistic to bulk phenomena. The cohesive energies, bulk moduli and lattice constants are presented as a function of cluster size and are found to agree favorably with other theoretical and experimental perfect crystal results.

Keywords

Cohesive Energy Lithium Atom Occupied Orbital Nuclear Position Bulk Modulo 
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.
    P. Hohenberg and W. Kohn, Phys. Rev. B 136:864 (1964); W. Kohn and L.J. Sham, Phys. Rev. A 140:1133 (1965).CrossRefGoogle Scholar
  2. 2.
    M.R. Pederson, B.M. Klein, and J.Q. Broughton, Phys. Rev. B 38:3825 (1988).CrossRefGoogle Scholar
  3. 3.
    M.R. Pederson, “Proceedings of the Third International Conference on Supercomputing”, Vol. I, 179 (1988).Google Scholar
  4. 4.
    W.E. Pickett, “Proceedings of the Third International Conference on Supercomputing”, Vol. I, 172 (1988).Google Scholar
  5. 5.
    We use the parametrization of the Ceperley-Alder exchange correlation potential of J.P. Perdew and A. Zunger, Phys. Rev. B 23:5048 (1981).CrossRefGoogle Scholar
  6. 6.
    H. Hellmann, Einfuhrung in die Quantenchemie, (Deutick, Leipzig, 1937); R.P. Feynman, Phys. Rev. 56:340 (1939).Google Scholar
  7. 7.
    R. Car and M. Parrinello, Phys. Rev. Lett. 55:2471 (1985).CrossRefGoogle Scholar
  8. 8.
    W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, “Numerical Recipes: The Art of Scientific Computing”, (University Press, Cambridge, 1986).Google Scholar
  9. 9.
    C. Kittel, “Introduction of Solid State Physics”, 5th Ed., (John Wiley and Sons, Inc. 1976).Google Scholar
  10. 10.
    V.L. Moruzzi, J.F. Janak, and A.R. Williams, “Calculated Electronic Properties of Metals”, (Pergamon Press, 1974).Google Scholar
  11. 11.
    J. Callaway, X. Zou and D. Bagayoko, Phys. Rev. B 27:634 (1983).CrossRefGoogle Scholar
  12. 12.
    M. Mehl and H. Krakauer (unpublished data). For a discussion of the method see S.H. Wei and H. Krakauer, Phys. Rev. Lett. 55:1200 (1985).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • Mark R. Pederson
    • 1
  • Michael J. Mehl
    • 1
  • Barry M. Klein
    • 1
  • Joseph G. Harrison
    • 2
  1. 1.Condensed Matter Physics BranchNaval Research LaboratoryUSA
  2. 2.Department of PhysicsUniversity of Alabama at BirminghamBirminghamUSA

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