Quantum Mechanical Cluster Calculations of Solids: The ab initio Perturbed Ion Method

  • V. Luaña
  • M. Flórez
  • E. Francisco
  • A. M. Pendás
  • J. M. Recio
  • M. Bermejo
  • L. Pueyo
Part of the NATO ASI Series book series (NSSB, volume 283)


There has been, in the last few years, a significant interest in the application of molecular quantum mechanical methods to describe the bulk and surface electronic structure of solids [1–5]. We are justified to take this route due to the existence of clusters, i.e. electronic groups in the solid that correlate only slightly with its environs. Even so, the interaction energy between the cluster and the rest of the crystal is decisive for many cluster properties and cannot be ignored in the calculation. The accurate representation of the embedding of the cluster is precisely the largest difference between methods derived to treat isolated molecules and those needed for solid state systems.


Correlation Energy Cohesive Property Interionic Distance Electronic Group Surface Electronic Structure 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Yu. Shashkin and W.A. Goddard III, Optical spectrum and Jahn-Teller splitting of Cu 2+ sites in K 2 CuF 4 based on ab initio studies of CuF 4 6 clusters, Phys. Rev. B 33 (1986) 1353.CrossRefGoogle Scholar
  2. 2.
    G.J.M. Janssen and W.C. Nieuwpoort, The band gap in NiO: a cluster study, Phys. Rev. B 38 (1988) 3449.Google Scholar
  3. 3.
    N.W. Winter and R. M. Pitzer, Configuration interaction calculation of the electronic spectra of MgF 2 .V 2+ , J. Chem. Phys. 89 (1988) 446.CrossRefGoogle Scholar
  4. 4.
    J. Meng, A.B. Kunz, and Ch. Woodward, Electronic structure and optical properties of the impurity Cu + in NaF, Phys. Rev. B 38 (1988) 10870.CrossRefGoogle Scholar
  5. 5.
    See a large list of references on this subject on J. Sauer, Molecular models in ab initio studies of solids and surfaces: from ionic crystals and semiconductors to catalysts, Chem. Rev. 89 (1989) 199;CrossRefGoogle Scholar
  6. 5a.
    and C.R.A. Catlow and G.D. Price, Computer modelling of solid-state inorganic materials, Nature 347 (1990) 243.CrossRefGoogle Scholar
  7. 6.
    R. McWeeny, The density matrix in many-electron quantum mechanics. I. Generalized product functions; factorization andphyisical interpretation of the density matrix, Proc. R. Soc. A253 (1959) 242.Google Scholar
  8. 7.
    S. Huzinaga and A.A. Cantú, Theory of separability of many-electron systems, J. Chem. Phys. 55 (1971) 5543.CrossRefGoogle Scholar
  9. 8.
    S. Huzinaga, D. Mc Williams, and A.A. Cantú, Projection operators in Hartree-Fock theory, Adv. Quantum Chem. 7 (1973) 187.CrossRefGoogle Scholar
  10. 9.
    Z. Barandiarán and L. Seijo, The ab initio model potential representation of the crystalline environment. Theoretical study of Cu +: NaCl, J. Chem. Phys. 89 (1988) 5739.Google Scholar
  11. 10.
    V. Luaña and L. Pueyo, Simulation of ionic transition-metal crystals: the cluster model and the cluster-lattice interaction in the light of the Theory of Electronic Separability, Phys. Rev. B 39 (1989) 11093.CrossRefGoogle Scholar
  12. 11.
    V. Luafta, M. Bermejo, M. Flórez, J.M. Recio, and L. Pueyo, Effects of a quantum-mechanical lattice on the electronic structure and d-d spectrum of the MnF 4 6 ~ cluster in Mn 2+:KZnF 3 , J. Chem. Phys. 90 (1989) 6409.CrossRefGoogle Scholar
  13. 12.
    V. Luafia and L. Pueyo, Simulation of ionic crystals: the ab initio perturbed-ion method and application to alkali hydrides and halides, Phys. Rev. B 41 (1990) 3800.CrossRefGoogle Scholar
  14. 13.
    V. Luafta, J.M. Recio, and L. Pueyo, Quantum-mechanical description of ions in crystals: electronic structure of magnesium oxide, Phys. Rev. B 42 (1990) 1791.CrossRefGoogle Scholar
  15. 14.
    L. Pueyo, V. Luaña, M. Flórez, and E. Francisco, Quantum mechanical description of ionic solids, in Structure, Interactions and Reactivity, S. Fraga, editor (Elsevier, in press).Google Scholar
  16. 15.
    A. Martin Pendás, E. Francisco, V. Luaña, and L. Pueyo, Quantum-mechanical description of atoms in crystals: electronic structure of solid neon, (to be published).Google Scholar
  17. 16.
    V. Bonifacic and S. Huzinaga, Atomic and molecular calculations with the model potential method, J. Chem. Phys. 60 (1974) 2779.CrossRefGoogle Scholar
  18. 17.
    C.C.J. Roothaan and P.S. Bagus, Atomic SCF calculations by the expansion method, in Methods in Computational Physics, vol. 2, p. 47, (Academic, New York, 1963).Google Scholar
  19. 18.
    E. Clementi and C. Roetti, At. Data Nucl. Data Tables 14 (1974) 177.CrossRefGoogle Scholar
  20. 19.
    P.P Ewald, Ann. Phys. (Leipzig) 64 (1921) 253.Google Scholar
  21. 20.
    W. Van Gool and A.G. Piken, Lattice self-potentials and Madelung constants for some compounds, J. Mater. Sci. 4 (1969) 95.Google Scholar
  22. 21.
    J.Q. Broughton and P.S. Bagus, Self-Consistent-Field studies of core-level shifts in ionic crystals. II. MgO and BeO, Phys. Rev. 36 (1987) 2813.CrossRefGoogle Scholar
  23. 22.
    H.J. Silverstone and R.K. Moats, Expansion of a function about a displaced center, Phys. Rev. A 16 (1977) 1731.CrossRefGoogle Scholar
  24. 23.
    A. Martin Pendás and E. Francisco, Overlap, Effective-potential, and projection-operator bicentric integrals over complex Slater-type orbitals, Phys. Rev. A xx (1991) xxx.Google Scholar
  25. 24.
    E. Francisco (unpublished). Google Scholar
  26. 25.
    E. Clementi, IBM J. Res. Dev. 9 (1965) 2.CrossRefGoogle Scholar
  27. 26.
    S J. Chakravorty and E. Clementi, Soft coulomb hole for the Hartree-Fock model to estimate atomic correlation energies, Phys. Rev. A 39 (1989) 2290.CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1992

Authors and Affiliations

  • V. Luaña
    • 1
  • M. Flórez
    • 1
  • E. Francisco
    • 1
  • A. M. Pendás
    • 1
  • J. M. Recio
    • 1
  • M. Bermejo
    • 2
  • L. Pueyo
    • 1
  1. 1.Departamento de Quimica Fisica y AnaliticaUniversidad de OviedoOviedoSpain
  2. 2.Departamento de FisicaUniversidad de OviedoOviedoSpain

Personalised recommendations