Skip to main content
SpringerLink
Log in

The Constrained Search Formulation of Density Functional Theory

  • Chapter
Density Functional Methods In Physics

Part of the book series: NATO ASI Series ((ASIB,volume 123))

Abstract

Consider N interacting electrons in a local spin-independent external potential v. The Hamiltonian is

$$ {\text{H = T + Vee + }}\sum\limits_{i = 1}^N {v(\vec r_i )} ,$$
(1)

where T and Vee are, respectively, the kinetic and electron-electron repulsion operators.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136: B864 (1964).

    Article  MathSciNet  Google Scholar 

  2. M. Levy, Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem, Proc. Natl. Acad. Sci. (USA) 76:6062 (1979); M. Levy, Universal functionals of the density and first-order density matrix, Bull. Amer. Phys. So.c. 24: 626 (1979).

    ADS  Google Scholar 

  3. M. Levy, Electron densities in search of hamiltonians, Phys. Rev. A 26: 1200 (1982).

    Article  Google Scholar 

  4. E. H. Lieb, Density functionals for coulomb systems, in “Physics as Natural Philosophy: Essays in Honor of Laszlo Tisza on his 75th Birthday”, H. Feshbach and A. Shimony, eds., M.I.T. Press, Cambridge (1982); E. H. Lieb, Density functionals for coulomb systems, Int. J. Quantum Chem. 24:243 (1983).

    Google Scholar 

  5. M. R. Nyden and R. G. Parr, Restatement of conventional electronic wavefunction determination as a density functional procedure, J. Chem. Phys. 78:4044 (1983); M. R. Nyden, An orthogonality constrained generalization of the Weizacker density functional method, J. Chem. Phys. 78: 4048 (1983).

    ADS  Google Scholar 

  6. G. Zumbach and K. Maschke, New approach to the calculation of density functionals, Phys. Rev. A 28: 544 (1983).

    Article  MathSciNet  Google Scholar 

  7. J. E. Harriman, Orthonormal orbitals for the representation of an arbitrary density, Phys. Rev. A 24: 680 (1981).

    Article  Google Scholar 

  8. M. Levy, T.-S. Nee, and R. G. Parr, Method for direct determination of localized orbitals, J. Chem. Phys. 63: 316 (1975).

    Article  ADS  Google Scholar 

  9. P. A. Christiansen and W. E. Palke, A study of the ethane internal rotation barrier, Chem. Phys. Lett. 31: 462 (1975).

    Article  ADS  Google Scholar 

  10. W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140: A1133 (1965).

    Article  MathSciNet  Google Scholar 

  11. J. C. Slater, “The Self-Consistent Field for Molecules and Solids”, McGraw-Hill, New York (1974); J. W. D. Connally, The Xa Method, in Modern Theoretical Chemistry 7, G. A. Segal, ed., Plenum, New York (1977).

    Google Scholar 

  12. H. Englisch and R. Englisch, Hohenberg-Kohn theorem and non-v-representable densities, Physica 121A: 253 (1983).

    Article  MathSciNet  Google Scholar 

  13. M. Levy and J. P. Perdew, Generalized density-functional orbital theories and v-representability, unpublished.

    Google Scholar 

  14. J. P. Perdew and A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems, Phys. Rev. B 23:5048 (1981). They have also proved that regardless of the v-representability status of a given orbital it must be free of self interaction in the exact theory.

    Google Scholar 

  15. M. Levy, J. P. Perdew, and V. Sahni, Exact differential equation for the density of a many-particle system, unpublished.

    Google Scholar 

  16. J. Harris, The role of occupation numbers in HKS theory, Int. J. Quantum Chem. S13:189 (1980); J. Harris, The adiabatic-connection approach to Kohn-Sham, unpublished.

    Google Scholar 

  17. J. K. Percus, The role of model systems in the few-body reduction of the N-Fermion problem, Int. J. Quantum Chem. 13: 89 (1978).

    Article  Google Scholar 

  18. P. W. Payne, Density functionals in unrestricted Hartree-Fock theory, J. Chem. Phys. 71: 490 (1979).

    Article  ADS  Google Scholar 

  19. K. F. Freed and M. Levy, Direct first principles algorithm for the universal electron density functional, J. Chem. Phys. 77: 396 (1982).

    Article  ADS  Google Scholar 

  20. This section, equations (35) to (46), was sent to Englisch and Englisch in January, 1983. See the addendum which they kindly include in their article (reference 12). Englisch and Englisch independently assert these equations in reference 12. We thank them for having sent us a copy of their manuscript before publication.

    Google Scholar 

  21. E. H. Lieb, excited-state section of his chapter in this book. We thank him for kindly having sent us a copy of his excited-state section before publication.

    Google Scholar 

  22. U. von Barth, Density functional theory for solids, NATO ’ Advanced Study Institute, Gent, Summer 1982, Plenum, in press.

    Google Scholar 

  23. U. von Barth, Local-density theory of multiplet structure, Phys. Rev. A 20: 1693 (1979).

    Article  Google Scholar 

  24. A. K. Theophilou, The energy density functional formalism for excited states, J. Phys. C 12:5419 (1979); J. Katriel, An alternative interpretation of Theophilou’s extension of the Hohenberg-Kohn theorem to excited states, J. Phys. C 13: L375 (1980).

    Google Scholar 

  25. S. M. Valone and J. F. Capitani, Bound excited states in density-functional theory, Phys. Rev. A, 23: 2127 (1981).

    Article  Google Scholar 

  26. O. Gunnarsson and B. I. Lundqvist, Exchange and correlation in atoms, molecules, and solids by the spin-density functional formalism, Phys. Rev. B 13: 4274 (1976).

    Article  Google Scholar 

  27. S. M. Valone, A one-to-one mapping between one-particle densities and some n-particle ensembles, J. Chem. Phys. 73:4653 (1980); S. M. Valone, Consequences of extending 1 matrix energy functions from pure-state representable to all ensemble representable 1 matrices, J. Chem. Phys. 73: 1344 (1980).

    MathSciNet  ADS  Google Scholar 

  28. W. Kohn, “V-representability and density functional theory”, Phys. Rev. Lett. 51: 1596 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  29. H. Englisch and R. Englisch, V-representability in finite-dimensional space, unpublished. S.e also S. T. Epstein and C. M. Rosenthal, The Hohenberg-Kohn theorem, J. Chem. Phys. 64:247 (1976); J. Katriel, C. J. Appelof, and E. R. Davidson, Mapping between local potentials and ground state densities, Int. J. Quantum Chem. 19: 293 (1981).

    Google Scholar 

  30. J. T. Chayes, L. Chayes, and E. H. Lieb, The inverse problem in classical statistical mechanics, unpublished manuscript.

    Google Scholar 

  31. D. C. Langreth and J. P. Perdew, The exchange-correlation energy of a metallic surface, Solid State Commun. 17:1425 (1975); Exchange-correlation energy of a metallic surface: wave-vector analysis, Phys. Rev. B 15: 2884 (1977).

    Article  Google Scholar 

  32. C. 0. Almbladh, Technical Report, University of Lund (1972).

    Google Scholar 

  33. U. von Barth and L. Hedin, A local exchange-correlation potential for the spin-polarized case I, J. Phys. C 5: 1629 (1972).

    Article  ADS  Google Scholar 

  34. A. K. Rajagopal and J. Callaway, Inhomogeneous electron gas, Phys. Rev. B 7:1912 (1973). See also A. K. Rajagopal, Adv. in Chem. Phys. 41:59 (1980).

    Google Scholar 

  35. J. F. Capitani, R. F. Nalewajski, and R. G. Parr, Non-BornOppenheimer density functional theory of molecular systems, J. Chem. Phys. 76: 568 (1982).

    Article  ADS  Google Scholar 

  36. A. K. Rajagopal, A density functional formalism for condensed matter systems, chapter in this book.

    Google Scholar 

  37. L. J. Bartolotti, Time-dependent extension of the HohenbergKohn-Levy energy-density functional, Phys. Rev. A 24: 1661 (1982).

    Article  MathSciNet  Google Scholar 

  38. Erich Runge and E.K.U. Gross, Phys. Rev. Lett. 52: 997 (1984).

    Article  ADS  Google Scholar 

  39. H. Stoll and A. Savin, Density functionals for correlation energies of atoms and molecules, chapter in this book, and references within.

    Google Scholar 

  40. G. A. Henderson, Variational theorems for the single-particle probability density and density-matrix in momentum space, Phys. Rev. A 23: 19 (1981).

    Article  Google Scholar 

  41. R. N. Pathak, P. V. Panat, and S. R. Gadre, Local-density functional model for atoms in momentum space, Phys. Rev. A 26: 3073 (1982).

    Article  Google Scholar 

  42. G. E. W. Bauer, unpublished. See also G. E. W. Bauer, General operator ground-state expectation values in the Hohenberg-Kohn-Sham density-functional formalism, Phys. Rev. B 27: 5912 (1983).

    Google Scholar 

  43. J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz, Jr., Density-functional theory for fractional particle number: Derivative discontinuities of the energy, Phys. Rev. Lett. 49: 1691 (1982).

    Article  ADS  Google Scholar 

  44. R. G. Parr, R. A. Donnelly, M. Levy, and W. E. Palke, Electronegativity: The density functional viewpoint, J. Chem. Phys. 68: 3801 (1978).

    Article  ADS  Google Scholar 

  45. R. G Parr and L. J. Bartolotti, Some remarks on the density functional theory of few electron systems, J. Phys. Chem. 87: 2810 (1983).

    Article  Google Scholar 

  46. C.-O. Almbladh and U. von Barth, Exact results for the charge and spin densities, exchange-correlation potentials, and density-functional eigenvalues, unpublished manuscript (1983). See also chapter in this book; C.-0. Almbladh and A. C. Pedroza, unpublished manuscript (1983).

    Google Scholar 

  47. J. P. Perdew and M. Levy, Density functional theory for open systems, in “Many-Body Phenomena at Surfaces”, D. C. Langreth and H. Suhl, eds., Academic, in press.

    Google Scholar 

  48. J. P. Perdew and M. Levy, Physical content of the exact Kohn-Sham orbital energies: Band gaps and derivative discontinuities, Phys. Rev. Lett. 51: 1884 (1983); L. S. Sham and M. Schluter, Density functional theory of the energy gap, Phys. Rev. Lett. 51: 1888 (1983).

    ADS  Google Scholar 

  49. M. Levy, On long-range behavior and ionization potentials, technical report, University of North Carolina, Chapel Hill (1975).

    Google Scholar 

  50. J. P. Perdew, What do the Rohn-Sham orbital energies mean? How do atoms dissociate?, chapter in this book.

    Google Scholar 

  51. M. Levy, J. P. Perdew, and V. Sahni, Exact differential equation for the density of a many-particle system, unpublished manuscript (1983). This manuscript contains an extensive discussion and a convincing theorem which states that the Rohn-Sham effective potential tends asymptotically to zero. See also references 14, 22, 43, and 46–50.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departments of Chemistry and Physics, Tulane University, New Orleans, Louisiana, 70118, USA

    Mel Levy & John P. Perdew

Authors
  1. Mel Levy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John P. Perdew
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Theoretical Physics, Johann Wolfgang Goethe University, Frankfurt/Main, Federal Republic of Germany

    Reiner M. Dreizler

  2. Department of Physics, University of Coimbra, Coimbra, Portugal

    João da Providência

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Plenum Press, New York

About this chapter

Cite this chapter

Levy, M., Perdew, J.P. (1985). The Constrained Search Formulation of Density Functional Theory. In: Dreizler, R.M., da Providência, J. (eds) Density Functional Methods In Physics. NATO ASI Series, vol 123. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0818-9_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-0818-9_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-0820-2

  • Online ISBN: 978-1-4757-0818-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation