Quantal Density Functional Theory of the Density Amplitude

  • Viraht Sahni


In quantal density functional theory (Q-DFT) and Kohn-Sham density functional theory (KS-DFT), the basic idea is the construction of the model S system of N noninteracting Fermions whereby the density ρ(r) and total energy E equivalent to that of the interacting electronic system is obtained. In Q-DFT, both the total energy E and the local electron-interaction potential energy υ ee(r) of the model Fermions, are defined in terms of fields and quantal sources. The potential energy υ ee(r) is the work done to move the Fermion in a conservative field. The components of the total energy E are expressed in integral virial form in terms of fields associated with these components. In time-independent KS-DFT, the energy E is expressed in terms of component energy functionals of the ground state density ρ(r). The potential energy υ ee(r) of the model Fermions is then defined as the functional derivative of the KS electron-interaction energy functional component. Irrespective of the definition of the potential energy employed to generate the Fermion orbitals, the S system differential equation must be solved N times to obtain the density ρ(r).


Potential Energy Ground State Energy Interact System Schrodinger Equation Functional Derivative 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Levy, J.P. Perdew, and V. Sahni, Phys. Rev. A 30, 2745 (1984)ADSCrossRefGoogle Scholar
  2. 2.
    See N.H. March, Electron Density Theory of Atoms and Molecules,Academic Press, London, 1992, and references thereinGoogle Scholar
  3. 3.
    J.P. Perdew, R.G. Parr, M. Levy, and J.L. Balduz, Phys. Rev. Lett. 49, 161 (1982)CrossRefGoogle Scholar
  4. 4.
    N.H. March and A.M. Murray, Proc. Roy. Soc. A256, 400 (1960)MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    N.H. March, Phys. Lett. 113A, 66 (1985); 113A, 476 (1986)Google Scholar
  6. 6.
    B.M. Deb and S.K. Ghosh, Int. J. Quantum Chem. 23, 1 (1983)CrossRefGoogle Scholar
  7. 7.
    C.F. von Weizsäcker, Z. Phys. 96, 431 (1935)MATHCrossRefGoogle Scholar
  8. 8.
    M. Levy and H. Ou—Yang, Phys. Rev. A 38, 625 (1988)CrossRefGoogle Scholar
  9. 9.
    G. Hunter, Int. J. Quantum Chem. 9, 237 (1975); ibid. 29, 197 (1986)Google Scholar
  10. 10.
    A. Holas and N.H. March, Phys. Rev. A 44, 5521 (1991)ADSCrossRefGoogle Scholar
  11. 11.
    X.Y. Pan and V. Sahni, Phys. Rev. A 67, 012 501 (2003)Google Scholar
  12. 12.
    Z. Qian and V. Sahni, Int. J. Quantum Chem. 79, 205 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Viraht Sahni
    • 1
  1. 1.Department of PhysicsBrooklyn College and the Graduate School of the City University of New YorkBrooklyn, New YorkUSA

Personalised recommendations