Radial and Electron Correlation Effects for Helium and Some Helium Like Ions

  • Khalil H. AL-bayati
  • Esraa F. Saeed


The radial and electronic correlation effects for intra-electronic shell have been examined within two-electron system, helium atom, and compared with two helium like ions, Li+ and Be++ using the uncorrelated Hartree Fock wave function published by Clementi and Rotti (At Data Nucl Data Tables 14:177, 1974) and the correlated configuration interaction wave function published by Weiss (Phys Rev 122:1826, 1961). Some atomic properties have been studied to exam the radial correlation effects such as; (i) one-particle radial distribution function and one-particle expectation value when k=−2 to 2, (ii) two-particle radial distribution function and two-particle expectation value when k=−2 to 2, (iii) the inter-particle distribution function and inter-particle expectation value when k=−2 to 2, and, (iv) the partial distribution function. In addition to these atomic properties, coulomb hole, partial coulomb hole, the radial correlation for one and two-particles distribution function and the radial correlation energy are very important in studying the physical and chemical properties of these ions or atoms. The results were compared with that calculated in previous published work using partitioning technique.


Radial Distribution Function Configuration Interaction Correlate Wave Function Radial Correlation Coulomb Hole 
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.


  1. 1.
    Roothaan CCJ, Sachs L, Weiss AW (1960) Rev Mod Phys 32(2):186CrossRefGoogle Scholar
  2. 2.
    Weiss AW (1961) Phys Rev 122:1826CrossRefGoogle Scholar
  3. 3.
    Banyard KE (1968) J Chem Phys 48:2121CrossRefGoogle Scholar
  4. 4.
    Baker CC, Banyard KE (1969) Phys Rev 188:57–62CrossRefGoogle Scholar
  5. 5.
    AL-Khafaji KS (2005) A study of correction function to Hartree-Fock orbitals derived from correlated wave function. PhD thesis, Al-Mustansiriyah university, Baghdad, IraqGoogle Scholar
  6. 6.
    Coulson CA, Neilson AH (1961) Proc Phys Soc 78:831CrossRefGoogle Scholar
  7. 7.
    Curl RF, Coulson CA (1965) Proc Phys Soc 85:647CrossRefGoogle Scholar
  8. 8.
    Banyard KE, Seddon GJ (1973) J Chem Phys 58(3):1132CrossRefGoogle Scholar
  9. 9.
    Seddon GJ, Banyard KE (1973) J Chem Phys 59:572CrossRefGoogle Scholar
  10. 10.
    Boyd RJ (1975) J Chem Phys 53:592Google Scholar
  11. 11.
    Aman Alla SM (2007) Electron correlation for many atomic and ionic system. MSc thesis, College of Education (Ibn AL-Haitham). University of Baghdad, Baghdad, IraqGoogle Scholar
  12. 12.
    AL-Robayi EM (2002) A study of Coulomb hole for the ground state in momentum space for He-like and Li-like ions. MSc thesis, College of Education (Ibn AL-Haitham), University of Baghdad, Bagdad, IraqGoogle Scholar
  13. 13.
    Shalhoub GM (1997) Properties of radial wave function, 2nd edn. New YorkGoogle Scholar
  14. 14.
    Lopez EP (1995) Physical chemistry: a practical approach. Williamstown, p 99Google Scholar
  15. 15.
    Avery J (1980) The quantum theory of atoms, molecules, and photons. Mc Graw Hill, New YorkGoogle Scholar
  16. 16.
    Wiess AW (1963) J Chem Phys 39:1262Google Scholar
  17. 17.
    Clementi E, Roetti J (1974) Roothaan-Hartree-Fock atomic wave functions: basis functions and their coefficients for ground and certain excited states of neutral and ionized atoms, Z >= 54. At Data Nucl Data Tables 14:177CrossRefGoogle Scholar
  18. 18.
    AL-Tamimei NC (2005) Calculation of effect of electronic correlation force on the energy of some atoms. MSc thesis, College of Science for Women, Baghdad University, Baghdad, IraqGoogle Scholar
  19. 19.
    McWeeny R, Sutcliffe BT (1969) Method of molecular quantum mechanics. Academic, New YorkGoogle Scholar
  20. 20.
    Banyard KE, Mobbs RJ (1981) Coulomb hole and correlation coefficients for electronic shells: a comparative analysis of several wave functions for be. J Chem Phys 75(7):3433CrossRefGoogle Scholar
  21. 21.
    Banyard KE, Al-Bayati KH (1986) J Phys B At Mol Phys 19:2211CrossRefGoogle Scholar
  22. 22.
    AL-Meshhedany WA (2006) A study for nuclear magnetic shielding constant for Z = 2 to10. MSc thesis, College of Science, Nahrain university, Baghdad, IraqGoogle Scholar
  23. 23.
    Banyard KE, Baker CC (1969) Analysis of electron correlation in two-electron system. I, H−, He and Li. J Chem Phys 51:2680CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Physics, College of Science for WomenBaghdad UniversityBaghdadIraq
  2. 2.Department of Physics, College of ScienceHahrain UniversityBaghdadIraq

Personalised recommendations