Journal of Chemical Sciences

, Volume 96, Issue 3–4, pp 231–239 | Cite as

Improved Z-dependence of the ground-state energies of neutral atoms

  • P K Chattaraj
  • A Mukherjee
  • M P Das
  • B M Deb


Threesimulated expressions are suggested regarding the Z-dependence of groundstate energies of neutral atoms at the Hartree-Fock, exact nonrelativistic and relativistic levels. The Hartree-Fock-level Z−1/3-expansion contains three previously derivedplus two newly derived terms, the latter signifying exchange corrections from the ‘inner core’ and the ‘core mantle’ of the Lieb atom. This leads to better agreement than any previous expression, with every coefficient being physically transparent. The Z-dependence of the correlation energy is obtained from a semiempirical Wigner-type correlation potential while the relativistic correction is taken to be in between the values suggested separately by Scott and Schwinger. Agreement with reference values is again better than before. It appears, however, that the atomic Z−1/3-expansion should not proceed beyond terms O(Z).


Z−1/3-expansion atomic binding energy Thomas-Fermi theory exchange correlation energy single-particle density 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aguilera-Navarro V C, de Llano M, Rojo O and Verardi S L L 1982J. Chem. Phys. 77 6131CrossRefGoogle Scholar
  2. Ballinger R A and March N H 1955Philos. Mag. 46 246Google Scholar
  3. Bander M 1982Ann. Phys. 144 1CrossRefGoogle Scholar
  4. Brual G and Rothstein S M 1978J. Chem. Phys 69 1177CrossRefGoogle Scholar
  5. Ceperley D M and Alder B J 1978Phys. Rev. B18 3126Google Scholar
  6. Ceperley D M and Alder B J 1980Phys. Rev. Lett 45 566CrossRefGoogle Scholar
  7. Clementi E and Roetti C 1974At. Data Nucl, Data Tables 14 177CrossRefGoogle Scholar
  8. Conlon J G 1983J. Math. Phys 24 184CrossRefGoogle Scholar
  9. Cowan R D 1981The theory of atomic structure and spectra (Berkeley: Univ. of California Press) p. 205Google Scholar
  10. Csavinszky P and Vosman F 1983Int. J. Quantum Chem. 23 1973CrossRefGoogle Scholar
  11. Desclaux J P 1973At. Data Nucl. Data Tables 12 311CrossRefGoogle Scholar
  12. Dirac P A M 1930Proc. Cambridge Philos. Soc. 26 376Google Scholar
  13. Dmitrieva J K and Plindov G I 1975Phys. Lett. A55 3CrossRefGoogle Scholar
  14. Gross E K U and Dreizler R M 1981Z. Phys. A302 103Google Scholar
  15. Hernandez E and Gazquez J L 1982Phys. Rev. A25 107CrossRefGoogle Scholar
  16. Kohn W and Sham L J 1965Phys. Rev. 140 A1133CrossRefGoogle Scholar
  17. Lieb E H 1976Rev. Mod. Phys. 48 553CrossRefGoogle Scholar
  18. Lieb E H 1981Rev. Mod. Phys. 53 603CrossRefGoogle Scholar
  19. Lieb E H and Simon B 1977Adv. Math. 23 22CrossRefGoogle Scholar
  20. March N H 1953Philos. Mag. 44 1193Google Scholar
  21. March N H 1957Adv. Phys. 6 1Google Scholar
  22. March N H and Parr R G 1980Proc. Natl. Acad. Sci. USA 77 6285CrossRefGoogle Scholar
  23. March N H and Plaskett J S 1956Proc. R. Soc. London A235 419CrossRefGoogle Scholar
  24. McWean A D and McLean R S 1981At. Data Nuel. Data Tables 26 197CrossRefGoogle Scholar
  25. McWeeny R 1976 inThe new world of quantum chemistry (eds) B Pullman and R G Parr (Dordrecht: D Reidel) p. 27Google Scholar
  26. Schwinger J 1980Phys. Rev. A22 1827CrossRefGoogle Scholar
  27. Schwinger J 1981Phys. Rev. A24 2353CrossRefGoogle Scholar
  28. Scott J M C 1952Philos. Mag. 43 859Google Scholar
  29. Shakeshaft R and Spruch L 1981Phys. Rev. A23 2118CrossRefGoogle Scholar
  30. Shakeshaft R, Spruch L and Mann J B 1981J. Phys. B14 L121Google Scholar
  31. Shih C C 1976Phys. Rev. A14 919CrossRefGoogle Scholar
  32. Shih C C 1980J. Chem. Phys. 72 1404CrossRefGoogle Scholar
  33. Shih C C, Murphy D R and Wang W P 1980J. Chem. Phys. 73 1340CrossRefGoogle Scholar
  34. Tal Y and Bartolotti L J 1982J. Chem. Phys. 76 4056CrossRefGoogle Scholar
  35. Tal Y and Levy M 1981Phys. Rev. A23 408CrossRefGoogle Scholar
  36. Veillard A and Clementi E 1968J. Chem. Phys. 49 2415CrossRefGoogle Scholar
  37. Vosko S H, Wilk L and Nusair M 1980Can. J. Phys. 58 1200CrossRefGoogle Scholar
  38. Wilk L, Nusair M and Vosko S H 1981Can. J. Phys. 59 585Google Scholar

Copyright information

© Indian Academy of Sciences 1986

Authors and Affiliations

  • P K Chattaraj
    • 1
  • A Mukherjee
    • 2
  • M P Das
    • 3
  • B M Deb
    • 1
  1. 1.Department of ChemistryPanjab UniversityChandigarhIndia
  2. 2.Department of PhysicsIndian Institute of TechnologyKanpurIndia
  3. 3.Department of PhysicsSambalpur UniversityBurlaIndia

Personalised recommendations