Journal of Advances in Applied Physics

Download PDF (226.6 KB) PP. 20 - 25 Pub. Date: May 1, 2020

DOI: 10.22606/jaap.2020.22002

• Eric Ouma Jobunga^*
  Department of Mathematics and Physics, Technical Univeristy of Mombasa, P. O. Box 90420-80100, Mombasa, Kenya

Electron-electron correlation forms the basis of difficulties encountered in multi-electron systems. Accurate treatment of the correlation problem is likely to unravel some nice physical properties of matter embedded in this correlation. In an effort to tackle this multi-electron problem, two complementary parameter-free pseudopotentials for n-electron atoms are suggested in this study. Using one of the pseudopotentials, near-exact values of the groundstate ionization energies of helium, lithium, and berrylium atoms have been calculated. The other pseudopotential also proves to be capable of yielding reasonable and reliable ionization energies within the non-relativistic quantum mechanics framework.

Electron-electron interaction, electron correlation, pseudopotential, multipole expansion.

[1] N. M. Hugenholtz, “Quantum theory of many-body systems,” Reports on Progress in Physics, vol. 28, no. 1, p. 201, 1965.

[2] S. Verdebout, P. Rynkun, P. Jönsson, G. Gaigalas, C. F. Fischer, and M. Godefroid, “A partitioned correlation function interaction approach for describing electron correlation in atoms,” Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 46, no. 8, p. 085003, 2013.

[3] W. Tobocman, “Many-body perturbation theory,” Phys. Rev., vol. 107, pp. 203–208, Jul 1957.

[4] D. Cremer, “From configuration interaction to coupled cluster theory: The quadratic configuration interaction approach,” Wiley Interdisciplinary Reviews: Computational Molecular Science, vol. 3, no. 5, pp. 482–503, 2013.

[5] W. Kohn and L. J. Sham, “Self-consistent equations including exchange and correlation effects,” Phys. Rev., vol. 140, pp. A1133–A1138, Nov 1965.

[6] C. J. Cramer, Essentials of Computational Chemistry. Chichester: John Wiley and Sons, Inc, 2002.

[7] E. A. Hylleraas, “Neue berechnung der energie des heliums im grundzustande, sowie des tiefsten terms von ortho-helium,” Zeitschrift für Physik, vol. 54, no. 5, pp. 347–366, 1929.

[8] M. L. Cohen, “Application of the pseudopotential model to solids,” Ann. Rev. Mater. Sci, vol. 14, pp. 119–144, 1984.

[9] J. J. Hellmann, “A new approximation method in the problem of many electrons,” J. Chem Phys, vol. 3, p. 61, 1935.

[10] J. Callaway and P. S. Laghos, “Application of the pseudopotential method to atomic scattering,” Physical Review, vol. 187, no. 1, pp. 192–200, 1969.

[11] E. O. Jobunga, “Alternative multipole expansion of the electron correlation term,” arXiv, p. 1704.02009, 2017.

[12] E. O. Jobunga and S. O. Okeyo, “Mutipole expansion of the powers of a cosine of a function,” Research Gate, Preprint (DOI: 10.13140/RG.2.2.12877.08166/1), 2018.

[13] E. O. Jobunga, “Partitioning of the electron correlation energy,” arXiv, p. 1708.04061, 2017. 14. B. H. Bransden and C. J. Joachain, Physics of atoms and molecules. Essex: Longman Scientific & Technical, 1990. 15. NIST, “Physical data for atoms and ions,” http://www.physics.nist.gov/PhysRefData/Handbook/Tables, 2020. 16. Angelfire, “Lithium configuration and energies,” http://www.angelfire.com, 2017.