Anyanninuola, O.S.Ewa, I.I.Umar, I.Liman, M.S.2023-12-142023-12-142016-08-28Adhikari SK 1998. Variational Principles for the Numerical Solution of Scattering Problems. New York: Wiley, pp. 56-75. Dill D 2006. Many-Electron Atoms: Fermi Holes and Fermi Heaps. Chapter 3.5, pp. 60-73. Doves R 1987. The Electronic Structure of -quartz: A periodic Hartree-Fock Calculatio. J. Chem. Phys, 86. Froese F 1997. The Hartree-Fock method for Atoms: A Numerical Approach. John Willey and Sons, New York, p. 109 Gray CG, Karl G & Novikov VA 1996. A General Method of Calculation for the STATIONARY STATES of any Molecular System. Proc. Roy. Soc. (London), pp. 542- 544. Gray CG, Karl G & Novikov VA 2003. Progress in Classical and Quantum Variational Principles. Physics/0312071 Classical Physics, pp. 120-124. Ismail K, Ikome T & Smith HI 1992. Quantum Effect, Physics Electronics and Applications, pp. 121-188. Levente S 1991. The Electronic Structure of Atoms, Physics Dept. Fordham University Bronx, New York, pp. 115-238https://keffi.nsuk.edu.ng/handle/20.500.14448/6012In this work, FORTTRAN program has been applied to evaluate the energy level of generally small atomic systems. The program was specifically directed to compute the Hartree-Fock equations. The ground state structures of small atomic systems are obtained using Hartree-Fock approximation. The total energies calculated for each of the state (1s, 2s, 2p) approximately agreed with those of experimental results as compared. Due to non-linearities introduced by Hartree-Fock approximation, the equations are solved using non-linear method such as iteration. The physical implication of this important finding has helped to identified clearly the parameter space accessible to the Hartree-Fock method.enAtom, energy density, electronic structure, hartree-fock, orbital, wave functionArticle