A systematic study of the non-relativistic Hartree-Fock method and its relativistic version, Dirac-Fock method for the average of configuration have been presented. In the non-relativistic case, a fully derivation of the Hartree-Fock equations were presented and relativistic corrections (mass-velocity, Darwin and spin-orbit terms) are treated as first-order perturbation. For the relativistic case, Dirac-Fock equations were derived, and Breit interaction operator is used as the relativistic correction for the interelectronic Coulomb interaction, and is treated as the first-order perturbation. Expressions for the matrix elements of the Breit interaction operator (magnetic and retardation terms) are given for the average of configuration. Numerical results of some atomic properties for the ground states of (Rb, Zr, Pd, Sn, Cs, Ba, Lu, Ir, Hg, Tl, Bi, Rn ) atoms computed and compared with their corresponding experimental values. The relativistic effect on the orbital energies is important on the inner shells especially for the 1s and 2s shells and this effect becomes more pronounced as Z increases. The contribution of Breit interaction is about 2% of the relativistic shift (mass-velocity and Darwin correction). The Hartree-Fock calculations and relativistic correction gives reasonably good approximation for heavy atoms while Dirac-Fock calculation and Breit interaction gives high precision calculations.
