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The relativistic Hartree-Fock-Roothaan equation for closed-shell configurations of atoms is derived. The relativistic Hamiltonian consists of the sum of the Dirac Hamiltonians and the interelectronic Coulomb repulsion terms. The atomic wave function is assumed to be an antisymmetrized product of 4-component orbitals whose radial functions are expanded in terms of the Slater-type basis functions. The Breit interaction operator is used as the relativistic interelectronic interaction term, and is treated as the first-order perturbation. Expressions for the matrix elements of the Breit interaction operator are given for the closed-shell configurations. Numerical results for the ground states of He, Be, and Ne atoms computed according to this formalism are also presented.
Yong‐Ki Kim (Sun,) studied this question.