Relativistic Correction for Analytic Hartree-Fock Wave Functions

The relativistic energy associated with the closed-shell ground states of the atoms of the first three rows of the periodic table is computed by perturbation methods for recently obtained Hartree-Fock functions. The computations are extended to the isoelectronic series of the 2, 4, 10, 12, and 18 electron atoms with closed-shell configurations. The analysis of the data obtained reveals that, (1) different Hartree-Fock functions for a given atom give about the same relativistic energy provided the number of basis functions are about the same, (2) the contribution to the relativistic energy from electrons of a given subshell is approximately a constant, independent of the number of electrons in the outer shells, (3) the empirical estimate of the relativistic energy agrees with our theoretical computation within a few percent except for low $Z$ where the disagreement is only slightly larger.