Fermi and Coulomb correlated relativistic local-density method for atoms

A parameter-free local-density method called the Ξ method was developed earlier for atoms [N. Vaidehi and M. S. Gopinathan, Phys. Rev. A 29, 1679 (1984)]. This method, which considered only the Fermi correlation in the potential, was shown to be close to Hartree-Fock accuracy. Its relativistic extension [V. Selvaraj and M. S. Gopinathan, Phys. Rev. A 29, 3007 (1984)] was also shown to give results that were close to Dirac-Hartree-Fock accuracy. In the present article, the relativistic Ξ method is modified by incorporating the spin-orbit interaction term in the Hamiltonian and the Coulomb correlation between the electrons of opposite spin. Using this fully correlated relativistic method, total energy, expectation values of $r^n$ (n=-1,1,2), and spin-orbit parameters for various atoms are calculated. Correlation energies for all the atoms in the Periodic Table are reported. Ionization energy and electron affinity of atoms are also discussed.