Ab initio effective core potentials including relativistic effects. I. Formalism and applications to the Xe and Au atoms

An effective core potential system has been developed for heavy atoms in which relativistic effects are included in the effective potentials (EP). The EP’s are based on numerical Dirac–Hartree–Fock calculations for atoms and on the Phillips–Kleinman transformation with other aspects similar to the treatments of Goddard and Melius and Kahn, Baybutt, and Truhlar. The EP’s may be written U^EP=Σ_l Σ_j=*l−1/2*^l+1/2 Σ_m=−j^j U_lj^EP(r) ‖ljm≳<ljm‖, where ‖ljm≳ is a two‐component angular basis function that is a product of a two‐component Pauli spinor and spherical harmonics. The numerical functions U_lj^EP(r) are approximated as expansions in terms of Gaussian or exponential functions. The use of these EP’s enables one to use the jj‐coupling scheme for subsequent applications in all‐valence‐electron calculations on heavy atoms and their molecules. A standard atomic SCF program has been modified to accommodate these EP’s and Gaussian and exponential basis sets having the proper j angular dependence. Energy levels for many atomic states of Xe and Au were calculated. The study of Xe excited states indicates that the spin–orbit splittings are reasonably approximated and that the numerical DHF calculations are adequately reproduced. Au has been treated as an atom with 1, 11, 17, 19, or 33 valence electrons to investigate the effects of redefinition of the core.