Relativistic effects on atomic orbitals across the periodic table: insights from spin-separated Dirac–Coulomb–Breit Hamiltonian

Neutral closed-shell atoms across the periodic table (Be, Mg, Ca, Sr, Ba, Ra, Ne, Ar, Kr, Xe, Rn, Zn, Cd, Hg, Cn, Yb, and No) were investigated with spin-separated Dirac-Coulomb (DC), Dirac-Coulomb-Gaunt (DCG), and Dirac-Coulomb-Breit (DCB) Hamiltonians. Focus was given to changes in orbital characteristics such as energy, radial expectation value, and radial distribution function upon changing relativistic Hamiltonian. We find that both Hamiltonian substitutions of an exact 2-component (X2C) with the 4-component DC and of DC with DCG can produce large shifts (>0.1 eV) for all occupied orbitals of heavy elements-even for scalar-relativistic Hamiltonians. Substitution of DCG with DCB yields large energy changes in deep- to shallow-core orbitals. Based on our findings, a cancellation of error is likely to occur for f orbitals of p-, d-, and f-block atoms, where the scalar-relativistic DC to DCG substitution is similar in magnitude but opposite in sign with the sum of X2C to DC and DCG to DCB substitutions. For radial expectation values and radial distribution functions of orbitals, we find no significant changes (>0.01 bohr) for (scalar-relativistic) DC to DCG or DCG to DCB substitutions.