Examination of accuracy of electron–electron Coulomb interactions in two-component relativistic methods

We examined the accuracy of two-component quantum-chemical methods, focusing on relativistic treatments of the electron–electron Coulomb interaction. We observed SCF energies, orbital energies, and spin–orbit splittings of He-like and noble-gas atoms up to Uuo (atomic number 118). These were calculated by using either the two-electron term generated by the first-order Foldy–Wouthuysen (2e-FW1) or the infinite-order Douglas–Kroll–Hess (2e-IODKH) transformation, both of which are incorporated with the one-electron terms generated by the IODKH transformation. The 2e-FW1 term was much superior to the lowest-order (c−2) two-electron Breit–Pauli correction, and the 2e-IODKH term gave energies essentially equivalent to four-component Dirac–Fock/Coulomb energies.