Two-component relativistic methods for the heaviest elements

Different generalized Douglas-Kroll transformed Hamiltonians (DKn, n=1, 2,…,5) proposed recently by Hess et al. are investigated with respect to their performance in calculations of the spin–orbit splittings. The results are compared with those obtained in the exact infinite-order two-component (IOTC) formalism which is fully equivalent to the four-component Dirac approach. This is a comprehensive investigation of the ability of approximate DKn methods to correctly predict the spin–orbit splittings. On comparing the DKn results with the IOTC (Dirac) data one finds that the calculated spin–orbit splittings are systematically improved with the increasing order of the DK approximation. However, even the highest-order approximate two-component DK5 scheme shows certain deficiencies with respect to the treatment of the spin–orbit coupling terms in very heavy systems. The meaning of the removal of the spin-dependent terms in the so-called spin-free (scalar) relativistic methods for many-electron systems is discussed and a computational investigation of the performance of the spin-free DKn and IOTC methods for many-electron Hamiltonians is carried out. It is argued that the spin-free IOTC rather than the Dirac-Coulomb results give the appropriate reference for other spin-free schemes which are based on approximate two-component Hamiltonians. This is illustrated by calculations of spin-free DKn and IOTC total energies, r−1 expectation values, ionization potentials, and electron affinities of heavy atomic systems.