The Douglas-Kroll-Hess Approach

The Douglas Kroll (DK) approach decouples the large and small components of the Dirac spinors in the presence of an external potential by repeating several unitary transformations. The DK transformation correct to second order in the external potential has been extensively studied by Hess and co-workers. To reduce the computational effort for evaluating the full SO Hamiltonian, several approximations have been proposed. Hess et al. introduced a pseudo-one-electron Fock-type SO operator based on a mean-field (MF) approximation to the full SO Hamiltonian. The spinorbit eigenstates are obtained by the diagonalization of the spinorbit Hamiltonian over a basis consisting of all the spin components of wave functions constructed using the spin-free eigenstates. Melo et al. applied the DK approximation to the calculation of NMR spinspin couplings. The first- and second-order DK transformed Hamiltonians of the magnetic interaction terms were derived following Fukuda et al.