Relativistic corrections to magnetic properties

Relativistic corrections to magnetic properties (in principle to all orders in c−1) are derived at a one-electron level. We start from the Dirac equation in a magnetic field and use direct perturbation theory (DPT). Thus, the singularities of methods based on the Foldy–Wouthuysen transformation are avoided. The nondegenerate case (where to zeroth order one must use a perturbation adapted nonrelativistic wave function) and the quasidegenerate case (which leads to effective Hamiltonians) are treated. The final results can be expressed on different levels: in terms of four-component spinors; in terms of two-component spinors representing the upper (large) and lower (small) components; and with complete elimination of the lower components, making use of the turnover rule that has to be understood in the distribution sense. Special attention is given to the magnetic susceptibilities and the NMR chemical shift.