Orbital magnetism and chemical shielding in the projector augmented-wave formalism

We show how to compute the orbital magnetization, as the first-order change of the energy due to an homogeneous magnetic field, within the projector augmented-wave (PAW) formalism of density functional theory, for systems with periodic boundary conditions. To accomplish this, magnetic translation symmetry is invoked together with a perturbative treatment of the density operator, yielding well-posed expressions that account fully for all PAW terms. The terms may be computed in a standard PAW implementation using density functional perturbation theory to compute the necessary wave-function derivatives, rather than the finite-difference approach that has been used previously. In order to obtain nontrivial magnetization, we also impose nuclear magnetic dipole moments on atomic sites of interest, which gives direct access to the chemical shielding, as measured in nuclear magnetic resonance spectroscopy. The resulting expressions have been implemented and tested, and results are shown both for atoms and solids.