e-mail:Francesco.Mauri@lmcp.jussieu.fr

I present a theory for the ab initio calculation of all-electron magnetic response in molecules and solids with pseudopotentials [C. J. Pickard, F. Mauri, Phys. Rev. B 63, 245101 (2001)]. So far, derivations of pseudopotential Hamiltonians have not dealt with magnetic fields. To correctly describe the interaction between orbital degrees of freedom and magnetic fields within a pseudopotential approach, we introduce an extension of Blochl's Projector Augmented-Wave (PAW) method, that we call the Gauge Including Projector Augmented-Wave (GIPAW) approach. Contrary to the original PAW formalism, the GIPAW method is invariant upon translation in presence of a constant magnetic field. Using GIPAW i) we derive a pseudo-Hamiltonian in presence of a constant magnetic field, ii) we compute the linear perturbation of pseudo-wavefunctions with respect to a constant magnetic field, iii) we reconstruct the induced all-electron current from the perturbed pseudo-wavefunctions. Finally, the knowledge of the induced all-electron current allows us to compute the induced magnetic field at the nuclear positions, which defines the NMR chemical shifts. We successfully validate our theory by comparison with all-electron results. With respect to previous all-electron approaches, we can treat for the first time extended systems; moreover, the efficiency of the plane-wave pseudopotential scheme allows us to deal with systems of hundreds of atoms (including heavy elements) with a very manageable computational cost. I will illustrate the method with applications to porphyrins, and to icosahedral boron carbide [F. Mauri, N. Vast, and C. J. Pickard, Phys. Rev. Lett. 87, 085506 (2001)}.