\textit{Ab Initio} Theory of Nuclear Magnetic Resonance Shifts in Metals

A comprehensive approach for the first-principles determination of all-electron NMR shifts in metallic systems is presented. Our formulation is based on a combination of density-functional perturbation theory and all-electron wavefunction reconstruction, starting from periodic-boundary calculations in the pseudopotential approximation. The orbital contribution to the NMR shift (the chemical shift) is obtained by combining the gauge-including projector augmented-wave approach (GIPAW), originally developed for the case of insulators\footnote{C.~J.~Pickard, Francesco Mauri, Phys.~Rev.~B, {\bf 63}, 245101(2001)}, with the extension of linear-response theory to the case of metallic systems\footnote{S.~{de Gironcoli}, Phys.~Rev.~B, {\bf 51}, 6773(1995)}. The spin contribution (the Knight shift) is obtained as a response to a finite uniform magnetic field, and through reconstructing the hyperfine interaction between the electron-spin density and the nuclear spins with the projector augmented-wave method (PAW\footnote{C.~G.~{Van de Walle}, P.~E.~Bl\"ochl, Phys.~Rev.~B, {\bf 47}, 4244(1993)}). Our method is validated with applications to the case of the homogeneous electron gas and of simple metals. (Work supported by MURI grant DAAD 19-03-1-0169 and MIT-France)