Calculating NMR chemical shifts using the augmented plane-wave method

Density functional theory (DFT) calculations of the magnetic shielding for solid state nuclear magnetic resonance (NMR) provide an important contribution for the understanding of the experimentally observed chemical shifts. Therefore, methods allowing us to compute those parameters with high precision are very valuable. Recently, we have presented a formalism for computing the NMR parameters in solids based on the augmented plane wave (APW) method [Phys. Rev. B 85, 035132 (2012)]. In the present work we derive an improvement of the original schema, which greatly boosts its precision and efficiency. Although the APW method is virtually an exact method for the ground state wave functions in a solid, its optimized basis set is incomplete and we need to extend it by including basis functions containing the radial derivative of the standard APW basis functions in order to efficiently describe the perturbation due to a magnetic field. In addition we also include the core states in the first-order perturbation formula correcting an error resulting from separation of the core and valence states. These allow us to obtain the NMR parameters that are nearly numerically exact within a given DFT functional.