Calculation of NMR chemical shifts for extended systems using ultrasoft pseudopotentials

We present a scheme for the calculation of magnetic response parameters in insulators using ultrasoft pseudopotentials. It uses the gauge-including projector augmented wave method [C. J. Pickard and F. Mauri, Phys. Rev. B 63, 245101 (2001)] to obtain all-electron accuracy for both finite and infinitely periodic systems. We consider in detail the calculation of NMR chemical shieldings. The approach is successfully validated first for molecular systems by comparing calculated chemical shieldings for a range of molecules with quantum chemistry results and then in the solid state by comparing ${}^{17}\mathrm{O}$ NMR parameters calculated for silicates with experiment.

Figure 1

(Color online) Isotropic chemical shielding for nuclear sites in a range of molecules (Ref. 35). The graphs show shieldings obtained with the GIPAW-USP method plotted against all-electron shielding (Ref. 30). The straight line represents perfect agreement. The upper figure (a) shows the contribution without GIPAW augmentation $({\sigma }_{\text{bare}}+{\sigma }_{\text{core}})$; the lower figure (b) plots the total contribution.

Figure 2

Convergence with plan-ewave cutoff energy of the ${}^{17}\mathrm{O}$ isotropic chemical shielding in a $\mathrm{O}\text{−}{\left(\mathrm{Si}{\mathrm{H}}_3\right)}_2$ cluster derived from the $\alpha$-quartz structure. The all-electron result is taken from Ref. 15.