First-Principles Calculation of ¹⁷O, ²⁹Si, and ²³Na NMR Spectra of Sodium Silicate Crystals and Glasses

This paper presents results of first-principles calculations of nuclear magnetic resonance (NMR) parameters: the chemical shielding tensor and the electric field gradient tensor, of some crystalline and amorphous sodium silicate systems. The calculations have been performed using the recently introduced gauge including projector augmented wave (GIPAW) method, which was especially devised for periodic systems. It provides an attractive alternative to the cluster approximation, used in the previous NMR theoretical studies of silicates systems. Moreover, within the GIPAW formalism, amorphous systems can be efficiently described via a supercell approach as demonstrated in this work. Five reference crystalline compounds of known structure (α-quartz, α-cristobalite SiO 2, and the sodium silicates Na 2 SiO 3, α-Na 2 Si 2 O 5, and β-Na 2 Si 2 O 5 ) and two molecular dynamics models of the sodium tetrasilicate glass Na 2 Si 4 O 9 (NS4) have been studied. The NS4 glass models were generated by a combination of classical and Car-Parrinello molecular dynamics simulations. The good agreement of the simulated 29 Si MAS NMR and 17 O, 23 Na 3Q-MAS NMR spectra with the corresponding experimental data demonstrates the accuracy of the GIPAW method. Using these numerically generated data, we have also been able to gain insight into the correlation between NMR parameters and local structural features.