Effect of Dynamical Motion in ab Initio Calculations of Solid-State Nuclear Magnetic and Nuclear Quadrupole Resonance Spectra

Solid-state nuclear magnetic resonance (SSNMR) and nuclear quadrupole resonance (NQR) spectra provide detailed information about the electronic and atomic structure of solids. Modern ab initio methods such as density functional theory (DFT) can be used to calculate NMR and NQR spectra from first-principles, providing a meaningful avenue to connect theory and experiment. Prediction of SSNMR and NQR spectra from DFT relies on accurate calculation of the electric field gradient (EFG) tensor associated with the potential of electrons at the nuclear centers. While static calculations of EFGs are commonly seen in the literature, the effects of dynamical motion of atoms in molecules and solids have been less explored. In this study, we develop a method to calculate EFGs of solids while taking into account the dynamics of atoms through DFT-based molecular dynamics simulations. The method we develop is general, in the sense that it can be applied to any material at any desired temperature and pressure. Here, we focus on application of the method to NaNO2 and study in detail the EFGs of N-14, O-17, and Na-23. We find in the cases of N-14 and O-17 that the dynamical motion of the atoms can be used to calculate mean EFGs that are in closer agreement with experiments than those of static calculations. For Na-23, we find a complex behavior of the EFGs when atomic motion is incorporated that is not at all captured in static calculations. In particular, we find a distribution of EFGs that is influenced strongly by the local (changing) bond environment, with a pattern that reflects the coordination structure of Na-23. We expect the methodology developed here to provide a path forward for understanding materials in which static EFG calculations do not align with experiments.