The Calculation of NMR Chemical Shifts in Periodic Systems Based on Gauge Including Atomic Orbitals and Density Functional Theory

Abstract

We present here a method that can calculate NMR shielding tensors from first principles for systems with translational invariance. Our approach is based on Kohn-Sham density functional theory and gauge-including atomic orbitals. Our scheme determines the shielding tensor as the second derivative of the total electronic energy with respect to an external magnetic field and a nuclear magnetic moment. The induced current density due to a periodic perturbation from nuclear magnetic moments is obtained through numerical differentiation, whereas the influence of the responding perturbation in terms of the external magnetic field is evaluated analytically. The method is implemented into the periodic program BAND. It employs a Bloch basis set made up of Slater-type or numeric atomic orbitals and represents the Kohn-Sham potential fully without the use of effective core potentials. Results from calculations of NMR shielding constants based on the present approach are presented for isolated molecules as well as systems with one-, two- and three-dimensional periodicity. The reported values are compared to experiment and results from calculations on cluster models.

Probing nitrite ion dynamics in NaNO2 crystals by solid‐state 17O NMR

“…The final 17 O NMR tensor parameters for solid NaNO 2 are reported in Table . To obtain an independent confirmation about the 17 O NMR tensor orientations in the crystal lattice of NaNO 2 , we performed quantum chemical calculations using the periodic DFT code BAND . The computational results are also listed in Table .…”

“…Quantum chemical calculations of 17 O magnetic shielding and EFG tensors were performed with the periodic DFT code BAND within ADF Modeling Suite 2016 . The crystal structure of NaNO 2 was used as the starting structures for geometry optimization.…”

Chapter 2. Solid‐State NMR in Drug Discovery and Development

“…For example, calculations of s and V can be performed in a periodic system using Slater-type basis sets with the ADF-BAND package. 112,113 This package has extensive features for calculations of relativistic effects. The DMol3 package uses highly efficient numerical basis sets that enable EFG calculations on many large API crystal structures of interest, even though s and J cannot be calculated with this approach.…”

Relativistic calculations of magnetic resonance parameters: background and some recent developments

“…For the other systems, the chemical shifts obtained with hybrid and non-hybrid functionals were similar. It is noted in passing that a corresponding ZORA NMR shielding module for periodic solids, using Slater-type AO basis functions, has been implemented at the SF level [194].…”