Refining Crystal Structures with Quadrupolar NMR and Dispersion-Corrected Density Functional Theory

Nuclear electric
field gradient (EFG) tensors obtained from solid-state
NMR spectroscopy are highly responsive to variations in structural
features. The orientations and principal components of EFG tensors
show great variation between different molecular structures; hence,
extraction of EFG tensor parameters, either experimentally or computationally,
provides a powerful means for structure determination and refinement.
Here, dispersion-corrected plane-wave density functional theory (DFT)
is used to refine atomic coordinates in organic crystals determined
initially through single-crystal X-ray diffraction (XRD) or neutron
diffraction methods. To accomplish this, an empirical parametrization
of a two-body dispersion force field is illustrated, in which comparisons
of experimental and calculated 14N, 17O, and 35Cl EFG tensor parameters are used to assess the quality of
energy-minimized structures. The parametrization is based on a training
set of 17 organic solids. The analysis is applied subsequently to
the structural refinements of structural models from over 60 different
materials. For the prediction of 35Cl EFG tensor parameters
in particular, the optimization protocols described herein lead to
a substantial improvement in agreement with experiment relative to
structures obtained by XRD methods or by refinement with plane-wave
DFT without the inclusion of the force field. The results further
demonstrate that crystal structures with atomic coordinates refined
with the present methods are able to pinpoint the positions of hydrogen
atoms participating in H···Cl– hydrogen
bonding with a higher degree of precision than is possible through
neutron diffraction. This methodology, which is facile to implement
within most DFT software packages, should prove to be very useful
for future structural refinements using NMR crystallographic methods.