  The resolving power of solid-state nuclear magnetic resonance (NMR)
crystallography depends heavily on the accuracy of computational predictions of
NMR chemical shieldings of candidate structures, which are usually taken to be
local minima in the potential energy. To test the limits of this approximation,
we systematically study the importance of finite-temperature and quantum
nuclear fluctuations for $^1$H, $^{13}$C, and $^{15}$N shieldings in polymorphs
of three paradigmatic molecular crystals -- benzene, glycine, and succinic
acid. The effect of quantum fluctuations is comparable to the typical errors of
shielding predictions for static nuclei with respect to experiments, and their
inclusion to improve the agreement with measurements, translating to more
reliable assignment of the NMR spectra to the correct candidate structure. The
use of integrated machine-learning models, trained on first-principles energies
and shieldings, renders rigorous sampling of nuclear fluctuations affordable,
setting a new standard for the calculations underlying NMR structure
determinations.
