We present a study of molecular crystals, focused on
the effect
of nuclear quantum motion and anharmonicity on their electronic properties.
We consider a system composed of relatively rigid molecules, a diamondoid
crystal, and one composed of floppier molecules, NAI-DMAC, a thermally
activated delayed fluorescence compound. We compute fundamental electronic
gaps at the density functional theory (DFT) level of theory, with
the Perdew–Burke–Erzenhof (PBE) and strongly constrained
and approximately normed (SCAN) functionals, by coupling first-principles
molecular dynamics with a nuclear quantum thermostat. We find a sizable
zero-point renormalization (ZPR) of the band gaps, which is much larger
in the case of diamondoids (0.6 eV) than for NAI-DMAC (0.22 eV). We
show that the frozen phonon (FP) approximation, which neglects intermolecular
anharmonic effects, leads to a large error (∼50%) in the calculation
of the band gap ZPR. Instead, when using a stochastic method, we obtain
results in good agreement with those of our quantum simulations for
the diamondoid crystal. However, the agreement is worse for NAI-DMAC
where intramolecular anharmonicities contribute to the ZPR. Our results
highlight the importance of accurately including nuclear and anharmonic
quantum effects to predict the electronic properties of molecular
crystals.