Combining double-hybrid functionals with rSCAN yields solid-state ¹³C chemical shifts with sub-ppm accuracy

Ab initio calculations of NMR shieldings are often used to assign spectra and help refine crystal structures in the growing field of NMR crystallography. In periodic calculations, GGA exchange-correlation functionals such as PBE and BLYP are most often used, but a "monomer correction" has recently been proposed that incorporates a "higher quality" treatment of local electronic structure into calculated shieldings. The meta-GGA functional rSCAN reportedly generates improved geometries, particularly in systems with important dispersion interactions, but has scarcely been tested for its performance in periodic shielding calculations, with or without monomer corrections. Here, the performance of rSCAN is evaluated by comparing experimental chemical shifts from 75 diverse ¹³C environments in 13 molecular solids, to chemical shifts calculated by rSCAN and PBE on geometries optimised by rSCAN, PBE and BLYP. We find rSCAN gives marginally improved geometries but produces less accurate chemical shifts than PBE. However, after a monomer correction is applied to the shieldings, corrected rSCAN consistently performs better than corrected PBE, indicating that rSCAN describes long-range contributions to shieldings more accurately than local effects. Monomer correction with a double-hybrid functional has previously been found to provide no additional benefit compared to correction with conventional hybrids. However, we show the double-hybrid mPW2PLYP predicts substantially improved chemical shifts when the monomer correction method is paired with an implicit solvation model, yielding better results than a correction with a cluster of molecules using a conventional hybrid functional. The method we find maximises agreement with experiment is a mPW2PLYP-CPCM correction to rSCAN periodic calculations on rSCAN-optimised geometries. When used on a larger set of organic crystals, with 132 ¹³C environments, this method yields unprecedented accuracy, with root-mean-square error of 0.8 ppm and mean absolute error of 0.6 ppm.