Deciphering the NMR fingerprints of the disordered system with quantum chemical studies

Recent developments in solid-state NMR techniques helped acquire high-resolution NMR spectra for solid systems with structural disorder. But the structural origin of the observed chemical shift nonequivalence in these systems has not been revealed. We report a quantum chemical investigation of the solid-state NMR spectrum in N,N-bis(diphenylphosphino)-N-((S)-alpha-methylbenzyl)amine, where eight nonequivalent (31)P NMR chemical shifts were resolved with a range of 13.0 ppm. Results from using different quantum chemical methods, computational algorithms, intermolecular effects, and structures indicate that for the disordered system, geometry optimization gives the best accord with experimental NMR chemical shifts, which has a theory-versus-experiment correlation R(2) = 0.949 and SD = 1.1 ppm, or R(2) = 0.994 and SD = 0.4 ppm when the average of two unassigned NMR shifts for each molecule is used. In addition, these calculations indicate that the experimental chemical shift nonequivalence in this system is mainly a consequence of the different geometries around the phosphorus atoms due to disordered environments. The experimental (31)P NMR chemical shifts are well correlated (R(2) = 0.981) with two conformation angles and one bond length, each associated with one of the three bonding interactions around the phosphorus atoms. These results will facilitate the use of quantum chemical techniques in structural characterization of disordered solids and elucidation of NMR properties.