Protein NMR chemical shift calculations based on the automated fragmentation QM/MM approach

An automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach has been developed to routinely calculate ab initio protein NMR chemical shielding constants. The AF-QM/MM method is linear-scaling and trivially parallel. A general fragmentation scheme is employed to generate each residue-centric region which is treated by quantum mechanics, and the environmental electrostatic field is described with molecular mechanics. The AF-QM/MM method shows good agreement with standard self-consistent field (SCF) calculations of the NMR chemical shieldings for the mini-protein Trp cage. The root-mean-square errors (RMSEs) for ¹H, ¹³C, and ¹⁵N NMR chemical shieldings are equal to or less than 0.09, 0.32, and 0.78 ppm, respectively, for all Hartree-Fock (HF) and density functional theory (DFT) calculations reported in this work. The environmental electrostatic potential is necessary to accurately reproduce the NMR chemical shieldings using the AF-QM/MM approach. The point-charge models provided by AMBER, AM1/CM2, PM3/CM1, and PM3/CM2 all effectively model the electrostatic field. The latter three point-charge models are generated via semiempirical linear-scaling SCF calculations of the entire protein system. The correlations between experimental ¹H NMR chemical shifts and theoretical predictions are >0.95 for AFQM/MM calculations using B3LYP with the 6-31G^**, 6-311G^**, and 6-311++G^** basis sets. Our study, not unexpectedly, finds that conformational changes within a protein structure play an important role in the accurate prediction of experimental NMR chemical shifts from theory.