Converging nuclear magnetic shielding calculations with respect to basis and system size in protein systems

Ab initio chemical shielding calculations greatly facilitate the interpretation of nuclear magnetic resonance (NMR) chemical shifts in biological systems, but the large sizes of these systems requires approximations in the chemical models used to represent them. Achieving good convergence in the predicted chemical shieldings is necessary before one can unravel how other complex structural and dynamical factors affect the NMR measurements. Here, we investigate how to balance trade-offs between using a better basis set or a larger cluster model for predicting the chemical shieldings of the substrates in two representative examples of protein-substrate systems involving different domains in tryptophan synthase: the N-(4'-trifluoromethoxybenzoyl)-2-aminoethyl phosphate (F9) ligand which binds in the α active site, and the 2-aminophenol quinonoid intermediate formed in the β active site. We first demonstrate that a chemically intuitive three-layer, locally dense basis model that uses a large basis on the substrate, a medium triple-zeta basis to describe its hydrogen-bonding partners and/or surrounding van der Waals cavity, and a crude basis set for more distant atoms provides chemical shieldings in good agreement with much more expensive large basis calculations. Second, long-range quantum mechanical interactions are important, and one can accurately estimate them as a small-basis correction to larger-basis calculations on a smaller cluster. The combination of these approaches enables one to perform density functional theory NMR chemical shift calculations in protein systems that are well-converged with respect to both basis set and cluster size.