Efficient Methods for the Quantum Chemical Treatment of Protein Structures: The Effects of London-Dispersion and Basis-Set Incompleteness on Peptide and Water-Cluster Geometries

We demonstrate how quantum chemical Hartree-Fock (HF) or density functional theory (DFT) optimizations with small basis sets of peptide and water cluster structures are decisively improved if London-dispersion effects, the basis-set-superposition error (BSSE), and other basis-set incompleteness errors are addressed. We concentrate on three empirical corrections to these problems advanced by Grimme and co-workers that lead to computational strategies that are both accurate and efficient. Our analysis encompasses a reoptimized version of Hobzas P26 set of tripeptide structures, a new test set of conformers of cysteine dimers, and isomers of the water hexamer. These systems reflect features commonly found in protein crystal structures. In all cases, we recommend Grimmes DFT-D3 correction for London-dispersion. We recommend usage of large basis sets such as cc-pVTZ whenever possible to reduce any BSSE effects and, if this is not possible, to use Grimmes gCP correction to account for BSSE when small basis sets are used. We demonstrate that S-S and C-S bond lengths are very prone to basis-set incompleteness and that polarization functions should always be used on S atoms. At the double-zeta level, the PW6B95-D3-gCP DFT method combined with the SVP and 6-31G* basis sets yields accurate results. Alternatively, the HF-D3-gCP/SV method is recommended, with inclusion of polarization functions for S atoms only. Minimal basis sets offer an intriguing route to highly efficient calculations, but due to significant basis-set incompleteness effects, calculated bond lengths are seriously overestimated, making applications to large proteins very difficult, but we show that Grimmes newest HF-3c correction overcomes this problem and so makes this computational strategy very attractive. Our results provide a useful guideline for future applications to the optimization, quantum refinement, and dynamics of large proteins.