A Basis Size Dependence Study of Carbon-13 Nuclear Magnetic Resonance Spectroscopic Shielding in Alanyl and Valyl Fragments: Toward Protein Shielding Hypersurfaces

We have investigated the effects of basis set quality on the accuracy and speed of ab initio calculations of C^α, C^β chemical shifts (or shieldings) of alanine and valine residues in proteins. Five basis set combinations were studied: a uniform 3-21G and a 4-31G/3-21G “locally dense” basis, both producing 88 contracted functions; a 6-311G+(2d)/3-21G and a 6-311G+(2d)/6-31G basis, each giving a total of 108 contracted functions; and a uniform STO-3G basis, giving 48 contracted functions. We find that results obtained by using small Gaussian basis sets correlate well with calculations performed using very large (6-311G++(2d,2p)/6-31G) basis sets, with only changes in slope and offset being required in order to bring results into excellent agreement, while the time necessary for the calculations is significantly reduced. This marked decrease in computational time using small, locally dense basis sets has permitted the first calculation of a three-dimensional chemical shielding hypersurface for valine. Chemical shifts predicted by using the ϕ,ψ, χ¹ shielding hypersurface are in good accord with chemical shift values determined experimentally. These results open up new opportunities for the relatively rapid evaluation of amino acid shielding hypersurfaces for future use in protein structure prediction and refinement.