Evaluation of Density Functionals and Basis Sets for Carbohydrates

Correlated ab initio wave function calculations using MP2/aug-cc-pVTZ model chemistry have been performed for three test sets of gas phase saccharide conformations to provide reference values for their relative energies. The test sets consist of 15 conformers of α- and β-d-allopyranose, 15 of 3,6-anhydro-4-O-methyl-d-galactitol, and four of β-d-glucopyranose. For each set, conformational energies varied by about 7 kcal/mol. Results obtained with the Hartree-Fock method, with pure density functional approximations (DFAs) like LSDA, PBEsol, PBE, and TPSS and with hybrid DFAs like B3PW91, B3LYP, PBEh, and M05-2X, were then compared to the reference and local MP2 relative energies. Basis sets included 6-31G*, 6-31G**, 6-31+G*, 6-31+G**, 6-311+G**, 6-311++G**, cc-pVTZ(-f), cc-pVTZ, and aug-cc-pVTZ(-f). The smallest basis set that gives good DFA relative energies is 6-31+G**, and more converged results can be obtained with 6-311+G**. The optimized geometries obtained from a smaller basis set, 6-31+G*, were useful for subsequent single point energy calculations with larger basis sets. The best agreement with MP2 was shown by M05-2X, but only when using a dense DFT grid. The popular B3LYP functional is not the best for saccharide conformational studies. The B3PW91 functional gives systematically better results, but other hybrid functionals like PBEh or TPSSh are even better. Overall, the nonempirical PBE GGA and TPSS meta-GGA functionals also performed better than B3LYP.