DFT study of alpha- and beta-D-mannopyranose at the B3LYP/6-311++G** level

Thirty-five conformations of alpha- and beta-d-mannopyranose, the C-2 substituted epimer of glucopyranose, were geometry optimized using the density functional (B3LYP), and basis set (6-311++G**). Full geometry optimization was performed on the hydroxymethyl rotamers (gg/gt/tg) and an analytical hessian program was used to calculate the harmonic vibrational frequencies, zero point energy, enthalpy, and entropy. The lowest energy conformation investigated is the beta-tg in the (4)C(1) chair conformation. The in vacuo calculations showed little energetic preference for either the alpha or beta anomer for mannopyranose in the (4)C(1) chair conformation. Results are compared to similar glucopyranose calculations in vacuo where the alpha anomer is approximately 1kcal/mol lower in electronic energy than the beta anomer. In the case of the generally higher energy (1)C(4) chair conformations, one low-energy, low-entropy beta-gg-(1)C(4) chair conformation was identified that is within approximately 1.4kcal/mol of the lowest energy (4)C(1) conformation of mannopyranose. Other (1)C(4) chair conformations in our investigation are approximately 2.9-7.9kcal/mol higher in overall energy. Many of the (3,O)B, B(3,O), (1,4)B, and B(1,4) boat forms passed through transitions without barriers to (1)S(3), (5)S(1), (1)S(5) skew forms with energies between approximately 3.6 and 8.9kcal/mol higher in energy than the lowest energy conformation of mannopyranose. Boat forms were found that remained stable upon gradient optimization. As with glucopyranose, the orientation and interaction of the hydroxy groups make a significant contribution to the conformation/energy relationship in vacuo.