B3LYP/6-311++G** study of monohydrates of alpha- and beta-D-glucopyranose: hydrogen bonding, stress energies, and effect of hydration on internal coordinates

Twenty-six monohydrates of alpha- and beta-D-glucopyranose were studied using gradient methods at the B3LYP/6-311++G** level of theory. Geometry optimization was carried out with the water molecules at different configurations around the glucose molecule. A new nomenclature for hydrated carbohydrates was developed to describe the water configurations. Zero-point vibrational energy, enthalpy, entropy, and relative free energy were obtained using the harmonic approximation. Hydrogen-bond energies for the monohydrates range from approximately -5 to -12 kcal/mol, and the average relative free energy is approximately 5 kcal/mol. The 1-hydroxy position is the most energetically favored site for hydration, and the region between the two and three positions is the next-most favored site. A water molecule approaching alpha-D-glucose between the 1- and 2-hydroxy positions pulls the 2-hydroxyl hydrogen atom away from the 1-hydroxy oxygen atom, thus increasing the hydrogen-bond length and also increasing the alpha-D-glucose energy. The increase in energy that occurs with a similar interaction on the beta-anomer is much less effective since the hydrogen bond is much longer. Using the calculated free energies of all 26 configurations, the anomer population (alpha/beta) increases in the beta-anomer population relative to the in vacuo case by approximately 10% at the expense of the alpha-anomer, giving an (alpha/beta) ratio of approximately 50/50. This result arises from entropy contributions favoring the beta-anomer more than the alpha-anomer. From analysis of donor and acceptor hydrogen-bond lengths, excellent correlation is found between the DFT calculated distances and those taken from carbohydrate structures in the Cambridge Crystallographic Data Bank.