B3LYP/6-311++G** geometry-optimization study of pentahydrates of alpha- and beta-D-glucopyranose.

Five water molecules were placed in 37 different configurations around alpha- and beta-D-glucopyranose in the gt, gg, and tg conformational states, and the glucose-water complexes were geometry optimized using density functionals at the B3LYP/6-311++G** level of theory. The five water molecules were organized in space and energy minimized using an empirical potential, AMB02C, and then further geometry optimized using DFT algorithms to minimum energy positions. Electronic energy, zero point vibrational energy, enthalpy, entropy, stress energy on glucose and the water cluster, hydrogen-bond energy, and relative free energy were obtained for each configuration using thermodynamic procedures and an analytical Hessian program. The lowest energy complex was that of a clustering of water molecules around the 1- and 6-hydroxyl positions of the beta-gt anomer. Configurations in which the water molecules created a favorable network completely around and under glucose were found to have low energy for both alpha and beta anomers. Calculation of the alpha/beta anomeric ratio using the zero point corrected energy gave, approximately 32/68%, highly favoring the beta anomer in agreement with the experimental approximately 36/64% value. This ratio is better than the approximately 50/50% ratio found in our previous monohydrate study. An approximate hydroxymethyl population was obtained by noting average relative energies among the three conformational states, gt, gg, and tg. In the beta anomer complexes the gt conformation was favored over the gg state, while in the alpha anomer complexes the gg state was favored over the gt conformation, with the tg conformations all being of higher energy making little or no contribution to the rotamer population. Some geometry variances, found between glucose in vacuo and glucose after interaction with water molecules, are described and account for some observed C-5-C-6 bond length anomalies reported by us previously for the vacuum glucose structures.