Quantum mechanics studies of cellobiose conformations

Abstract

Three regions of the conformation space that describes the relative orientations of the two glucose residues of cellobiose were analyzed with quantum mechanics. A central region, in which most crystal structures are found, was covered by a 9 × 9 grid of 20° increments of the linkage torsion angles ϕ and ψ. Besides these 81 constrained minimizations, we studied two central subregions and two regions at the edges of our maps of complete ϕ,ψ space with unconstrained minimization, for a total of 85 target geometries. HF/6-31G(d) and single-point HF/6-311+G(d) calculations were used to find the lowest energies for each geometry. B3LYP/6-31G+G(d) and single point B3LYP/6-11+G(d) calculations were also used for all unconstrained minimizations. For each target, 181 starting geometries were tried (155 for the unconstrained targets). Numerous different starting geometries resulted in the lowest energies for the various target structures. The starting geometries came from five different sets that were based on molecular mechanics energies. Although all five sets contributed to the adiabatic map, use of any single set resulted in discrepancies of 3–7 kcal/mol (1 cal = 4.184 J) with the final map. For most of the targets, the starting geometry that gave the lowest energy depended on the basis set and whether the HF or B3LYP method was used. However, each of the above four calculations gave the same overall lowest energy structure that was found previously by Strati et al. This global minimum, stabilized by highly cooperative hydrogen bonds, is in a region that is essentially not populated by crystal structures. HF/6-31G(d) energy contours of the mapped central region were compatible with the observed crystal structures. Observed structures that lacked O3···O5′ hydrogen bonds were about 1 kcal/mol above the map's minimum, and observed structures that have a pseudo twofold screw axis ranged from about 0.4 to 1.0 kcal/mol. The HF/6-311+G(d) map accommodated the observed structures nearly as well.Key words: cellulose, carbohydrate, conformation, energy, flexibility, folding, helix, shape.