Conformational pathways of saturated six-membered rings. A static and dynamical density functional study.

The conformation of the six-membered ring of pyranosyl sugars has pronounced effects on the physical and chemical properties of carbohydrates. We present a method to determine key features of the potential energy surfaces, such as transition states associated with the inversion pathways of the model compounds cyclohexane, tetrahydropyran, p-dioxane, m-dioxane, s-trioxane, and 2-oxanol. Finally, we make the first determination of the pathways for inversion of penta-O-methyl-alpha-D-glucopyranose and penta-O-methyl-beta-D-glucopyranose. For both anomers, a transition state with five coplanar atoms with appreciable (O)E character was found. The method is based on constrained Car-Parrinello ab initio molecular dynamics, as implemented in the projector augmented-wave (PAW) method. The constraints are derived from the normal modes of six-membered rings and are described in terms of the canonical conformations (1)C(4) chair, (1,4)B boat, and (O)S(2) skew-boat. The PAW derived trajectories are in agreement with previous suggestions in the literature that pseudorotation is an important feature of such conformational interconversions. The dynamic nature as well as the internal coordinate-based constraints provide a method which can reliably accommodate pseudorotation. To determine semiquantitative energies, we recalculate key conformations using standard quantum mechanical calculations while keeping the ring dihedral angles frozen at their values found in the dynamics. In all cases where experimental barriers are known, our results are in excellent agreement.