Cellulose and the twofold screw axis: modeling and experimental arguments

Crystallography indicates that molecules in crystalline cellulose either have twofold screw-axis (2(1)) symmetry or closely approximate it, leading to short distances between H4 and H1' across the glycosidic linkage. Therefore, modeling studies of cellobiose often show elevated energies for 2(1) structures, and experimental observations are often interpreted in terms of intramolecular strain. Also, some computer models of cellulose crystallites have an overall twist as well as twisted individual chains, again violating 2(1) symmetry. To gain insight on the question of inherent strain in 2(1) structures, modeling was employed and crystal structures of small molecules were surveyed. (Residues in a disaccharide cannot be related by 2(1) symmetry because they are not identical but if their linkage geometry would lead to 2(1) symmetry for an infinite cellulose chain, the disaccharide would have 2(1) pseudo symmetry.) Several initial structures in quantum mechanics (QM) studies of cellobiose minimized to structures having 2(1) pseudo symmetry. Similarly, a number of relevant small molecules in experimental crystal structures have pseudo symmetry. While the QM models of cellobiose with 2(1) pseudo symmetry had inter-residue hydrogen bonding, the experimental studies included cellotriose undecaacetate, a molecule that cannot form conventional hydrogen bonds. Limitations in characterizing symmetry based on the linkage torsion angles I center dot and psi were also explored. It is concluded that 2(1) structures have little intrinsic strain, despite indications from empirical models.