DFT Optimization of Isolated Molecular Chain Sheet Models Constituting Native Cellulose Crystal Structures

Because of high crystallinity and natural abundance, the crystal structures of the native cellulose allomorphs have been theoretically investigated to elucidate the cellulose chain packing schemes. Here, we report systematic structure optimization of cellulose chain sheet models isolated from the cellulose Iα and Iβ crystals by density functional theory (DFT). For each allomorph, the three-dimensional chain packing structure was partitioned along each of the three main crystal planes to construct either a flat chain sheet model or two stacked chain sheet models, each consisting of four cello-octamers. Various combinations of the basis set and DFT functional were investigated. The flat chain sheet models constituting the cellulose Iα (110) and Iβ (100) planes, where the cellulose chains are mainly linked by intermolecular hydrogen bonds, exhibit a right-handed twist. More uniform and symmetrical sheet twists are observed when the flat chain sheet models are optimized using a basis set with diffuse functions (6-31+G(d,p)). The intermolecular interactions are more stable when the chain sheet models are optimized with the two hybrid functionals CAM-B3LYP and M06-2X. Optimization of the two stacked chain sheet models, where van der Waals interactions predominated between adjacent chains, gave differing results; those retaining the initial structures and those losing the sheet appearance, corresponding to the cellulose Iα/Iβ (010)/(11̅0) and (100)/(110) chain sheet models, respectively. The cellulose Iβ (11̅0) chain sheet model is more stable using the M06-2X functional than using the CAM-B3LYP functional.