Study of the phase space structure for a two-degrees of freedom model of a symmetric glycosidic linkage

Classical dynamics calculations have been carried out on a two-degrees of freedom model Hamiltonian representing the symmetric glycosidic linkage of β,β-trehalose. The Hamiltonian depends on coordinates Φ and Φ′ and their conjugate momenta, where Φ and Φ′ are the torsional angles M-C-1-O-1-C-1′ and M′-C-1′-O-1-C-1 defined by the carbon and oxygen atoms of the glycosidic linkage and by pseudo-atoms M and M′ representing the effect of the pyranose rings. We have employed a simplified potential function reproducing the major features of molecular mechanics results in the literature. All relevant initial conditions for energy values ranging up to the energy of rotation have been tried. Results have been examined by considering the plots Φ(t) and Φ′(t), the trajectories in the configuration space (Φ,Φ′) for single initial conditions, and the Poincaré Surfaces of Sections, which describe the behavior of the system in the phase space, for all initial conditions at fixed energy.