Ordered and chaotic dynamics of collective variables in a butane molecule

We have simulated the dynamics of a butane molecule and computed the time evolution of two sets of collective variables: (a) internal variables (stretchings, bendings, and dihedral angle) and (b) variables derived from a principal component analysis (PCA). We have characterized each collective variable by a coherence time, the time needed to develop its chaotic behavior. The coherence times diminish significantly when the temperature is raised into and above the range where conformational transitions of the dihedral angle set in. Below this transition region the coherence times of some variables reach hundreds of picoseconds (principal components) or even nanoseconds (internal variables); moreover, there are large differences among variables, as their coherence time can be much larger or much smaller than the Lyapunov time of the whole molecule. This result reflects the prediction of Nekhoroshev’s theorem. Crossing the transition region, the coherence times of both sets of variables drop to few picoseconds, and the differences among variables diminish. Still, the coordinates and velocities characterized by the largest fluctuations in the PCA appear to be also the most coherent ones, below and above the transition region.