Fluctuation, relaxation and rearrangement dynamics of a model (H2O)20 cluster: Non-statistical dynamical behavior

Relaxation phenomena in a model $({\mathrm{H}}_{\mathrm{2}}\mathrm{O}{)}_{\mathrm{20}}$ cluster are investigated by considering energy fluctuations and dielectric relaxation, making connections with the underlying hydrogen-bond rearrangement dynamics. In particular, we relate these effects to the potential energy surface, including rearrangement mechanisms, minimum energy pathways and normal mode excitations. The statistical behavior of structural transitions in this water cluster is also examined. The transition rates estimated from RRKM theory are compared with those obtained by molecular dynamics (MD) simulations. The RRKM rates are 1–3 orders of magnitude larger than the MD values and the difference is larger at low energy. To find the origin of this discrepancy, the mechanism of coupling among various modes is examined. We find that there is significant coupling only among a subset of the normal modes in the low energy dynamics. A modified statistical theory, assuming that only a subset of modes contributes to the reaction rate, reproduces the energy dependence of the MD transition rates quite well. It is also found that the energy fluctuations and dielectric relaxation are non-Debye in character, and instead exhibit so-called $\text{1/f}$ spectra.