Effective-mode analysis of the dynamics of weakly bound molecular systems by an example of hydrogen-bonded water clusters

Abstract

A method for the analysis of internal dynamics of nonlinear weakly bound polymolecular systems based on the effective-mode approach is proposed. The method enables one to estimate the number of the governing collective degrees of freedom of the system of interest at a preset accuracy under particular conditions and analyze the character of the modes depending on the activation energy of the system and the duration of its dynamic propagation, which provides qualitative and quantitative information about the coupling of diverse motions and the respective energy redistribution. The method is applied to the analysis of the dynamics of small water clusters stabilized by hydrogen bonds, which are unique spectacular examples of the systems with a pronounced coupling between the intramolecular and substantially delocalized intermolecular oscillations. The dynamic trajectories were generated in the adiabatic approximation at the Born-Oppenheimer level with the use of the quantum chemical description of selected clusters at the $\mathrm{MP}2/6\ensuremath{-}311++G(d,p)$ level. The initial conditions corresponded to different variants of the excitation of low-frequency normal modes, and the dynamic runs were carried out at a time step of 0.5 fs and the whole duration of 50 to 100 ps. Different prevailing characters of the cluster dynamics were identified depending on the molecular size, the total activation energy, and the mean potential-energy-increment to kinetic-energy-increment ratio, from an efficient accumulation of the excess kinetic energy on the effective modes of the cluster to the dissociation of the cluster into constituting fragments. The signs of the corresponding processes in the overlap matrices of the effective-mode vectors, kinetic-energy distribution over the modes, and the correlation between the number of the modes and the mean kinetic energy of the cluster are distinguished.