Hamiltonian approach to the dissociation of a coupled nonlinear exciton-vibron system

We study the dissociation dynamics of polyatomic molecules using a Hamiltonian approach. Our model system consists of two molecular units, each having one electronic or vibrational state. An excitation is transferred between these two states with transfer matrix elements that depend on the intermolecular distance. The coupling with the intramolecular vibrations is included approximately through a cubic nonlinearity term while the intermolecular oscillations take place in a Morse potential. Dissociation in this model is a direct outcome of the coupling between the excitonic and vibrational subsystems leading to an energy exchange between the two. For small values of the transfer matrix elements we use the Melnikov function approach and show analytically the presence of homoclinic chaos in the system leading to dissociation for some bond configurations. The initial state preparation can drastically alter the dissociation process. We find that excitonic delocalization leads to enhanced dissociation rates. For larger intersite matrix elements we use the Chirikov overlap criterion to predict the onset of global phase space stochasticity, leading to dissociation for most bond lengths. The coupling to the intramolecular vibrations is seen to have an important effect on the dissociation phenomenon.