Single versus double bond breakage in a Morse chain under tension: higher index saddles and bond healing

We investigate the fragmentation dynamics of an atomic chain under tensile stress. We have classified the location, stability type (indices) and energy of all equilibria for the general $n$-particle chain, and have highlighted the importance of saddle points with index $> 1$. We show that for an $n=2$-particle chain under tensile stress the index 2 saddle plays a central role in organizing the dynamics. We apply normal form theory to analyze phase space structure and dynamics in a neighborhood of the index 2 saddle. We define a phase dividing surface (DS) that enables us to classify trajectories passing through a neighborhood of the saddle point using the values of the integrals associated with the normal form. We also generalize our definition of the dividing surface and define an emph{extended dividing surface} (EDS), which is used to sample and classify all trajectories that pass through a phase space neighborhood of the index 2 saddle at total energies less than that of the saddle. Classical trajectory simulations are used to study single versus double bond breakage for the $n=2$ chain under tension. Initial conditions for trajectories are obtained by sampling the EDS at constant energy. We sample trajectories at fixed energies both above and below the energy of the saddle. The fate of trajectories (single versus double bond breakage) is explored as a function of the location of the initial condition on the EDS, and a connection made to the work of Chesnavich on collision-induced dissociation. A significant finding is that we can readily identify trajectories that exhibit bond emph{healing}. Such trajectories pass outside the nominal (index 1) transition state for single bond dissociation, but return to the potential well region, possibly several times, before ultimately dissociating.