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

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