Bond breaking in a Morse chain under tension: Fragmentation patterns, higher index saddles, and bond healing

Abstract

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 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 fragmentation patterns for the n = 2 chain under tension. That is, we investigate the relative probability for breaking one bond versus concerted fission of several (two, in this case) bonds. 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 multiple 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 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.

Roaming: A Phase Space Perspective

“…These are relevant to reaction dynamics (see, for example, 10, 54-56). More recently, index-two (57-59) and higher-index (60) saddles have also been studied (see [61][62][63].…”

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone

“…35 There is even richer variety of phase space structures and invariant manifolds associated with index two saddles of the potential energy surface, and their implications for reaction dynamics have begun to be explored. 27,31,32 Fundamental theorems assure the existence of these phase space structures and invariant manifolds for a range of energy above that of the saddle. 34 However, the precise extent of this range, as well as the nature and consequences of any bifurcations of the phase space structures and invariant manifolds that might occur as energy is increased, is not known and is a topic of continuing research.…”

“…More recently, index two [26][27][28] and higher index 29 saddles have been studied (see also Refs. [30][31][32].…”

Model studies of force-dependent kinetics of multi-barrier reactions

“…Such force-dependent reactivity is thought to account for the behaviour of polymeric materials, melts and solutions under load, may be exploited to yield new stress-responsive, actuating and energy transducing materials [1][2][3][4][5][6][7][8][9][10] and may even allow characterization of transition states. 11 Considerable theoretical, 3,[12][13][14][15][16][17][18][19] computational 13,[20][21][22][23][24][25][26] and experimental [27][28][29][30][31][32][33][34] effort has been devoted to refine and validate a model of forcedependent kinetics for elementary (single-barrier) reactions. Yet many reactions proceed through one or more intermediates, that is, multiple activation barriers separate the reactant(s) from the product(s).…”