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

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10.1063/1.4798641

### 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.

© 2013 American Institute of Physics

Received 11 December 2012
Accepted 15 March 2013
Published online 05 April 2013

Acknowledgments: F.A.L.M., P.C., and S.W. acknowledge the support of the Office of Naval Research (Grant No. N00014-01-1-0769) and the Leverhulme Trust.

Article outline:

I. INTRODUCTION

II. MORSE OSCILLATOR CHAIN UNDER TENSION: HAMILTONIAN AND EQUILIBRIA

A. One particle Morse chain

B. *n*-particle Morse chain under tension

III. PHASE SPACE STRUCTURE AND DYNAMICS IN A NEIGHBORHOOD OF THE INDEX 2 SADDLE

A. The normal form

B. Phase space structures in normal form coordinates

1. Crossing and non-crossing trajectories

2. Dividing surfaces, extended dividing surfaces, and NHIMs

IV. SINGLE VERSUS MULTIPLE BOND FISSION FOR THE *n* = 2 CHAIN

A. General considerations

B. Results

1. Energy above the index 2 saddle

2. Energy below the index 2 saddle and “bond healing”

V. CONCLUSIONS AND PERSPECTIVES

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2014-04-16

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