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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
/content/aip/journal/jcp/138/13/10.1063/1.4798641
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/13/10.1063/1.4798641

Figures

Image of FIG. 1.
FIG. 1.

(a) Potential function of Eq. (2.1) for different values of the force parameter f. (b) Locations of the equilibrium points of the 1 DoF Hamiltonian (2.1) as a function of the force parameter  f.

Image of FIG. 2.
FIG. 2.

Definition of “external” (space-fixed) coordinates (x 1, x 2) and “internal” (bond) coordinates (r 1, r 2) for the n = 2 atom Morse chain.

Image of FIG. 3.
FIG. 3.

(a) Contour plot of the potential energy surface for the n = 2 Morse chain with f = 0.1. (b) Energies of the different equilibria as a function of the force parameter f.

Image of FIG. 4.
FIG. 4.

Schematic representation of the dynamics in the two saddle planes in physical normal form coordinates.

Image of FIG. 5.
FIG. 5.

Schematic representation of the EDS in the case of an index 1 saddle. (a) Positive energy and positive saddle action. (b) Positive energy and saddle action positive or negative. (c) Negative energy.

Image of FIG. 6.
FIG. 6.

Toroidal representation of the extended dividing surface.

Image of FIG. 7.
FIG. 7.

Potential energy contours and projections of eigenvectors obtained by linearizing Hamilton's equations about the equilibrium point EP4.

Image of FIG. 8.
FIG. 8.

Subsets of the EDS, labelled by symbol codes ( f 1+ ; i 1−). (a) (++; +−). (b) (++; −−). (c) (−+; +−). (d) (−+; −−).

Image of FIG. 9.
FIG. 9.

Subsets of the EDS ( f 1+ ; i 1+). (a) (++; −+). (b) (−+; ++).

Image of FIG. 10.
FIG. 10.

Subsets of EDS ( f 1− ; i 1+). (a) (+−; ++). (b) (+−; −+). (c) (−−; ++). (d) (−−; −+).

Image of FIG. 11.
FIG. 11.

Subsets of EDS ( f 1− ; i 1−). (a) (+−; −−). (b) (−−; +−).

Image of FIG. 12.
FIG. 12.

(a) Trajectory type as a function of location along the 1D cut of the EDS: Q 1 = 0.2, P 1 ∈ [−0.35; 0.0], E = 0.03. (b) Magnified segment showing the appearance of type 2 trajectories at the boundary between type 11 and 12.

Image of FIG. 13.
FIG. 13.

EDS subsets ( f 1+ ; i 1−). (a) (++; +−). (b) (−+; −−).

Image of FIG. 14.
FIG. 14.

EDS subsets ( f 1+ ; i 1+). (a) (++; −+). (b) (−+; ++). (c) (++; ++). (d) (−+; −+).

Image of FIG. 15.
FIG. 15.

EDS subsets ( f 1− ; i 1+). (a) (+−; ++). (b) (−−; −+).

Image of FIG. 16.
FIG. 16.

EDS subsets ( f 1− ; i 1−). (a) (+−; +−). (b) (+−; −−). (c) (−−; +−). (d) (−−; −−).

Image of FIG. 17.
FIG. 17.

Global representation of the EDS using the toroidal representation. Energy E = −0.03.

Image of FIG. 18.
FIG. 18.

(a) Trajectory type as a function of location along the 1D cut of the EDS: Q 1 = 0, P 1 ∈ [−0.1; 0.1], E = −0.03. (b) Trajectory exit time s in time units along the cut.

Image of FIG. 19.
FIG. 19.

(a) and (b) Examples of trajectories exhibiting the phenomenon of “bond healing.”

Tables

Generic image for table
Table I.

Pascal's triangle structure of the indices of the different saddles (k) depending on the number of particles in the chain (n). Index 0 means a stable center (well).

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/content/aip/journal/jcp/138/13/10.1063/1.4798641
2013-04-05
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Bond breaking in a Morse chain under tension: Fragmentation patterns, higher index saddles, and bond healing
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/13/10.1063/1.4798641
10.1063/1.4798641
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