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Index k saddles and dividing surfaces in phase space with applications to isomerization dynamics
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10.1063/1.3602465
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Affiliations:
1 School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom
2 Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
3 School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom
a) Electronic mail: gse1@cornell.edu.
b) Electronic mail: stephen.wiggins@mac.com.
J. Chem. Phys. 134, 244105 (2011)
/content/aip/journal/jcp/134/24/10.1063/1.3602465
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/24/10.1063/1.3602465
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## Figures

FIG. 1.

Schematic representation of sequential versus concerted isomerizing pathways in a model 4-well potential. (a) Sequential. (b) Concerted.

FIG. 2.

Projections of the index 2 saddle phase space extended dividing surface, parameter values λ1 = 1, , E = 1.0, with 0 ⩽ R ⩽ 1. (a) Coordinates (, , ). (b) Coordinates (, , ). (c) Coordinates (, , ). (d) Coordinates (, , ).

FIG. 3.

Projections of the index 2 saddle phase space dividing surface with the constraints (4.5), parameter values λ1 = 1, , E = 1.0. (a) Coordinates (, , ). (b) Coordinates (, , ). (c) Coordinates (, , ). (d) Coordinates (, , ).

FIG. 4.

Projections of the portion of the index 2 saddle phase space dividing surface associated with trajectories of symbolic type ++ − −. Parameter values λ1 = 1, , E = 1.0. (a) Coordinates (, , ). (b) Coordinates (, , ).

FIG. 5.

Trajectories initiated on the DS and propagated forwards and backwards in time. Saddle energy is 0.01. (a) Concerted crossing trajectories ( + +; − − ). (b) Concerted crossing trajectories ( + −; − + ). (c) Non-CC trajectories ( + −; − − ), I 2 < 0. (d) Non-CC trajectories ( + +; − + ), I 2 < 0.

FIG. 6.

Trajectories initiated on the DS and propagated forwards and backwards in time. Saddle energy is 0.1. (a) Concerted crossing trajectories ( + +; − − ). (b) Concerted crossing trajectories ( + −; − + ). (c) Non-CC trajectories ( + −; − − ), I 2 < 0. (d) Non-CC trajectories ( + +; − + ), I 2 < 0.

FIG. 7.

Trajectories initiated on the DS and propagated forwards and backwards in time. Saddle energy is 0.5. (a) Concerted crossing trajectories ( + +; − − ). (b) Concerted crossing trajectories ( + −; − + ). (c) Non-CC trajectories ( + −; − − ), I 2 < 0. (d) Non-CC trajectories ( + +; − + ), I 2 < 0.

FIG. 8.

Segment of the boundary between CC and non-CC trajectories defined by the condition I 2 = 0. Crosses indicate configuration space projections of boundary points with 0 ⩽ R ⩽ 0.1 and E = 0.01. Each phase point on the boundary is propagated forwards and backwards in time.

FIG. 9.

Fraction F of crossing trajectories for initial conditions at constant energy in the plane with . NF predictions (green line) are show together with results obtained from integration of trajectories (red line). (a) E = 0.01, (b) E = 0.1, (c) E = 0.5.

FIG. 10.

Trajectories initiated on the DS and propagated forwards and backwards in time. Total energy E = 0.1. Bath coupling parameter c 1 = c 2 = 0.1. (a) Concerted crossing trajectories ( + +; − − ). (b) Concerted crossing trajectories ( + −; − + ). (c) Non-CC trajectories ( + −; − − ), I 2 < 0. (d) Non-CC trajectories ( + +; − + ), I 2 < 0.

FIG. 11.

Trajectories initiated on the DS and propagated forwards and backwards in time. Total energy E = 0.1. Bath coupling parameter c 1 = c 2 = 0.5. (a) Concerted crossing trajectories ( + +; − − ). (b) Concerted crossing trajectories ( + −; − + ). (c) Non-CC trajectories ( + −; − − ), I 2 < 0. (d) Non-CC trajectories ( + +; − + ), I 2 < 0.

/content/aip/journal/jcp/134/24/10.1063/1.3602465
2011-06-23
2014-04-21

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