A periodic orbit formula for quantum reactions through transition states

A. Goussev; R. Schubert; H. Waalkens; S. Wiggins

doi:10.1063/1.3498119

A periodic orbit formula for quantum reactions through transition states

A. Goussev^*, R. Schubert, H. Waalkens, S. Wiggins

^*Corresponding author for this work

School of Mathematics & Physics

Research output: Contribution to journal › Conference article › peer-review

Abstract

Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized in phase space using an explicit algorithm. The quantization has been demonstrated to lead to an efficient procedure to compute cumulative reaction probabilities and the associated Gamov-Siegert resonances. These results are used here to derive a formula which expresses the cumulative reaction probability as an absolutely convergent sum over periodic orbits contained in the transition state.

Original language	English
Pages (from-to)	1593-1596
Number of pages	4
Journal	AIP Conference Proceedings
Volume	1281
DOIs	https://doi.org/10.1063/1.3498119
Publication status	Published - 17 Sept 2010
Event	International Conference on Numerical Analysis and Applied Mathematics 2010, ICNAAM-2010 - Rhodes, Greece Duration: 19 Sept 2010 → 25 Sept 2010

Keywords

quantum reactions
semiclassics
transition state theory

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10.1063/1.3498119

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abstract = "Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized in phase space using an explicit algorithm. The quantization has been demonstrated to lead to an efficient procedure to compute cumulative reaction probabilities and the associated Gamov-Siegert resonances. These results are used here to derive a formula which expresses the cumulative reaction probability as an absolutely convergent sum over periodic orbits contained in the transition state.",

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AU - Goussev, A.

AU - Schubert, R.

AU - Waalkens, H.

AU - Wiggins, S.

PY - 2010/9/17

Y1 - 2010/9/17

N2 - Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized in phase space using an explicit algorithm. The quantization has been demonstrated to lead to an efficient procedure to compute cumulative reaction probabilities and the associated Gamov-Siegert resonances. These results are used here to derive a formula which expresses the cumulative reaction probability as an absolutely convergent sum over periodic orbits contained in the transition state.

AB - Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized in phase space using an explicit algorithm. The quantization has been demonstrated to lead to an efficient procedure to compute cumulative reaction probabilities and the associated Gamov-Siegert resonances. These results are used here to derive a formula which expresses the cumulative reaction probability as an absolutely convergent sum over periodic orbits contained in the transition state.

KW - quantum reactions

KW - semiclassics

KW - transition state theory

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U2 - 10.1063/1.3498119

DO - 10.1063/1.3498119

M3 - Conference article

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JF - AIP Conference Proceedings

T2 - International Conference on Numerical Analysis and Applied Mathematics 2010, ICNAAM-2010

Y2 - 19 September 2010 through 25 September 2010

ER -

A periodic orbit formula for quantum reactions through transition states

Abstract

Keywords

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