Semiclassical initial value representation techniques for chaotic systems

B. R. McQuarrie; Paul Brumer

doi:10.1016/S0009-2614(00)00053-1

Semiclassical initial value representation techniques for chaotic systems

B. R. McQuarrie, Paul Brumer

Research output: Contribution to journal › Article › peer-review

34 Scopus citations

Abstract

Semiclassical wavefunction propagation for chaotic systems suffer from numerical difficulties due to the chaotic nature of classical trajectories, resulting in reduced accuracy for standard initial value representation (IVR) methods. We compare four recent IVR methods developed to overcome these difficulties (Herman-Kluk with trajectory truncation; stationary-phase Herman-Kluk (SPHK); cellularized frozen Gaussian approximation; stationary-phase Monte Carlo) by computing the Franck-Condon spectrum of the 2-dimensional Henon-Heiles and quartic oscillator systems. The SPHK is found to be the most successful of the four methods. The SPHK is then used to determine the spectrum for collinear CO₂ photodissociation.

Original language	English (US)
Pages (from-to)	27-44
Number of pages	18
Journal	Chemical Physics Letters
Volume	319
Issue number	1-2
DOIs	https://doi.org/10.1016/S0009-2614(00)00053-1
State	Published - Mar 10 2000
Externally published	Yes

Bibliographical note

Funding Information:
The authors would like to thank Prof. Ken Kay (Bar-Ilan University) for a helpful communication regarding symmetry adaption for the quartic oscillator potential. This work was supported by the US Office of Naval Research and by the Natural Sciences and Engineering Research Council of Canada.

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abstract = "Semiclassical wavefunction propagation for chaotic systems suffer from numerical difficulties due to the chaotic nature of classical trajectories, resulting in reduced accuracy for standard initial value representation (IVR) methods. We compare four recent IVR methods developed to overcome these difficulties (Herman-Kluk with trajectory truncation; stationary-phase Herman-Kluk (SPHK); cellularized frozen Gaussian approximation; stationary-phase Monte Carlo) by computing the Franck-Condon spectrum of the 2-dimensional Henon-Heiles and quartic oscillator systems. The SPHK is found to be the most successful of the four methods. The SPHK is then used to determine the spectrum for collinear CO2 photodissociation.",

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AU - Brumer, Paul

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N2 - Semiclassical wavefunction propagation for chaotic systems suffer from numerical difficulties due to the chaotic nature of classical trajectories, resulting in reduced accuracy for standard initial value representation (IVR) methods. We compare four recent IVR methods developed to overcome these difficulties (Herman-Kluk with trajectory truncation; stationary-phase Herman-Kluk (SPHK); cellularized frozen Gaussian approximation; stationary-phase Monte Carlo) by computing the Franck-Condon spectrum of the 2-dimensional Henon-Heiles and quartic oscillator systems. The SPHK is found to be the most successful of the four methods. The SPHK is then used to determine the spectrum for collinear CO2 photodissociation.

AB - Semiclassical wavefunction propagation for chaotic systems suffer from numerical difficulties due to the chaotic nature of classical trajectories, resulting in reduced accuracy for standard initial value representation (IVR) methods. We compare four recent IVR methods developed to overcome these difficulties (Herman-Kluk with trajectory truncation; stationary-phase Herman-Kluk (SPHK); cellularized frozen Gaussian approximation; stationary-phase Monte Carlo) by computing the Franck-Condon spectrum of the 2-dimensional Henon-Heiles and quartic oscillator systems. The SPHK is found to be the most successful of the four methods. The SPHK is then used to determine the spectrum for collinear CO2 photodissociation.

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Semiclassical initial value representation techniques for chaotic systems

Abstract

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