DOI: 10.1063/1.447598. Semiclassical spectral quantization: Application to two and four coupled molecular degrees of freedom

Semiclassical spectral quantization: Application to two and four coupled molecular degrees of freedom

10.1063/1.447598

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

Semiclassical quantization of the quasiperiodic vibrational motion of molecules is usually based on Einstein–Brillouin–Keller (EBK) conditions for the quantization of the classical actions. Explicit use of the EBK conditions for molecular systems of K degrees of freedom requires K quantization conditions. Therefore, explicit use of the EBK conditions becomes increasingly difficult if not impossible for polyatomic systems of three or more degrees of freedom. In this paper we propose a semiclassical quantization method which makes explicit use of phase coherence of the de Broglie wave associated with the trajectory rather than the EBK conditions. We show that taking advantage of phase coherence reduces the K quantization conditions to a single quantum condition—regardless of the number of degrees of freedom. For reasons that will become obvious we call this method ‘‘spectral quantization.’’ Polyatomic vibrational wave functions and energy eigenvalues are generated from quasiperiodic classical trajectories. The spectral method is applied to an ABA linear triatomic molecule with two degrees of freedom and to an anharmonic model of the molecule cyanoacetylene. The usefulness of the technique is demonstrated in this latter calculation since the cyanoacetylene model will have four coupled vibrational degrees of freedom.

Bibliography

De Leon, N., & Heller, E. J. (1984). Semiclassical spectral quantization: Application to two and four coupled molecular degrees of freedom. The Journal of Chemical Physics, 81(12), 5957â5975.

Authors 2

N. De Leon (first)
E. J. Heller (additional)

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Dates

Type	When
Created	22 years, 6 months ago (Feb. 28, 2003, 12:34 p.m.)
Deposited	1 year, 6 months ago (Feb. 9, 2024, 9:57 p.m.)
Indexed	1 day, 9 hours ago (Sept. 3, 2025, 7:01 a.m.)
Issued	40 years, 8 months ago (Dec. 20, 1984)
Published	40 years, 8 months ago (Dec. 20, 1984)
Published Print	40 years, 8 months ago (Dec. 20, 1984)

Funders 0

None

BibTeX

@article{De_Leon_1984, title={Semiclassical spectral quantization: Application to two and four coupled molecular degrees of freedom}, volume={81}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.447598}, DOI={10.1063/1.447598}, number={12}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={De Leon, N. and Heller, E. J.}, year={1984}, month=dec, pages={5957–5975} }

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  "abstract": "<jats:p>Semiclassical quantization of the quasiperiodic vibrational motion of molecules is usually based on Einstein\u2013Brillouin\u2013Keller (EBK) conditions for the quantization of the classical actions. Explicit use of the EBK conditions for molecular systems of K degrees of freedom requires K quantization conditions. Therefore, explicit use of the EBK conditions becomes increasingly difficult if not impossible for polyatomic systems of three or more degrees of freedom. In this paper we propose a semiclassical quantization method which makes explicit use of phase coherence of the de Broglie wave associated with the trajectory rather than the EBK conditions. We show that taking advantage of phase coherence reduces the K quantization conditions to a single quantum condition\u2014regardless of the number of degrees of freedom. For reasons that will become obvious we call this method \u2018\u2018spectral quantization.\u2019\u2019 Polyatomic vibrational wave functions and energy eigenvalues are generated from quasiperiodic classical trajectories. The spectral method is applied to an ABA linear triatomic molecule with two degrees of freedom and to an anharmonic model of the molecule cyanoacetylene. The usefulness of the technique is demonstrated in this latter calculation since the cyanoacetylene model will have four coupled vibrational degrees of freedom.</jats:p>",
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