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

Journal Article · Thu Dec 20 04:00:00 EST 1984 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.447598· OSTI ID:6148824

De Leon, N; Heller, E J

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.

• Research Organization: Theoretical Division, T-12, MS J569, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
• OSTI ID: 6148824
• Journal Information: J. Chem. Phys.; (United States), Journal Name: J. Chem. Phys.; (United States) Vol. 81:12; ISSN JCPSA
• Country of Publication: United States
• Language: English

Related Subjects

640305* -- Atomic
Molecular & Chemical Physics-- Atomic & Molecular Theory-- (-1987)
74 ATOMIC AND MOLECULAR PHYSICS
ENERGY LEVELS
EXCITED STATES
FUNCTIONS
MOLECULES
ORGANIC COMPOUNDS
ORGANIC NITROGEN COMPOUNDS
POLYATOMIC MOLECULES
SEMICLASSICAL APPROXIMATION
SPECTRA
VIBRATIONAL STATES
WAVE FUNCTIONS