Complex periodic orbits in the rotational spectrum of molecules: The example of SF/sub 6/

Journal Article · Wed Mar 15 04:00:00 EST 1989 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.39.2838· OSTI ID:6208042

Robbins, J M; Creagh, S C; Littlejohn, R G

Periodic orbit theory expresses, in a semiclassically approximate way, the trace of the energy-dependent Green's function of a quantum-mechanical system in terms of a sum over periodic orbits of the corresponding classical system. In this paper a periodic orbit sum is carried out for a Hamiltonian describing the rotational dynamics of the SF/sub 6/ molecule. Following Miller (J. Phys. Chem. 83, 960 (1979)), classically forbidden, or ''tunneling'' orbits are included in the sum. A closed-form expression for the trace of the energy-dependent Green's function is obtained; it depends on the actions and Maslov indices of the classical orbits, as well as the irreducible representatives of the generators of the molecular point group. The expression reproduces the rich structure characteristic of the rotational spectra of symmetric molecules, including the exponentially near degeneracies for large angular momentum, and the periodicities in eigenvalue symmetry assignments. The methods used here complement the extensive studies of Harter and Patterson.

• Research Organization: Department of Physics, University of California, Berkeley, California 94720
• OSTI ID: 6208042
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 39:6; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

640302* -- Atomic
Molecular & Chemical Physics-- Atomic & Molecular Properties & Theory
74 ATOMIC AND MOLECULAR PHYSICS
ELECTRONIC STRUCTURE
ENERGY LEVELS
EQUATIONS
EXCITED STATES
FLUORIDES
FLUORINE COMPOUNDS
FUNCTIONS
GREEN FUNCTION
HALIDES
HALOGEN COMPOUNDS
ROTATIONAL STATES
SULFUR COMPOUNDS
SULFUR FLUORIDES
SUM RULES
TUNNEL EFFECT