Transition state theory, Siegert eigenstates, and quantum mechanical reaction rates

Journal Article · Thu Aug 01 04:00:00 EDT 1991 · Journal of Chemical Physics; (USA)

DOI:https://doi.org/10.1063/1.461025· OSTI ID:5662076

Seideman, T; Miller, W H ^[1]

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1. Department of Chemistry, University of California, and Chemical Sciences Division, Lawrence Berkeley Laboratory, Berkeley, California 94720 (US)

The good'' action variables associated with a transition state (i.e., the saddle point of a potential energy surface), on which a general semiclassical transition state theory is based, are shown to be the semiclassical counterpart of the Siegert eigenvalues of the system. (Siegert eigenvalues are the complex eigenvalues of the Schroedinger equation with outgoing wave boundary conditions.) By using flux correlation functions, it is then shown how the exact quantum mechanical reaction rate can be expressed in terms of the Siegert eigenvalues (and eigenfunctions). Applications to some test problems show these Siegert-based rate expressions to be rapidly convergent with respect to the sum over Siegert states.

• DOE Contract Number: AC03-76SF00098
• OSTI ID: 5662076
• Journal Information: Journal of Chemical Physics; (USA), Journal Name: Journal of Chemical Physics; (USA) Vol. 95:3; ISSN JCPSA; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
400201* -- Chemical & Physicochemical Properties
CHEMICAL REACTION KINETICS
CORRELATION FUNCTIONS
EIGENSTATES
EIGENVALUES
FUNCTIONS
KINETICS
MECHANICS
QUANTUM MECHANICS
REACTION KINETICS