1. The flux-flux correlation function for anharmonic barriers
- Author
-
Holger Waalkens, Roman Schubert, Arseni Goussev, and Stephen Wiggins
- Subjects
PROBABILITIES ,CHEMICAL-REACTIONS ,F300 ,Computation ,Astrophysics::High Energy Astrophysical Phenomena ,F100 ,FOS: Physical sciences ,General Physics and Astronomy ,NONSEPARABLE SYSTEMS ,TRANSITION-STATE THEORY ,01 natural sciences ,PHASE-SPACE ,Transition state theory ,Quantum mechanics ,Physics - Chemical Physics ,0103 physical sciences ,SEMICLASSICAL THEORY ,Physical and Theoretical Chemistry ,010306 general physics ,Quantum ,Saddle ,Mathematical Physics ,G100 ,Chemical Physics (physics.chem-ph) ,Physics ,Quantum Physics ,010304 chemical physics ,CONSTRUCTION ,QUANTUM-MECHANICS ,Anharmonicity ,REACTION-RATE CONSTANTS ,Mathematical Physics (math-ph) ,Nonlinear Sciences - Chaotic Dynamics ,DAMPED SYSTEMS ,Formalism (philosophy of mathematics) ,Fourth order ,Phase space ,Chaotic Dynamics (nlin.CD) ,Quantum Physics (quant-ph) - Abstract
The flux-flux correlation function formalism is a standard and widely used approach for the computation of reaction rates. In this paper we introduce a method to compute the classical and quantum flux-flux correlation functions for anharmonic barriers essentially analytically through the use of the classical and quantum normal forms. In the quantum case we show that the quantum normal form reduces the computation of the flux-flux correlation function to that of an effective one dimensional anharmonic barrier. The example of the computation of the quantum flux-flux correlation function for a fourth order anharmonic barrier is worked out in detail, and we present an analytical expression for the quantum mechanical microcanonical flux-flux correlation function. We then give a discussion of the short-time and harmonic limits., 9 pages, 2 figures
- Published
- 2010