Quantum mechanical and semiclassical approaches to molecular dynamics
A new multichannel exchange kernel formalism for reactive scattering is introduced. The central feature of the method is the expansion of the reactive scattering wavefunction in terms of the non-reactive coupled-channel scattering waves in all of the arrangements. The exact S matrix is found from the non-reactive wavefunction and the exchange kernel which are computed from the non-reactive coupled-channel scattering calculations in each arrangement. An approximate version of formula is obtained by virtue of the distorted wave Born approximation (DWBA) where the non-reactive coupled-channel scattering wavefunction is utilized for distorted waves. Application to a standard test problem (collinear H+H/sub 2/) shows that multichannel DWBA is extremely accurate if the reaction probability is no larger than 0.1 and if approx. 3 to 4 vibrational states are included in the non-reactive coupled channel expansion, and that the full exact calculation is stable, accurate and easy to implement. Semiclassical perturbation theory combined with two approximate models for polyatomic Hamiltonian - the reaction path model and the kinetic coupling model - leads to extremely simple, analytical formulae for S-matrix and the spectra of overtone. The numerical tests indicate that these simple approximate methods are of useful accuracy. A new semiclassical approach is proposed. In this approach the evolution of the states of a system, which are parameterized by label variables, is determined by calculating the time development of the label variables classically. The formalism for calculating the S-matrix within this framework is developed. Sample calculations show that this method is very simple and describes quantum phenomena very well. 12 figures, 12 tables.
- Research Organization:
- Lawrence Berkeley Lab., CA (USA)
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 6340535
- Report Number(s):
- LBL-18569; ON: DE85003458
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
Molecular & Chemical Physics-- Collision Phenomena
657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
ABSORPTION SPECTRA
AROMATICS
ATOM COLLISIONS
ATOM-MOLECULE COLLISIONS
BENZENE
COLLISIONS
DEUTERIUM COMPOUNDS
ELEMENTS
ENERGY LEVELS
EXCITED STATES
FLUIDS
GASES
HELIUM
HYDROCARBONS
HYDROGEN
HYDROGEN COMPOUNDS
MECHANICS
MOLECULE COLLISIONS
MOLECULE-MOLECULE COLLISIONS
MOLECULES
NONMETALS
ORGANIC COMPOUNDS
QUANTUM MECHANICS
RARE GASES
SCATTERING
SPECTRA
VIBRATIONAL STATES