Semiclassical methods for nonseparable systems

Technical Report · Mon Aug 01 04:00:00 EDT 1977

DOI:https://doi.org/10.2172/5351107· OSTI ID:5351107

Garrett, B C

Semiclassical techniques have been widely used for describing the dynamics of molecular collisions. The calculation of discrete energy eigenvalue spectra in bound systems has also employed semiclassical methods. Work has been done toward developing semiclassical theories for rate constants in reactive systems and semiclassical eigenvalues in bound systems. Application of these theories have been made to nonseparable multidimensional systems. Transition-state theory has played an important role in chemical kinetics, and is very useful for approximating reaction rate constants for molecular systems. Many shortcomings of transition-state theory can be attributed to the assumption of separability of motion along the reaction coordinate. Semiclassical approximations have been made to the quantum rate expression, and the resulting semiclassical theory has been applied to the reactive H + H/sub 2/ system. Comparison of this nonseparable theory with quantum scattering calculations shows agreement which is quite good. Although the quantum condition for one-dimensional bound systems is well-known, generalization of these results to multidimensional nonseparable systems is not obvious. Work has been done toward a semiclassical quantum condition which is closest to the approach of Born. The Hamilton--Jacobi equation for the systems is solved in action--angle variables; in this way the classical Hamiltonian can be expressed as a function of action variables which are constants of motion for the system. Requiring the action variables to be integers provides the semiclassical eigenvalues. Numerical calculations have been performed on a two-dimensional coupled potential well with good agreement with the quantum eigenvalues. 18 figures, 6 tables.

• Research Organization: California Univ., Berkeley (USA). Lawrence Berkeley Lab.
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 5351107
• Report Number(s): LBL-6662
• Country of Publication: United States
• Language: English

Related Subjects

640304* -- Atomic
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
AMMONIA
ATOM COLLISIONS
ATOM-MOLECULE COLLISIONS
BOUND STATE
COLLISIONS
CRYOGENIC FLUIDS
DIFFERENTIAL EQUATIONS
EIGENVALUES
ELEMENTS
ENERGY LEVELS
ENERGY SPECTRA
EQUATIONS
FLUIDS
HAMILTON-JACOBI EQUATIONS
HYDRIDES
HYDROGEN
HYDROGEN COMPOUNDS
KINETICS
MOLECULE COLLISIONS
NITROGEN COMPOUNDS
NITROGEN HYDRIDES
NONMETALS
REACTOR KINETICS
SEMICLASSICAL APPROXIMATION
SPECTRA