#### Abstract

We use an algebraic method to model the molecular collision dynamics of a collinear triatomic system. Beginning with a forced oscillator, we develop a mathematical framework upon which inelastic and reactive collisions are modeled. The model is considered algebraic because it takes advantage of the properties of a Lie algebra in the derivation of a time-evolution operator. The time-evolution operator is shown to generate both phase-space and quantum dynamics of a forced oscillator simultaneously. The model is considered semi-classical because only the molecule's internal degrees-of-freedom are quantized. The relative translation between the colliding atom and molecule in an exchange reaction (AB+C ->A+BC) contains no bound states and any possible tunneling is neglected so the relative translation is treated classically. The purpose of this dissertation is to develop a working model for the quantum dynamics of a collinear reactive collision. After a reliable model is developed we apply statistical mechanics principles by averaging collisions with molecules in a thermal bath. The initial Boltzmann distribution is of the oscillator energies. The relative velocities of the colliding particles is considered a thermal average. Results are shown of quantum transition probabilities around the transition state that are highly dynamic due to the coupling between the translational and transverse coordinate.

#### Degree

PhD

#### College and Department

Physical and Mathematical Sciences; Physics and Astronomy

#### Rights

http://lib.byu.edu/about/copyright/

#### BYU ScholarsArchive Citation

Wendler, Tim Glenn, "Algebraic Semi-Classical Model for Reaction Dynamics" (2014). *All Theses and Dissertations*. 5755.

http://scholarsarchive.byu.edu/etd/5755

#### Date Submitted

2014-12-01

#### Document Type

Dissertation

#### Handle

http://hdl.lib.byu.edu/1877/etd7444

#### Keywords

algebraic, reaction, dynamics, quantum, anharmonic, triatomic, collinear