#### Date of Award

3-9-2009

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Department of Engineering Physics

#### First Advisor

David E. Weeks, PhD

#### Abstract

Effective potential energy surfaces (PESs) are calculated for a nonadiabatic collision . This calculation employed 1 ^{2}*A'*, 2 ^{2}*A'* and 1 ^{2}*A"* adiabatic PESs numerically calculated at the state-averaged multiconfigurational self-consistent field (SA-MCSCF)/configuration interaction (CI) level for several values of the H_{2} bond length, H_{2} orientation angle, and boron distance. The associated nonadiabatic coupling terms (NACTs) were calculated from the SA-MCSCF/CI wave functions using analytic gradient techniques. A line integral through the NACTs was then used to determine the adiabatic-to-diabatic mixing angle required to transform from the 1 ^{2}*A'* and 2 ^{2}*A'* adiabatic basis to a corresponding diabatic basis. When all nonadiabatic coupling terms between all electronic states are considered, the line integral is path independent. However, only NACTs between the 1 ^{2}*A'* and 2 ^{2}*A'* states were considered in these calculations, and the line integral was therefore path dependent. The path dependence of the line integral was used to characterize the error introduced by employing a truncated set of adiabatic states. A method for reducing the effect of this error through the use of symmetry derived boundary conditions was developed. The resulting diabatic PESs were combined with the total B + H_{2} rotational kinetic energy and boron spin-orbit coupling to yield diabatic effective PESs. The diabatic effective PESs were diagonalized to yield adiabatic effective PESs. Diabatic effective PESs data was extracted for the equilibrium H_{2} bond length and used to calculate inelastic scattering matrix elements using the time dependent channel packet method.

#### AFIT Designator

AFIT-DS-ENP-09-J01

#### DTIC Accession Number

ADA494623

#### Recommended Citation

Garvin, Matthew B., "The Effective Potential Energy Surfaces of the Nonadiabatic Collision B(^{2}P_{j}_{a}) + H_{2}(^{1}Σ^{+}_{g},ν,j) ↔ B(^{2}P_{j'}_{a}) + H_{2}(^{1}Σ^{+}_{g},ν',j')" (2009). *Theses and Dissertations*. 2434.

https://scholar.afit.edu/etd/2434