Honors Program
University Honors, Honors in Mathematics
Date of Award
5-2014
Thesis Professor(s)
Frank Hagelberg
Thesis Professor Department
Physics and Astronomy
Thesis Reader(s)
Jeff Knisley, Mark Giroux
Abstract
In molecules, electronic state transitions can occur via quantum coupling of the states. If the coupling is due to the kinetic energy of the molecular nuclei, then electronic transitions are best represented in the adiabatic frame. If the coupling is instead facilitated through the potential energy of the nuclei, then electronic transitions are better represented in the diabatic frame. In our study, we modeled these latter transitions, called ``nonadiabatic transitions.'' For one nuclear degree of freedom, we modeled the de-excitation of a diatomic molecule. For two nuclear degrees of freedom, we modeled the de-excitation of an ethane-like molecule undergoing cis-trans isomerization. For both cases, we studied the dependence of the de-excitation on the nuclear configuration and potential energy of the molecule.
We constructed a numerical model to solve the time-dependent Schr\"{o}dinger Equation for two coupled wave functions. Our algorithm takes full advantage of the sparseness of the numerical system, leading to a final set of equations that is solved recursively using nothing more than the Tridiagonal Algorithm.
We observed that the most effective de-excitation occurred when the molecule transitioned from a stable equilibrium configuration to an unstable equilibrium configuration. This same mechanism is known to drive fast electronic transitions in the adiabatic frame. We concluded that while the adiabatic and diabatic frames are strongly opposed physically, the mathematical mechanism driving electronic transitions in the two frames is in some sense the same.
Document Type
Honors Thesis - Open Access
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.
Recommended Citation
Agrawal, Devanshu, "A Numerical Model for Nonadiabatic Transitions in Molecules" (2014). Undergraduate Honors Theses. Paper 193. https://dc.etsu.edu/honors/193
Copyright
Copyright by the authors.
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