On Adiabatic Quantum Molecular Dynamics

In this thesis, we consider the time-dependent Born-Oppenheimer approximation (BOA) of a non-relativistic quantum molecule involving a possibly large number of nuclei and electrons described by the Schrödinger equation. The full molecular equation is difficult to solve and compute approximations for due to the highly oscillatory nature of the solutions in space and time and due to the high dimensionality of the state space. In the spirit of Born and Oppenheimer, we study quantitatively the approximation of the molecular evolution. We obtain an iterable approximation of the molecular evolution to arbitrary order and we derive an effective equation for the reduced dynamics involving the nuclei, equivalent to the original Schrödinger equation and containing no electron variables (thus reducing the large state space of the full evolution). We estimate the coefficients of the new equation and find tractable approximations for it.

Department dc:contributor.department

Mathematics

Year dc:date.issued

2024

Author dc:creator

• Gherghe, Sebastian Tudor

Advisor dc:contributor.advisor

• Sigal, Israel M

• Adiabatic
• Born Oppenheimer
• Molecular dynamics
• Quantum mechanics

Handle dc:identifier.uri

http://hdl.handle.net/1807/140728

OAI identifier oai:identifier

oai:utoronto.scholaris.ca:1807/140728