The molecular shape of any nonlinear molecule can be strongly influenced by the coupling between electrons and vibrations (vibronic coupling) via the Jahn-Teller (JT) interaction within the molecule. This influence appears as a distortion of the symmetrical shape of the original molecule. In such molecules, the adiabatic potential energy surface (APES) possesses either a trough of minimum-energy points or several isoenergetic minima ('wells') depending on the nature of the interactions present. In the case when coupling is infinite, the wells are very deep and the system will be locked into one of these distorted states. The vibronic states associated with these wells are good eigenstates of the system in this limiting static case. However, real molecules have finite coupling, so the system can migrate from one well to another in a process that is often referred to as the dynamic JT effect. If the wells are deep, then the motion must involve quantum mechanical tunnelling. Generally, the motion between wells gives the illusion that the molecule has rotated and this type of motion is referred to as pseudorotation. The eigenstates of the general system can then be approximated by symmetry-adapted states (SAS) which are a linear combination of the states associated with the wells. In this thesis, we focus on studying the dynamical nature of the JT effect through investigating the pseudorotation mechanism in different systems using a simple method employing the time-evolution operator. This allows us to obtain analytical expressions for the probabilities that a system that starts off localised in one initial well, may become localised in another well at some later time. These expressions are plotted versus time to show the pseudorotation regime and a comparison between different cases of pseudorotation in different molecules is made. Determination of the rates of pseudorotation leads to a better knowledge of the strength and nature of the vibronic coupling in the system and is a quantity that is, in principle, experimentally measurable. Also, more information about the tunnelling splitting between the SASs can be gained from this study.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:491016 |
| Date | January 2008 |
| Creators | Sindi, Lubna |
| Publisher | University of Nottingham |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://eprints.nottingham.ac.uk/10594/ |
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