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Chemical reactions are ubiquitous and very important for life and many other processes taking place on earth. In both theoretical and experimental studies of reactivity a transition state is often used to rationalise the outcome of such studies. The present thesis deals with calculations of transition states in radical cation rearrangements, and a principle of least motion study of the rearrangements in the barbaralyl cation.

In particular, alternative quadricyclane radical cation (Q∙+) rearrangements are extensively studied. The rearrangement of Q∙+ to norbornadiene is extremely facile and is often used as a prototype for one-electron oxidations. However, electron spin resonance (ESR) experiments show that there are additional cations formed from Q∙+. Two plausible paths for the rearrangement of Q∙+ to the 1,3,5-cycloheptatriene radical cation are located. The most favourable one is a multistep rearrangement with two shallow intermediates, which has a rate-limiting step of 16.5 kcal/mol. In addition, a special structure, the bicyclo[2.2.1]hepta-2-ene-5-yl-7-ylium radical cation, is identified on these alternative paths; and its computed ESR parameters agree excellently with the experimental spectrum assigned to another intermediate on this path. Moreover, this cation show a homoconjugative stabilization, which is uncommon for radical cations.

The bicyclopropylidene (BCP) radical cation undergoes ring opening to the tetramethyleneethane radical cation upon γ-irradiation of the neutral BCP. This rearrangement proceeds through a stepwise mechanism for the first ring opening with a 7.3 kcal/mol activation energy, while the second ring opening has no activation energy. The dominating reaction coordinate during each ring opening is an olefinic carbon rehybridization.

The principle of least motion is based on the idea that, on passing from reactant to product, the reaction path with the least nuclear change is the most likely. By using hyperspherical coordinates to define a distance measure between conformations on a potential energy surface, a possibility to interpret reaction paths in terms of distance arises. In applying this measure to the complex rearrangements of the barbaralyl cation, a correct ordering of the conformations on this surface is found.