This semester I will be taking a tour of the important papers relating to finding trajectories of rare events. This week we will start from the beginning with Eugene Wigner's seminal paper
The transition state method is the first in a long series of theories using physics to explain chemical reactions. Wigner outlines a three part process for describing reactions – construct the energy surface, solve the rate of elementary reactions, consider the co-operation of multiple elementary reactions. This paper focuses solely on the middle step. Evans and Polanyi [doi: 10.1039/TF9353100875] developed a basic theory for constructing the energy surface based on theoretical models and experimental data. Wigner used their results as an example model for his theory.
Wigner's theory is based on three assumptions which are presented in great detail in his paper. The first is the adibatic assumption – the movements of the nuclei are slow relative to the electrons. Second, he assumes that the nuclei's motion under the given potential can be adequately described by classical mechanics. Third, the activation surface forms a saddle point near which all reactive trajectories pass. The first two are widely accepted, while the third was controversial. It turns out this assumption was correct and has been used many times since. This is the major advance provided in
Wigner begins by framing the current state of the art and where his theory fits. He then goes on to outline his work. These two sections make up the first half. The rest of the paper is spent arguing the valididty of his assumptions. This is a common structure for papers in the field.
Due to its age, I was expecing this paper to be a challenge read. I was wrong. I attribute the paper's approachability to the fact that chemistry was an established field at the time of publication. Despite being well written there are still a few opportunities for improvement. Adding more experimental data would provide justification for the assumptions made. As it turns out this was impossible at the time due to limitations in labratory technologies.