Chapter 16 - Transitions between electronic states

Abstract

Chemical transformation can occur without the collision between reactant molecules. This is the case of the transfer of energy from one molecule electronically excited to another one initially in the ground state and with an accessible excited state of lower energy than the excited reactant molecule. It is also the case of outer-sphere electron transfer reactions. This chapter addresses transitions between electronic states, including energy transfer reactions between two weakly coupled electronic states in different molecules. A brief discussion of electronic absorption, radiative and radiationless transitions, electronic energy transfer, and triplet–triplet annihilation sets the stage for a detailed presentation of the time-dependent Schrödinger equation and the derivation of the Golden Rule of time-dependent perturbation theory. Expressions are derived for radiative and radiationless transitions within a molecule. Franck–Condon factors are calculated for displaced identical harmonic oscillators. Simulations of absorption and emission spectra are presented. Radiationless transitions are calculated with a WKB (Wentzel, Kramers, Brillouin) expression for tunnelling between intersecting harmonic oscillators. The problem of triplet energy transfer between weakly interacting donor and acceptor states is discussed in detail. The electronic coupling is considered mostly in terms of the distance between donor and acceptor. Examples of calculations of triplet energy transfer rates and their dependence on the energy gap between donor and acceptor are presented in detail.