CHAPTER 1. FLUORESCENT SILICON CLUSTERS 10 Figure 1.3: Simplified energy level diagram of a nanoscale crystal with a high density of vibrational states at its surface. The small size of the crystal means that electrons delocalised over the conduction band quickly localise at the sur- face. They then relax non-radiatively by hopping across the vibrational states. at the surface is assumed to exist. The electronically excited electron ’finds’ the surface on a sub-femtosecond timescale, and relaxes by jumping down the energy ladder of vibrational states. Another simplification implicit in this picture of a dense spectrum of vibra- tional states is that the short timescales of non-radiative decay are ignored. The energy level scheme shown in figure 1.3 implies that the vibrational levels are time-averages. Under closer inspection, the consideration of relaxation pathways along such eigenstates in nanocrystals does not appear to be justified. Particularly in free clusters, the atoms at the surface can perform large amplitude vibrations. These large amplitude vibrations give rise to electronic-vibrational coupling, and open other, non-adiabatic routes for relaxation from electronically excited states to the ground state. The simple example of the triatomic, homonuclear molecule