CHAPTER 1. FLUORESCENT SILICON CLUSTERS 19 in free beams match measurements of band gap energies of silicon clusters de- posited on HOPG (Marsen et al., 2000). Such band gap energies were always smaller than those of their bulk counterparts, which agrees with a different geometric structure than the diamond cubic structure of the bulk. Also, a tran- sition region was found for sizes around 1.5 nm, corresponding to 44 atoms; larger clusters had no band gap. Band gap energies of cationic VSi + n were determined by X-ray spectroscopy using monochromatic synchrotron radiation and an ion trap to store the size- selected clusters (Lau et al., 2011). By measuring the ion yield of specific ion decay channels, it was possible to record a direct 2p photoionisation spectrum separately from the resonant 2p photoionisation spectrum, yielding the energy difference E$_{XAS}$ between the core level and the lowest unoccupied molecular or- bital (LUMO,) and E$_{CL}$ , the energy difference between the core and the vacuum level, E$_{V AC}$ . Measurement of the valence state photoionisation spectrum E$_{V B}$ yields the difference between the highest occupied molecular orbital (HOMO) and the the vacuum level, E$_{V AC}$ . For the band gap energy, E$_{g}$ , or, more pre- cisely, the HOMO-LUMO energy difference, it follows E$_{g}$ = E$_{V B}$ − E$_{CL}$ + E$_{XAS}$ . Photoionisation thresholds were measured for silicon clusters in the size range from n = 2 to 200 using laser photoionisation using RETOF mass spec- trometry detection (Fuke et al., 1993). The ionisation potential revealed fea- tures that were ascribed to a structural transition for sizes around n = 20. Measurements of the 2p core-level and valence electron binding energies using monochromatic synchrotron radiation and an ion trap show a similar size de- pendence (Vogel et al., 2012). Both 2p binding energy and ionisation potential show a linear dependence on the inverse cluster radius n − 1 / $^{3}$. Such a depen- dence is expected from the size-dependent charging energy, similar to metal clusters (Halder and Kresin, 2015). Furthermore, core level shifts were derived