We discuss the electronic properties of quantum-confined nanocrystals. In particular, we show how, starting from the discrete molecular states of small nanocrystals, an approximate band structure (quasi-band structure) emerges with increasing particle size. Finite temperature is found to broaden the discrete states in energy space forming even for nanocrystals in the quantum-confinement regime quasi-continuous bands in k-space. This bands can be, to a certain extend, interpreted along the lines of standard band structure theory, while taking also finite size and surface effects into account. We discuss this on various prototypical nanocrystal systems.
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