From Wikipedia:

Roughly, the HOMO level is to organic semiconductors what the valence band maximum is to inorganic semiconductors and quantum dots. The same analogy exists between the LUMO level and the conduction band minimum.

Why such distinction even exists? If it's the same physical concept, why use different names?

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    $\begingroup$ A band is a multitude of energy levels that are quasi-continuously distributed over a certain energy range. It comes about because of crystal (translational) symmetry. A HOMO/LUMO is just a single energy level. While thinking of the valence and conduction band edges as the "HOMO or LUMO of a crystal" is often quite fruitful, there are some effects present in solids that cannot be understood by this simple pov. $\endgroup$ – Philipp Oct 31 '15 at 15:56
  • $\begingroup$ The properties of solids simply are not as much influenced by single energy levels as is the case for molecules. Here bands are the appropriate conceptual unit to think of. $\endgroup$ – Philipp Oct 31 '15 at 16:02
  • $\begingroup$ @Philipp, so whenever "HOMO-LUMO" is used, the assumption is that energy levels are discrete? $\endgroup$ – Sparkler Oct 31 '15 at 16:05
  • $\begingroup$ Yes, unless you encounter some sloppy terminology. $\endgroup$ – Philipp Oct 31 '15 at 16:06
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    $\begingroup$ Have not worked in the area of quantum dots yet, so I can't really help you there. But I can recommend this book by Roald Hoffmann to you if you want to get a good understanding about the relations between molecular energy levels and crystal bands. It's a pretty short book but it really does a wonderful job at teaching you the links between solid state and molecular chemistry. $\endgroup$ – Philipp Oct 31 '15 at 16:16

Because convention. Yes, that’s not the answer you wished for but it’s the way it is.

Coming from an organic perspective, one would think of concepts such as linear combination of atomic orbitals or others to arrive at molecular orbitals for entire molecules. Since organic chemistry always deals with rather small molecules and since these have discreet energy levels with discreet differences, it makes sense to speak of a single HOMO, i.e. one single highest occupied orbital (and likewise for a LUMO). The larger a molecule gets, the more orbitals it has and the less the difference between HOMO and LUMO might turn out to be, but from an organic perspective it is still a molecule and must begin and end somewhere.

(Note that this applies to a lesser extent to polymers and carbon nanotubes etc. This is where the shady grey area in which unicorns live begins.)

From an inorganic perspective, if you are dealing with solid materials, they will usually be crystalline in some way; hence they have infinite extents by definition. It no longer makes sense to think of discreet orbitals but rather one realises that certain levels contain a large number of orbitals — hence bands.

If organic molecules end up being sufficiently large, there is no longer a relevant physical difference between HOMO/LUMO designations or bands. But because nobody likes throwing their traditions and customs overboard, the two different names exist.

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  • $\begingroup$ are all non-covalent arrays currently described in HOMO/LUMO? in other words, how closely packed small molecules need to be, to "justify" a band description? in particular, are supramolecular polymers described in bands or in HOMO/LUMO? $\endgroup$ – Sparkler Nov 1 '15 at 1:27
  • $\begingroup$ @Sparkler I don’t really work in the area, so I don’t really know, but since the underlying physics are the same I see no reason why there should be any rules on what can be called what. $\endgroup$ – Jan Nov 1 '15 at 1:33
  • $\begingroup$ I guess when energy levels are discrete, using "bands" is somewhat misleading. I'll use HOMO/LUMO when unsure, just to stay on the safe side... :) $\endgroup$ – Sparkler Nov 1 '15 at 1:47

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