Why do we use HOMO and LUMO in dye sensitized solar cells instead of excited and ground state ?
Is this similar to the general case of using HOMO and LUMO instead of valence and conduction bands for semiconducting metals?
Perhaps HOMO LUMO is giving you a definite value of energy of an electron and the band gap off-course. An electron can be excited to any of excited state energy levels eg S1, S2 and so on..... but it is the LUMO which decides the minimum energy required for excitation. Other reason can be the use of organic dyes in dssc. In case of organic molecule, the HOMO and LUMO of individual molecules retain their identity in solid state or in aggregates and do not converge to form valence and conduction bands as in case of inorganic semiconductors. So the terms HOMO and LUMO are more appropriate than using terms valence and conduction band which have a very wide range of energies.
One should keep some points in mind here: One often forgotten fact is that HOMO and LUMO depend on the level of theory that is used. For instance, Hartree-Fock yields MOs that are often quite similar to, but different from Kohn-Sham MOs when computed with similar basis sets. Second, there are systems like transition metal complexes, that have a high density of states near the "band gap"/Fermi energy. Then, it often is not sufficient to consider HOMO and LUMO alone, but HOMO-1, -2, -3 etc. and LUMO+1, +2, etc. have to be taken into account as well, such that a number of frontier orbitals have to be used to get a reasonable description of such systems. Also for systems with a high symmetry, degenerate orbitals have to be considered, often many more orbitals than just two. So concentrating on HOMO and LUMO alone yields only qualitatively correct results if the excited state is dominated by a one-electron excitation, and other excited states are lying at much higher energy. Then, other electron configurations probably do not mix in strongly. Also, spin-orbit coupling should be rather weak, such that mixing in of states with different spin-multiplicity is hopefully not important. Taking into account all these considerations, it is astonishing that the simple HOMO-LUMO description can be used to model quite a large number of systems rather well. It is the most simple model and thus, should be tried first but with some caution.
In my usage, "excited state" and "ground state" refer to the actual condition that a system is in as a whole, whereas HOMO and LUMO are just labels given to certain electronic levels. So the difference is that "excited state" and "ground state" consider the actual occupation, whereas HOMO and LUMO are not related to the actual occupation. (I know this sounds contradictive, since "HO" and "LU" refer to occupation, but that's just for identifying the relevant levels -- when the system is in its ground state!)
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