Hi Payal,

I just guess that it comes from their background, i.e. physicians say "band gap" even in molecular science; chemists say "homo--lumo" even in periodic systems. It is simply matter of culture. Actually I don't know about this issue but I just imagine. 

Does it make sense?  

HOMO/LUMO are Molecular Orbitals and the energy of them can in principle be calculated exactly, including all particle interactions. Band theory uses approximations based on the periodicity of the lattice in extended systems, and ignores many contributions to the specific energy of individual particles, such as electrons/holes upon optical excitation, requiring corrections to describe such "excitons". 

The terms should not be used interchangeably!

I agree with Hugh's opinion, however, I occasionally find following question: 

https://www.researchgate.net/post/What_is_the_different_if_we_determine_the_energy_band_gap_from_UV-vis_spectrum_and_from_Ehomo-Elumo

Fundamentally,  the concepts of homo-lumo and conduction-valence band are same. The energies of each state become broad because of the periodic boundary condition in semiconductors. So, I guess people mix these concept in some communities. 

I'm not sure whether my answer for this question was appropriate or not.   

The concepts of Conduction and Valence band come from semiconductor physics, as do the concepts of interband states, defect states etc. The physics of many phenomena such as excitons,  Urbach tails, etc. explore the deviations form the idealised case of many particle bands.

A molecular orbital is a molecular orbital..... a bit more complex than an atomic orbital.... but still a well defined energy state. Thins do get a bit more complicated as the molecule is extended, a classical case being conjugated polymers, in which beyond ~5-10 repeat units a band approximation begins to be more appropriate.

The bands correspond to orbitals. The well known understanding of band structures is the approach from a periodic boundary condition. There is however another approach. The energies of each orbit split into two when two atoms bind. If huge number of atoms bind, the energies also split into huge number. This is actually the band structure. 

It was thirty years ago that Prof. Okuda taught me this. It was impressive.   

Thank you Yoshiki Fukada and Hugh J Bryne.

I totally agree with Hugh J Bryne that HOMO-LUMO is just used for molecules but i have seen many ACS papers which are using the term HOMO-LUMO even for the periodic systems. I have asked from many researchers even in my institute which are using the same terminology of HOMO-LUMO even for periodic systems. but they are answering the same which Yoshiki Fukada said i.e.  physicians say "band gap" even in molecular science; chemists say "homo--lumo" even in periodic systems. But i thought the same which Hugh said that the two terms can't be used interchangeably. 

I appreciate that I really enjoyed this discussion. 

Now I confirmed that "homo-lumo" can not be mixed up with the bands. Homo-lumo and the bands are fundamentally same, however there are essential differences. Since a researcher must be an expert, he/she should aware these differences. 

Now a day, science and technology are so advanced, researchers are required to have wide range of knowledge and understandings. The understanding of a band structure from a periodic boundary condition is a perspective of physicians; the one from single to multiple atoms is the one of chemists. It is important to see things from multiple point of view. 

Thanks,   

You are right.

Thanks.

The classical model of energy says that any particle can have any energy. However, quantum physics proves that this is actually not true for confined particles like electrons, where the energy spectrum is quantized, that is, there are specific (discrete) values of energy that the particle can possess. These values are called the energy levels of the particle/orbital.

Energy bands, though, exist at not the atomic but the molecular level. When multiple atoms combine to form a molecule, the electrons are placed in molecular orbitals. The energy levels of each of the atoms’ orbitals are generally so close that they are almost continuous. The continuous ranges of values of the energy levels in these molecular orbitals are called energy bands.

Thanks for your answer.

But SIr, for band gap there must be periodicity of the atoms or in the molecule. For one molecule we talk about HOMO-LUMO gap. But in some papers even for the periodic systems HOMO-LUMO gap is being used, i just want to know the reason behind it.

When the intermolecularforce of attraction between the molecule is weak in that case we use MOT (molecular orbital theory) and HOMO-LUMO concept but when the intermolecularforce of attraction is very strong like in periodic solids in those cases we use band theory concept and hence band gap.

Hope this may help you.

I would like to add to this discussion a discussion thread raised by me before about organic and inorganic semiconductors:https://www.researchgate.net/post/It_is_required_to_compare_organic_and_inorganic_semiconductors

Thank you Sir!

When the intermolecular force of attraction between the molecule is weak in that case we use MOT (molecular orbital theory) and HOMO-LUMO concept but when the intermolecular force of attraction is very strong like in periodic solids in those cases we use band theory concept and hence bandgap.

Hope this may help you.

I really enjoyed this discussion.

When the size of a polyatomic system becomes progressively larger, the calculation of its electronic structure in terms of combinations of atomic orbitals becomes unfeasible.

However, simplifications arise if the system under study is a periodic, infinite crystal.. The electronic structure of crystalline solids can be in fact described in terms of periodic combinations of atomic orbitals ((Bloch-functions)).... In this model, a perfect translational symmetry of the crystal structure is assumed, while contributions from the surface of the crystal are neglected by assuming an infinite solid (periodic boundary conditions). The electrons are described as a superposition of plane waves extended throughout the solid, for that here used "energy gap" concept. as opposed to the case of atoms and molecules, the energy structure of a solid no longer consists of discrete energy levels, but rather of broad energy bands, Hence the term Homo/Lumo state in molecules where the energy levels are discrete (no assembled molecules) "as shown in pic"

Hope that's clear...

HOMO-LUMO gap for hug materials but Eg for semiconductors materials

I really enjoyed the discussion because I was struggling with the same thing,

But one question arises, please help me with this.

As per the discussion HOMO-LUMO gap and the Band gap is same, but the term can not be interchangeable.

My question is, if there is Zero band gap shown by the molecule, how can we explain it in terms of HOMO-LUMO gap?

Payal Wadhwa, Hugh J Byrne

I am not sure I know of any molecules which have zero HOMO-LUMO gap.

In both cases, we are talking about energy states of electrons, which are involved in the bonding of atoms. As a result of the bonding, the wavefunctions and therefore energy levels of the electrons of the atoms which are bound are modified. In, for example, organic conjugated oligomers, the evolution of the levels, and therefore the HOMO-LUMO gap, can be monitored as the number of binding (carbon) atoms increases, and this can even be described in terms of a simple particle in a box model. (see for example Article Structure−Property Relationships for Electron−Vibrational Co...

In the case where the oligomers become too long, or in the case of a solid (inorganic) state semiconductor, it becomes impractical to calculate the contributions of all atoms/electrons, and therefore the approximations of solid state physics are evoked, such as Bloch's theorem. The result is the band theory of solids, in which molecular orbitals become solid state bands, vibrations become phonons etc. Band theory does not deal well with localised excitations, and so the consept of excitons, polarons etc. are introduced.

To go back to the question, I think that any molecule with a zero band gap is so large that it falls outside the realm of molecular science (for example the progression from oligo-acenes or oligo-phenyls to graphene, and band theory should be used.

I hope this answers, or at least addrsses the question.

Thank you so much for clarification.

Hugh J Byrne

I know it has been a while since this question was asked but perhaps the following could be helpful (if not, please disregard). There are various gaps mentioned in the literature: Fundamental Gap (FG), HOMO-LUMO gap (HLG), optical gap (OG), Transport Gap (TG), and the Band gap (BG).

if IP= ionization potential and EA = electron affinity, then FG = IP-EA.

The HLG is an approximation of FG, and the goodness of the approximation depends on the rigorousness of the ab initio method employed. The BG is to multi-molecular systems (herein, materials) as the FG is to the molecular level.

One feature was not discussed here yet. In HOMO-LUMO diagram (in molecules), these levels are shown in real space, as there delocalization of electrons remains very low. When we have a clusters, there is a chance that we are dealing with free-electron approximation, in which we have impulse p instead of coordinate x at HOMO-LUMO presentation. I will refer here Figure placed by Omar Yousef. Note that even in case of organic 3D crystals we will not have enough electrons to form the E(k) spave