Sir, the HOMO-LUMO gap means difference between HOMO LUMO energies... LUMO-(-HOMO) gives you 0.3-(-0.4)= 0.1. 

Sir, the HOMO-LUMO gap means difference between HOMO LUMO energies... LUMO-(-HOMO) gives you 0.3-(-0.4)= 0.1. 

Kumar's answer is correct.

Both energies are negative, the difference between them is a gap. Depending on the accuracy of the method and the basis set, you may believe LUMO energy is -O.3. Some theo-chemists would say that we are not all the way to the top in the Jacobs ladder. That is uncertainty of EA is big.  

Nice answer  Choutipalli Venkata Surya Kumar. Actually the interesting  point for me is this:

Usually the value of  energy gab comes with difference but  what is the meaning of the minus if it is appear??

HOMO-LUMO=-0.4-(-0.3)= -0.1 eV=   the energy value is 0.1 & (-) : carriers needing energy to start react by transition.

The opposite case it means the carriers emitted the energy through the transition.   

LUMO is always higher in energy than HOMO. the HOMO-LUMO gap means LUMO-(HOMO) is positive. if it is negative means HOMO is higher in energy than LUMO which is im possible in ground state or ur system is in exited state. I think so........Rana Al Khaldi

Everyone, thanks for the answer. It was indeed helpful.

A gap means nothing else than the difference between two states. The correct mathematical description would therefore be

abs(LUMO)-abs(HOMO)= 0.1 eV

The magnitute of the HOMO-LUMO gap has very important chemical implications, even if qualiatively evaluated. A large gap implies good thermodynamic stability of the compound, whereas a small gap suggests an easy electronic transition. Even half population of the LUMO may induce a geometric rearrangement, depending on the character of the LUMO, hence the hosted electrons have an effect. For instance, population of a LUMO, which is antibonding between two bonded atoms, may trigger bond elongation or even cleveage cause a change in the molecular  geometry. A good strategy for understanding the meaning of a HOMO-LUMO gap is to construct a qualitative Walsh Diagram, which monitors the energy of the frontier levels along some specific coordinate (e.g., bond elongation or a relevant angle) and allows establishing how much the gap is controlled by geometry. Also, by looking at the evolving shapes of the levels, the intented structural modifications may be easily interpreted.   I have illustrated some of these basic points in a chapter of the online Encyclopedia of Life Support Systems devoted to Inorganic and Bio-inorganic Chemistry, [Ed. Ivano Bertini, 2006], which may be found here 

Dear  Carlo

Thank you for your great help.

GOOD POINT Rana; Why the LUMO has a negative energy?

Anyone familiar with these calculations knows that LUMO is an antibonding MO with a positive sign (destabilized).

In the words of uncle Albert, "the important thing is to never stop questioning"

Dear Dr. Carlo Mealli,

Thanks for the answer and the material as well.

By the way, since the HOMO (say -0.4) is invariably lower in energy than the LUMO, the energy gap is negative even if the LUMO (normally negative, say -0.3) is instead positive (say +0.5). Hence, possible gaps are -0.4-(-0.3)=--0.1 or -0.4-(+0.5) = -0.9).

As I said, the larger is the gap, the higher the stability. Consider that the LUMO of an optimized system is generally not very well defined by ab-initio calculations, since it is a  "virtual" orbital as all the cavant ones (i.e., it is not included in the Self Consistent Field procedure, which is only based on populated levels).   

Dr.  Carlo Mealli

 Many thanks really helpful for expand our thought for all possibles.  

Thank you Toka Swu for sharing us this important question and  leading us to this great answers and material.

Dr. Carlo Mealli,

thankyou once again. It was indeed enlightening.

Dear Rana, am glad that you learnt something out of my question.

I'm not sure I understand the question as stated.

True Homo-Lumo gaps are usually inferred spectroscopically from electronic spectroscopy e.g. Pi=>Pi* transition in benzene.

Reading between the lines are you talking about Huckel theory? If so those are pretty crude estimates - but elegant because the matrix form is simple.  I think one of the other answers addressed that energies in chemistry are defined to be NEGATIVE, the free electron has an energy of ZERO. The bound electron in H2 an energy of -13.6 eV, the various energy levels between those two limits are given pretty well by the Rydberg states (or Huckel theory, Hartree Fock, etc.)

At a guess, the link between BAND GAPS which are Fermi level to Conduction band gaps typically, and the HOMO-LUMO gap may be of some interest, but this neglects the very different results obtained from a MOLECULAR view (HOMO-LUMO) and a continuous MODEL view of the solid state (BAND GAP). Sadly the two theories meet up rather badly in the nano-domain and this is a true frontier area for research. That's because neither view is very good in this crossover domain.

Your question; Why is it that, in determination of HOMO-LUMO gap, many authors report without following mathematical rules?

The energy of HOMO is measured experimentally (PES) and the energy of LUMO is measured as Electron affinity (similar technique). These are reliable values, I don't argue. The calculated HOMO energy using CCSD (a-cc-QZV) give HOMO energies comparable to PES (occupied orbital). Not so the empty orbitals (LUMO). The only one thing that you have to look for in calculations is that LUMO must be above or near zero. LUMO is a destructive combination of wave function,

Funny, the destructive combination is above the constructive one. (nerd thought)

Dr. Carlo Mealli,

I happened to see the discussion on HOMO-LUMO, when I was browsing to know more about the importance of HOMO-LUMO in molecular modelling. I highly appreciate your interpretation.

Simle as Carlo Mealli's explaination. If we know carefully what HOMO and LUMO, the calculation for band gap is simple.

Thank you to all for suggestions !

I am new user of  Gaussian. Can anybody tell me any software for visualing HOMO-LUMO gap. I am doing H2O2 clusters (dimer, trimer etc.) calculations. I want to visualize HOMO-LUMO gap in H2O2.

Good tutorials and literature for the same !

Thank you to all

Shilendra

I'm using GaussView for viewing the HOMO-LUMO gap.

Dear Toka Swu, I want to ask which file you visualize in GaussView chk or fchk. My GaussView is not supporting chk file it shows some error. Might be some utility is missing in my GaussView.

Dear S.K. Sharma,

The Gaussian Output File (.LOG). However, GaussView supports .chk files also. May be, like you mentioned, some utility is missing in your GaussView. 

The accuracy depends a lot on the functional used and the basis set. So, what you really need to ask is, what is included in these calculations. You asked what rules? For calculation of the HOMO is rather simple. The exchange correlation in DFT gives a rather poor estimates of HOMO-LUMO gap than the Koopman theorem. The energy of LUMO is a very poor approximation, an empty orbital not well represented in GGA and other current dft approaches. Don't bet EA is the energy of LUMO, therefore the GAP. I think this publication is up to date and might help you.