A negative HOMO/LUMO gap should not be possible for ground states - the unoccupied orbital is always higher in energy than the occupied one. Either your simulation depicts an excited (and thus unstable) state or the optimization method you're using is unsuited for the given system.

Hello,

I agree with Dimitri. I think that you must have obtained an HOMO more negative than LUMO. The value of HOMO is always higher than LUMO but is a negative value. For example, I have a molecule with HOMO= -5.5 an LUMO= -2.6. The Band Gap is -2.6-(-5.5)=2.9eV. Always the LUMO must be with higher energy.

Regards

How could HOMO has higher energy than LUMO? Unoccupied states must have higher energy. 

One thing you can do, Show your Inputs and resultant energies here, HOMO as well as LUMO energy values. So that one can understand your problem. 

Thank you very much all for your valuable comments. I am truly thankful for your help. 

I think, the clusters are still in the excited state rather than ground state, so I am using different functional and basis set to optimize the structures. 

Can anyone please tell me, whether spin restricted calculation can yield justified homo-lumo gaps?

Shakait. What is the spin momentum of your cluster? The only possibility that I can imagine an empty KS-orbital wit lower energy that an occupied one is in the case that you are computing the "GS" of a given state with high multiplicity. In that case the branch of majority  spin (say alpha) may have occupied KS-MO of higher energy that the first empty MO of the beta branch. An example a Li_10 with "maximum" spin multiplicity  (11). However, this should not happen in low spin multiplicity cases.

Carlos has made an excellent point. When you have a SOMO rather than a HOMO, interesting things can happen. 

Thank you very much for your kind and very helpful answers Dr. Carlos A Cardenas and Dr. Robert Q. Topper. 

In my calculation I have used sextet spin multiplicity. 

What I am not understanding, first I checked the binding energy of the bimetallic clusters from singlet to octet and spin sextet gave the best binding energy. As far I understand, a cluster with high binding energy should have higher homo-lumo gap, too. So, if for this clusters the generated HOMO is actually a SOMO, shouldn't it have lesser binding energy as well? 

The other thing is, I doped this atom both in core and surface. For the core-doped cluster, I got logical homo-lumo gap, which matched  with the experimental value but for the surface doped cluster, I am getting negative homo-lumo gap using the very same functional and basis set, and I used the same spin mulpliticity sextet for both of the dft calculations. In addition, i ran the vibrational analysis and I got no imaginary frenquency; hence this cluster should be stable, as well the homo-lumo gap should be high. 

It would be great to know your thinking regarding this. 

Thanking you again for your kind help. 

I suggest a stability analysis of the wave function. In some situations you can have an unstable wave function, even with no imaginary frequency. One example is NO-. The singlet wave function is unstable, but the stretching frequency is positive.

I know this is about 4 years too late, but in line with Sergio Galembeck's answer, the Kohn-Sham potential is a nonlinear approximation to the true (linear) quantum Hamiltonian. Because of this, it is possible that when you put an electron into an orbital, its eigenvalue "pops" up to something higher than the LUMO. If you try to move the electron again, the orbital it came from shifts downward, and the new occupied orbital shifts upward. In such cases, it is not possible to get a ground state with integer occupation numbers. This is sort of an artifact of the approximations in the exchange-correlation functional, although it can also be proven that not all systems are pure-state V representable (in other words, not every system can be reproduced by filling the orbitals of a single particle potential in order).

Negative homo-lumo gap is only possible when your molecule has higher spin multiplicity. In this case the homo-lumo gap is meaningless due to alpha and beta mixing. Look for homo-lumo (try to calculate homo-lumo gap for alpha electron and beta electron.