Negative excitation energy means that you somehow starten in excited state rather than in ground state. This could happen because of wrong orbital population, wrong first approximation or even incorrect multiplicity or multiconfigurational charcter of true ground state

This often happens if you try to optimize the geometry with respect to an excited-state wavefunction. When you do a geometry optimization and an excited state calculation, you can ignore all excitation energies after the initial calculation because they are calculated with respect to the geometry at EVERY optimization step. If you started at an optimized structure (as you should have), that is the only set of energies that you should care about due to the Born-Oppenheimer effect (unless you really know what you're doing, I guess).

Thanks to you all for your responses. I have actually calculated the excited state energy for ZnS using  EOM-CCSD with basis aug-cc-pvdz. I also try basis tzvpp.I tried B3lyp with aforementioned basis. All gave me gave me negative homo-lumo. I tried calculating exicited state for isolated atoms like Sulphur, Selenium, Silicon using EOM_CCSD and b3lyp but the different between the occupied and unoccupied orbital is negative. Can I manually arrange the electrons into the orbitals under the ORCA platform?

Could you post here your ORCA input file for TDDFT, were you are getting negative HOMO-LUMO gap and excitation?

To switch your HOMO and LUMO use this code in your input:

########

! moread

%moinp "your_previous_wavefunction_file_with_wrong_order.gbw"

%scf rotate { x, y, 90} end end

########

Here x and y stand for HOMO and LUMO orbitals sequence numbers ( note, in ORCA orbitals numeration starts with 0 rather than with 1). Note also, that not only HOMO and LUMO could be in wrong order, check it.

Input file

%pal nprocs 8

end

%paras R =1.625

end

!RKS B3LYP Def2-TZVPP TightSCF Grid4

%tddft nroots 8

maxdim 44

triplets false

end

* xyz 0 1

Zn 0 {R} 0

S 0 {-R} 0

*

OUTPUT-excited states

TD-DFT/TDA EXCITED STATES (SINGLETS)

STATE 1: E= -0.010286 au -0.280 eV -2257.4 cm**-1

STATE 2: E= -0.010286 au -0.280 eV -2257.4 cm**-1

STATE 3: E= 0.128727 au 3.503 eV 28252.3 cm**-1

STATE 4: E= 0.148626 au 4.044 eV 32619.6 cm**-1

STATE 5: E= 0.148749 au 4.048 eV 32646.6 cm**-1

STATE 6: E= 0.148759 au 4.048 eV 32648.8 cm**-1

STATE 7: E= 0.168653 au 4.589 eV 37015.1 cm**-1

STATE 8: E= 0.168653 au 4.589 eV 37015.1 cm**-1

It looks like you have degenerate case and DFT along with other single-reference methods are not applicable here. You have some orbitals with equal energies. Simple CASSCF calculation I made also gives degenerate states.

This way somebody’s down-vote for my first answer was for nothing, it's indeed multireference case