Dear Rajendra,

Koopmans' theorem states that in closed-shell Hartree–Fock theory, the first ionization energy of a molecular system is equal to the negative of the orbital energy of the highest occupied molecular orbital (HOMO).

Koopmans' theorem is exact in the context of restricted Hartree–Fock theory if it is assumed that the orbitals of the ion are identical to those of the neutral molecule (the frozen orbital approximation). Ionization energies calculated this way are in qualitative agreement with experiment – the first ionization energy of small molecules is often calculated with an error of less than two electron volts.

A similar theorem exists in density functional theory (DFT) for relating the exact first vertical ionization energy and electron affinity to the HOMO and LUMO energies, although both the derivation and the precise statement differ from that of Koopmans' theorem. Ionization energies calculated from DFT orbital energies are usually poorer than those of Koopmans' theorem, with errors much larger than two electron volts possible depending on the exchange-correlation approximation employed. The error in the DFT counterpart of Koopmans' theorem is a result of the approximation employed for the exchange correlation energy functional.

So that, first, it much depends by the kind of functional used in your calculations and not always get through it with a good approximation. 

Please, take a look at this question asked some months ago:

https://www.researchgate.net/post/How_can_we_calculate_ionization_potential_and_electron_affinity_by_DFT

I hope it may be helpful.

Best,

A.

https://www.researchgate.net/post/How_can_we_calculate_ionization_potential_and_electron_affinity_by_DFT