Kohn-Sham theory Koopmans theorem

A popular alternative is to employ density functional theory (DFT) methods. Kohn-Sham (KS) orbital energies in the ground state are a more reliable predictor of the ion state ordering than Koopmans theorem. There are good theoretical reasons for interpreting them as approximate vertical IE." For transition metal compounds AE methods, the DFT equivalent... 

The most promising approaches for efficient electronic structure calculations on large molecules are generally based on density functional theory with Kohn-Sham orbitals [32-35]. The most efficient such method for CE-BEs is based on Koopmans theorem, but this approach has quite limited accuracy [36-39]. Better accuracy can be obtained from calculations based on an effective core potential [40-45], an equivalent core approximation [46-48], a fractionally occupied transition state [49-52], or with a ASCF approach [29, 31, 53-57]. Time-dependent density functional theory is also widely used for CEBE calculation [58-62], wherein the best results are usually given with functionals having a long-range correction [63, 64]. 

As typically implemented, DFT calculations are similar to HF calculations. A set of MOs called the Kohn-Sham orbitals are iteratively improved until they converge on self-consistency. The number, shape, and symmetry properties of the Kohn-Sham orbitals are similar to the HF orbitals. However, the orbital energies are generally not in good agreement with those from either HF theory or experiment, and so there is no analogue to Koopmans theorem in DFT. 

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