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note
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The transition energies of excited states with relatively long-range charge-transfer character, calculated in the framework of TD-DFT, are usually red-shifted. The simplest explanation for this is that the highest occupied molecular orbital (HOMO) in DFT still corresponds approximately to the ionization potential (IP) but the lowest unoccupied molecular orbital (LUMO) is more bound than in HF and cannot be related to the electron affinity (EA). Therefore, the negative of the LUMO energy is larger than the electron affinity and the orbital energy difference corresponding to CT is considerably lower than the realistic excitation energy. Moreover, the DFT orbital energy is subjected to the so-called self-interaction (SI) error. Since this error is of the same order of magnitude for the occupied and virtual orbitals, the orbital energy differences are relatively good approximations for the excitation energies of non-CT valence excited states. They do not require a change in the number of electrons within independent subsystems, which is necessary for CT states.
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