Hardness and excitation energy

The concept of the ensemble Kohn–Sham hardness is introduced. It is shown that the first excitation energy can be given by the Kohn–Sham hardness (i.e. the energy difference of the ground-state lowest unoccupied and highest occupied levels) plus an extra term coming from the partial derivative of the ensemble exchange-correlation energy with respect to the weighting factor w in the limitW→0. It is proposed that the first excitation energy can be used as a reactivity index instead of the hardness.