The derivative discontinuity in the exact exchange-correlation potential of ensemble Density Functional Theory (DFT) is investigated at the specific integer number that corresponds to the maximum number of bound electrons, $J_{ max}$. A recently developed complex-scaled analog of DFT is extended to fractional particle numbers and used to study ensembles of both bound and metastable states. It is found that the exact exchange-correlation potential experiences discontinuous jumps at integer particle numbers including $J_{ max}$. For integers below $J_{ max}$ the jump is purely real because of the real shift in the chemical potential. At $J_{ max}$, the jump has a non-zero imaginary component reflecting the finite lifetime of the $(J_{ max}+1)$ state.
Categories: quant-ph