Density-functional derivative discontinuities at the maximum number of bound electrons

Abstract

For every electronic many-body Hamiltonian with a one-body potential that goes to zero at infinity, there is a maximum number of bound electrons (${J}_{\mathrm{max}}$) that can be sustained in the system with an infinite lifetime. At this integer ${J}_{\mathrm{max}}$, the derivative discontinuity in the exact energy of ensemble density functional theory (DFT) is ill defined. However, we investigate the derivative discontinuity of the energy within the framework of density functional resonance theory [D. L. Whitenack and A. Wasserman, Phys. Rev. Lett. 107, 163002 (2011)], which reduces to ground-state DFT as a coordinate scaling parameter is taken to zero, and find that the exact exchange-correlation potential experiences discontinuous jumps at integer particle numbers, including ${J}_{\mathrm{max}}$. For integers below ${J}_{\mathrm{max}}$ the jump is purely real because of the real shift in the chemical potential. At ${J}_{\mathrm{max}}$, the jump has a nonzero imaginary component reflecting the metastability of the system upon addition of one more electron. In addition, the magnitude of the derivative discontinuity at ${J}_{\mathrm{max}}$ is larger than would have been expected by simply setting the affinity to zero.