System-dependent exchange-correlation functional with exact asymptotic potential and εHOMO ≈ - I.

Density scaling considerations are used to derive an exchange-correlation explicit density functional that is appropriate for the electron deficient side of the integer and which recovers the exact r → ∞ asymptotic behaviour of the exchange-correlation potential. The functional has an unconventional mathematical form with parameters that are system-dependent; the parameters for an N-electron system are determined in advance from generalised gradient approximation (GGA) calculations on the N- and (N - 1)-electron systems. Compared to GGA results, the functional yields similar exchange-correlation energies, but HOMO energies that are an order of magnitude closer to the negative of the vertical ionisation potential; for anions, the HOMO energies are negative, as required. Rydberg excitation energies are also notably improved and the exchange-correlation potential is visibly lowered towards the near-exact potential. Further development is required to improve valence excitations, static isotropic polarisabilities, and the shape of the potential in non-asymptotic regions. The functional is fundamentally different to conventional approximations.