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Exact results for the charge and spin densities, exchange-correlation potentials, and density-functional eigenvalues.

We derive asymptotically exact results for the charge and spin densities far away from finite systems (atoms and molecules) and far outside solid surfaces. These results are then used to obtain the correct asymptotic form of the exchange-correlation potential of density-functional (DF) theory and to prove that, for all systems, the eigenvalue of the uppermost occupied DF orbital equals the exact ionization potential. For spin-polarized finite systems we show that the uppermost DF eigenvalue in each spin channel is also given by exact excitation energies.