Recent arguments for and against the equivalence of the highest occupied or
bital eigenvalue of the Kohn-Sham theory and ionization energy are discusse
d. It is shown that for physically realistic systems with a nonintegral num
ber of electrons, which are described by the thermal average of two systems
, each with an integer number of electrons, an equivalent Kohn-Sham system
exists. This is done by writing explicit expressions for the exchange-corre
lation potential constructed to give the mixed-state density, and then rela
ting it to the mixed-state exchange-correlation energy functional by employ
ing the virial theorem sum rule of Levy and Perdew [phys. Rev. A 32, 2010 (
1985)]. Further, the functional derivative of the mixed-state exchange-corr
elation energy functional is obtained in terms of this potential. This is t
hen used to show, without recourse to Janak's theorem [Phys. Rev. B 18, 716
5 (1978)], that epsilon(max)(N)=-I(Z), where Z is an integer and (Z-1) <N<Z
. Thus the original arguments about the equivalence of the highest occupied
Kohn-Sham orbital eigenenergy and the ionization energy which were based o
n Janak's theorem are valid, and the two quantities are equal. [S0163-1829(
99)11131-7].