Correlated optimized effective-potential treatment of the derivative discontinuity and of the highest occupied Kohn-Sham eigenvalue: A Janak-type theorem for the optimized effective-potential model

A Janak theorem is derived for the correlated optimized effective-potential model of the Kohn-Sham exchange-correlation potential nu(xc). It is used t o evaluate the derivative discontinuity (DD) and to show that the highest o ccupied Kohn-Sham eigenvalue, epsilon(H)congruent to -I, the negative of th e ionization potential, when relaxation and correlation effects are include d. This reconciles an apparent inconsistency between the ensemble theory an d fractional occupation number approaches to noninteger particle number in density-functional theory. For finite systems, epsilon(H)= -I implies that nu(xc)(infinity)=0 independent of particle number, and that thr DD vanishes asymptotically as 1/r. The difference in behavior of the DD in the bull; a nd asymptotic regions means that the DD affects the shape of nu(xc), even a t fixed, integer particle number. [S0163-1829(99)04907-3].