A ug 1 99 5 A generalized local approximation to the exchange potential

One of the major challenges in the density functional theory [1–4] is to improve the treatment of the exchange and correlation energy terms in inhomogeneous systems. Among the most vigorously pursued schemes is the inclusion of generalized gradient corrections to the local density approximation (LDA) [4,5]. One of the persistent problems related to the current formulations of LDA is the fact that the single–particle energies obtained in these methods have no direct relationship with the actual single–particle spectrum of the systems under consideration (with the exception of the ionization energies though). In particular, the gaps in semiconductors are severely underestimated [6]. It has been argued [7] that the origin of this discrepancy is the very nature of the local approximation to the density functional theory. This is one reason why, following an earlier argument [8], the electronic properties of several compounds were recently computed in an exact treatment of the exchange energy [9]. An improvement to the gap problem in semiconductors seems to be provided by the so called self–interaction method [10]. Here we have chosen to explore another line of inquiry, inspired by the so called optimized effective potential (OEP) treatment of the exchange energy. This method was first introduced in atomic physics [11,12] and has been increasingly revisited lately [13]. This recent activity generated some significant developments, for instance, a time dependent extension of the OEP approach [14]. So far, most of the applications of the OEP have been devoted to the exchange only functionals. As in the OEP method, we shall consider the total energy of a many electron system Etot in the Hartree–Fock approximation only