The time-dependent optimized effective potential

Abstract

The optimized effective potential (OEP) method is a formally exact approach to treat orbital-dependent exchange-correlation functionals. The first part of this chapter reviews the static OEP method. Orbital-dependent exchange-correlation functionals are implicit density functionals. The associated exchange-correlation potential is constructed via an integral equation. In particular, the exact exchange potential is defined in this way, starting from the Fock exchange energy functional. The resulting exchange potential has the correct asymptotic behaviour, and has a discontinuity as a function of particle number. Several properties and applications of the static OEP are reviewed. The second part of the chapter discusses the time-dependent OEP method. Again, the time-dependent exchange-correlation potential is constructed with an integral equation, which is derived from a variational principle. Two case studies are discussed, which illustrate the memory dependence and the discontinuity of the exchange correlation potential. The linear-response limit of the time-dependent OEP is introduced.