Implementation of Orbital Functionals in the Context of Time-Dependent Density-Functional Theory

The computational implementation of orbital functionals has become one of the great modern challenges for density-functional theory (DFT). In static cases, the exact procedure of implementing orbital functionals is the so-called optimized effective potential method (OEP). In situations involving temporal variations, in the context of the time-dependent density-functional theory (TDDFT), TDOEP becomes the correct approach. However, both OEP and TDOEP are known by their severe computational costs, and for this reason they are used in a very restricted set of situations. Therefore, the development of approximations is important. In this work, using one-dimensional model systems, we investigate strategies for the implementation of time-dependent orbital functionals, in order to circumvent or avoid the use of TDOEP. We have found that a local scaling approximation to the TDOEP yields encouraging results aiming the numerical implementation of orbital functionals within the TDDFT context.