Density-functional derivatives from exact orbital functionals

We demonstrate a method to calculate the density-functional derivative of a physical quantity from its exact orbital-functional expression. For the Kohn–Sham (KS) exchange potential, the method is identical with the optimized effective potential method (OEP). The Krieger-Li-Iafrate (KLI) approximation is also applicable which enables us to calculate KLI derivatives for all functionals. This KLI derivative preserves many essential properties of the functional derivatives and can be used algebraically. As an application, the kinetic energy functional derivative is addressed by this approach. Finally the high-order derivatives and the variational equation are discussed, which also reveals the deficiency of the method.