Communication: Explicit construction of functional derivatives in potential-driven density-functional theory

We propose a method for imposing an important exact constraint on model Kohn-Sham potentials, namely, the requirement that they be functional derivatives of functionals of the electron density p. In particular, we show that if a model potential v(r) involves no ingredients other than rho, del rho, and del(2)rho, then the necessary and sufficient condition for v(r) to be a functional derivative is partial derivative v/partial derivative del rho=del(partial derivative v/partial derivative del(2)rho). Integrability conditions of this type can be used to construct functional derivatives without knowing their parent functionals. This opens up possibilities for developing model exchange-correlation potentials that do not lead to unphysical effects common to existing approximations. Application of the technique is illustrated with examples. (c) 2010 American Institute of Physics. [doi:10.1063/1.3483464]