Simple implementation of complex functionals: scaled self-consistency

We explore and compare three approximate schemes allowing simple implementation of complex density functionals by making use of self-consistent implementation of simpler functionals: (i) post-local-density approximation (LDA) evaluation of complex functionals at the LDA densities (or those of other simple functionals) (ii) application of a global scaling factor to the potential of the simple functional, and (iii) application of a local scaling factor to that potential. Option (i) is a common choice in density-functional calculations. Option (ii) was recently proposed by Cafiero and Gonzalez [Phys. Rev. A 71, 042505 (2005)]. We here put their proposal on a more rigorous basis, by deriving it, and explaining why it works, directly from the theorems of density-functional theory. Option (iii) is proposed here for the first time. We provide detailed comparisons of the three approaches among each other and with fully self-consistent implementations for Hartree, local-density, generalized-gradient, self-interaction corrected, and meta-generalized-gradient approximations, for atoms, ions, quantum wells, and model Hamiltonians. Scaled approaches turn out to be, on average, better than post approaches, and unlike these also provide corrections to eigenvalues and orbitals. Scaled self-consistency thus opens the possibility of efficient and reliable implementation of density functionals of hitherto unprecedented complexity.