Simple implementation of complex functionais:Scaled self-consistency

摘要

We explore and compare three approximate schemes allowing simple implementation of complex density functionais by making use of self-consistent implementation of simpler functionais:(i)post-local-density approximation(LDA)evaluation of complex functionais at the LDA densities(or those of other simple functionais)(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.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 functionais of hitherto unprecedented complexity.