Density functionals with spin-density accuracy for open shells.

Electrons in zero external magnetic field can be studied with the Kohn-Sham (KS) scheme of either density functional theory (DFT) or spin-DFT (SDFT). The latter is normally used for open-shell systems because its approximations appear to model better the exchange and correlation (xc) functional, but also because, so far the application of DFT implied a closed-shell-like approximation. In the first part of this Communication, we show that correcting this error for open shells allows the approximate DFT xc functionals to become as accurate as those in SDFT.

Improving the exchange and correlation potential in density-functional approximations through constraints.

We review and expand on our work to impose constraints on the effective Kohn-Sham (KS) potential of local and semi-local density-functional approximations. Constraining the minimisation of the approximate total energy density-functional invariably leads to an optimised effective potential (OEP) equation, the solution of which yields the KS potential. We review briefly our previous work on this and demonstrate with numerous examples that despite the well-known mathematical issues of the OEP with finite basis sets, our OEP equations are numerically robust.

Density-inversion method for the Kohn-Sham potential: Role of the screening density.

We present a method to invert a given density and find the Kohn-Sham (KS) potential in Density Functional Theory (DFT) that shares the density. Our method employs the concept of screening density, which is naturally constrained by the inversion procedure and thus ensures that the density being inverted leads to a smooth KS potential with correct asymptotic behavior. We demonstrate the applicability of our method by inverting both local and non-local (Hartree-Fock and coupled cluster) densities; we also show how the method can be used to mitigate the effects of self-interactions in common DFT potentials with appropriate constraints on the screening density.