Building Kohn–Sham Potentials for Ground and Excited States

Abstract

We analyze the inverse problem of Density Functional Theory using a regularized variational method. First, we show that given k and a target density $$\rho $$ , there exist potentials having kth bound mixed states which densities are arbitrarily close to $$\rho $$ . The state can be chosen pure in dimension $$d=1$$ and without interactions, and we provide numerical and theoretical evidence consistently leading us to conjecture that the same pure representability result holds for $$d=2$$ , but that the set of pure-state v-representable densities is not dense for $$d=3$$ . Finally, we present an inversion algorithm taking into account degeneracies, removing the generic blocking behavior of standard ones.