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No-go theorem for the description of Mott phenomena with conventional Density Functional Theory methods

Density functional theory provides the most widespread framework for the realistic description of the electronic structure of solids, but the description of strongly-correlated systems has remained so far elusive. Here we consider a particular limit of electrons in a periodic ionic potential in which a one-band description becomes exact all the way from the weakly-correlated metallic regime to the strongly-correlated Mott-Hubbard regime. We provide a necessary condition a density functional should fulfill to describe Mott-Hubbard behavior and show that it is not satisfied by standard and widely used local, semilocal and hybrid functionals. We illustrate the condition in the case of a few-atom system and provide an analytic approximation to the exact exchange-correlation potential based on a variational wave function which shows explicitly the correct behavior providing a robust scheme to combine lattice and continuum methods.