Simple impurity embedded in a spherical jellium: Approximations of density functional theory compared to quantum Monte Carlo benchmarks

We study the electronic structure of a spherical jellium in the presence of a central Gaussian impurity. We test how well the resulting inhomogeneity effects beyond spherical jellium are reproduced by several approximations of density functional theory (DFT). Four rungs of Perdew's ladder of DFT functionals, namely, local density approximation, generalized gradient approximation (GGA), meta-GGA, and orbital-dependent hybrid functionals are compared against our quantum Monte Carlo (QMC) benchmarks. We identify several distinct transitions in the ground state of the system as the electronic occupation changes between delocalized and localized states. We examine the parameter space of realistic densities (1{open_square}r{sub s}{open_square}5) and moderate depths of the Gaussian impurity (Z<7). The selected 18-electron system (with closed-shell ground state) presents 1d{yields}2s transitions, while the 30-electron system (with open-shell ground state) exhibits 1f{yields}2p transitions. For the former system, the accuracy for the transitions is clearly improving with increasing sophistication of functionals with meta-GGA and hybrid functionals having only small deviations from QMC. However, for the latter system, we find much larger differences for the underlying transitions between our pool of DFT functionals and QMC. We attribute these failures to an insufficiently accurate treatment of exchange by these functionals. Additionally, we amplify the inhomogeneity effectsmore » by creating the system with spherical shell, which leads to even larger errors in DFT approximations.« less