Correlation potential in density functional theory at the GWA level: Spherical atoms

As part of a project to obtain better optical response functions for nanomaterials and other systems with strong excitonic effects, we here calculate the exchange-correlation (XC) potential of density functional theory (DFT) at a level of approximation which corresponds to the dynamically screened exchange or GW approximation. In this process, we have designed a numerical method based on cubic splines, which appears to be superior to other techniques previously applied to the ``inverse engineering problem'' of DFT, i.e., the problem of finding an XC potential from a known particle density. The potentials we obtain do not suffer from unphysical ripple and have, to within a reasonable accuracy, the correct asymptotic tails outside localized systems. The XC potential is an important ingredient in finding the particle-conserving excitation energies in atoms and molecules, and our potentials perform better in this regard as compared to the local-density approximation potential, potentials from generalized gradient approximations, and a DFT potential based on MP2 theory.