Accurate Correlation Potentials from the Self-Consistent Random Phase Approximation

Density-functional theory (DFT) within the Kohn-Sham (KS) formalism is the most widely used approach to treat electronic structures of molecules and solids in physics, chemistry, and materials science, and the development of more accurate functionals for the KS exchange and correlation energy has been a major research focus for decades. The corresponding exchange and correlation potentials, on the other hand, have attracted little attention. Those cases for which reference potentials are available showed that in particular correlation potentials from common approximate density functionals are of poor quality and sometimes have little in common with the exact potentials. This hampers the further development of KS-DFT. Here, we show that highly accurate correlation potentials can be obtained within the random phase approximation (RPA). In conjunction with the exact exchange potential, which, like the RPA correlation potential, is accessible within the optimized effective potential method, highly accurate exchange-correlation potentials are available and provide a basis for the further development of DFT. We present a numerically stable approach for efficiently carrying out self-consistent RPA calculations and combine it with a KS inversion method to obtain reference correlation potentials from highly accurate electron densities from coupled cluster calculations. Accurate exchange-correlation potentials have to yield KS eigenvalues for the highest occupied molecular orbital that are close to the negative of the ionization potential. This is indeed the case, the RPA highest occupied molecular orbital eigenvalues yield ionization potentials that can compete with GW ionization potentials.