Correlation energies beyond the random-phase approximation: Inhomogeneous Singwi-Tosi-Land-Sjolander functional applied to spherical atoms and ions

The inhomogeneous Singwi, Tosi, Land, and Sjolander (ISTLS) correlation energy functional of Dobson, Wang, and Gould [Phys. Rev. B 66, 081108(R) (2002)] has proved to be successful at predicting correlation energies in semihomogeneous systems, showing promise as a robust next step fifth-rung functional by using dynamic correlation to go beyond the limitations of the direct random-phase approximation (dRPA), but with similar numerical scaling with system size. In this work we test the functional on spherically symmetric, neutral, and charged atomic systems and find it gives excellent results (within 2mHa/e(-) except Be) for the absolute correlation energies of the neutral atoms tested, and good results for the ions (within 4mHa/e(-) except B+). In all cases it performs better than the dRPA. When combined with the previous successes, these new results point to the ISTLS functional being potentially suitable for high-accuracy, benchmark DFT correlation energy calculations in a wide range of systems.