Electron affinities and ionisation potentials for atoms via "benchmark" tdDFT calculations with and without exchange kernels.

One of the known weaknesses of the adiabatic connection fluctuation dissipation (ACFD) correlation energy functional under the direct random-phase approximation (RPA) is its failure to accurately predict energy differences between dissimilar systems. In this work we evaluate ionisation potentials I and electron affinities A for atoms and ions with one to eighteen electrons using the ACFD functional under the RPA, and with the "PGG (Petersilka-Gossmann-Gross)" and "RXH (radial exchange hole)" model exchange kernels. All calculations are carried out using a real-space, all electron method with an exact exchange groundstate to minimise errors. As expected, the RPA is less accurate even than some regular density functional theory approaches, while the introduction of a dynamical exchange kernel improves results. In contrast to the case of atomic groundstate energies, the PGG kernel outperforms the RXH kernel for I and A. Mean absolute errors for I/A are found to be 3.27/2.38 kcal/mol, 4.38/5.43 kcal/mol, and 9.24/ 8.94 kcal/mol for the PGG, RXH, and RPA, respectively. We thus show that the inclusion of even the simple "RXH" kernel improves both quantities when compared to the RPA.