Real-time real-space TD-DFT for atoms: Benchmark computations on a nonspherical logarithmic grid

We present the results of benchmark, all-electron computations for the optical properties of atoms with up to 30 electrons, carried out within the adiabatic local density approximation (ALDA) of time-dependent density functional theory. Following the original approach proposed by Janak and Williams Phys. Rev. B 23 6301 (1981), Kohn-Sham orbitals are tabulated on a logarithmic mesh along a discrete set of rays coming out of the atomic nucleus, selected in such a way to accurately represent the angular dependence of ground and excited states. Optical properties are obtained by real-time propagation of the electronic states represented on an extended basis of filled and empty Kohn-Sham orbitals. As expected, the comparison with experimental results is affected by the known drawbacks of the ALDA method. We apply the computational tool to carry out a real-time simulation of Auger processes, whose results, once again, highlight basic (but expected) limitations of the TD-DFT-ALDA approach. We define a novel set of atomic-like basis functions (response functions) meant to optimize the convergence of time-dependent computations, and we measure their performance by comparison with the results of the benchmark computations.