Accurate atomic quantum defects from particle-particle random phase approximation

The accuracy of calculations of atomic Rydberg excitations cannot be judged by the usual measures, such as mean unsigned errors of many transitions. We show how to use quantum defect theory to (a) separate errors due to approximate ionization potentials, (b) extract smooth quantum defects to compare with experiment, and (c) quantify those defects with a few characteristic parameters. The particle-particle random phase approximation (pp-RPA) produces excellent Rydberg transitions that are an order of magnitude more accurate than those of time-dependent density functional theory with standard approximations. We even extract reasonably accurate defects from the lithium Rydberg series, despite the reference being open-shell. Our methodology can be applied to any Rydberg series of excitations with 4 transitions or more to extract the underlying threshold energy and characteristic quantum defect parameters. Our pp-RPA results set a demanding challenge for other excitation methods to match.