Accurate atomic quantum defects from particle-particle random phase approximation

TL;DR

This paper demonstrates how quantum defect theory can be used to evaluate and compare the accuracy of atomic Rydberg excitation calculations, showing that particle-particle RPA significantly outperforms standard TDDFT.

Contribution

The authors introduce a methodology using quantum defect theory to assess and compare the accuracy of Rydberg excitation calculations, highlighting the superior performance of pp-RPA.

Findings

pp-RPA yields Rydberg transition energies an order of magnitude more accurate than TDDFT.

Quantum defect analysis effectively separates errors due to ionization potentials.

Method can extract quantum defect parameters from Rydberg series with at least four transitions.

Abstract

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.