Accurate atomic quantum defects from particle–particle random phase approximation

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 (QD) theory to (a) separate errors due to approximate ionisation potentials, (b) extract smooth QDs 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 four transitions or more to extract the underlying threshold energy and characteristic QD parameters. Our pp-RPA results set a demanding challenge for other excitation methods to match.

GRAPHICAL ABSTRACT

KEYWORDS:

• Quantum defect
• Rydberg excitation
• particle–particle random phase approximation

Acknowledgments

We dedicate this article to Andreas Savin, whose many deep insights and great papers on density functional theory have inspired us over the years. Y.Y. appreciates the support as part of the Center for the Computational Design of Functional Layered Materials, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award DE-SC0012575. K.B. was supported by the U.S Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under award DE-FG02-08ER46496. W.Y. was supported by the National Science Foundation (CHE-1362927).

Supplemental data for this article can be accessed at: http://dx.doi.org/10.1080/00268976.2015.1123316.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Center for the Computational Design of Functional Layered Materials, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences [Grant Number DE-SC0012575]; U.S Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) [Grant Number DE-FG02-08ER46496]; National Science Foundation [Grant number CHE-1362927].