Abstract
ABSTRACTThe 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.
Highlights
An accurate description of electronic excited states has always been a major goal for theoretical and computational chemists
The difference between particleparticle Tamm-Dancoff approximation (pp-TDA) and particle-particle random phase approximation (pp-RPA) is almost undetectable for these species, so we report data computed with pp-TDA
We have demonstrated that our procedure can be used to extract extremely accurate threshold energies, and maximum errors of order 0.01 for Quantum defect (QD)
Summary
An accurate description of electronic excited states has always been a major goal for theoretical and computational chemists. There are a variety of well-established limitations of TDDFT with the standard semilocal functionals [5] These challenges include double excitations, charge transfer (CT) excitations, and Rydberg excitations[4, 6,7,8,9,10]. We include the experimental values, the pp-TDA results (details given later) and TDDFT calculations using the ALDA kernel and exact ground-state KS potential When average over 6-12, the order has been reversed, so that ALDA appears better when averaged over all transition This trend would continue, with the mean errors in ALDA going to zero as the total number of transitions included increases, while that of pp-TDA tends to about 1 mH. We show below that the pp-TDA results listed here are almost an order of magnitude better than the TDDFT results
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