Time-dependent density functional theory of high excitations: To infinity, and beyond

Abstract

We review the theoretical background for obtaining both quantum defects and scattering phase shifts from time-dependent density functional theory. The quantum defect on the negative energy side of the spectrum and the phase shift on the positive energy side merge continuously at E=0, allowing both to be found by the same method. We illustrate with simple one-dimensional examples: the spherical well and the delta well potential. As an example of a real system, we study in detail elastic electron scattering from the He${}^{+}$ ion. We show how the results are influenced by different approximations to the unknown components in (time-dependent) density functional theory: the ground state exchange-correlation potential and time-dependent kernel. We also revisit our previously obtained results for $e$-H scattering. Our results are remarkably accurate in may cases, but fail qualitatively in others.

Resubmitted version, Changed acknowledgments, 17 pages including supplementary table, submitted to PCCP themed issue on time-dependent density-functional theory

References in corpus (5)

• Rydberg transition frequencies from the Local Density Approximation
• Time-dependent Density Functional calculation of e-H scattering
• The quantum defect: the true measure of time-dependent density-functional results for atoms
• A new challenge for time-dependent density-functional theory
• Perturbative and non-perturbative studies with the delta function potential

Cited by in corpus (10)

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• Atoms in boxes: from confined atoms to electron-atom scattering
• Electron Scattering in Time-Dependent Density Functional Theory
• Linear-response range-separated density-functional theory for atomic photoexcitation and photoionization spectra
• Real-time ab initio simulation of inelastic electron scattering using the exact, density functional, and alternative approaches
• Must Kohn-Sham Oscillator Strengths be Accurate at Threshold?
• Accurate atomic quantum defects from particle-particle random phase approximation
• The Role of Exact Conditions in TDDFT