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

TL;DR

This paper reviews how time-dependent density functional theory can be used to calculate quantum defects and scattering phase shifts, demonstrating its effectiveness and limitations through simple models and real system applications.

Contribution

It introduces a unified method within TDDFT to compute both quantum defects and phase shifts, bridging negative and positive energy spectra.

Findings

Accurately predicts quantum defects and phase shifts in simple models.

Shows influence of approximations on scattering results.

Identifies cases where TDDFT succeeds or fails qualitatively.

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.