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

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 many cases, but fail qualitatively in others.