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arXiv · 0901.3418

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

Meta van Faassen·Kieron Burke
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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.

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Meta van Faassen, Kieron Burke. 2009-01-22. Time-dependent density functional theory of high excitations: To infinity, and beyond. https://doi.org/10.1039/b901402k

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