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Phys. Chem. Chem. Phys., 2009, 11, 4437 - 4450, DOI: 10.1039/b901402k
Time-dependent density functional theory of high excitations: to infinity, and beyond
Meta van Faassen and Kieron Burke
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.
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