Eur. Phys. J. B (2018) 91: 96
https://doi.org/10.1140/epjb/e2018-90101-2

Regular Article

Electron scattering in time-dependent density functional theory^★

¹ Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, NY 10065, USA
² Department of Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
³ The Physics Program and the Chemistry Program of the Graduate Center of the City University of New York, 695 Park Avenue, New York, NY 10065, USA

^a e-mail: liolacombe@gmail.com
^b e-mail: yasumitsu.suzuki@rs.tus.ac.jp
^c e-mail: kazuyuki@rs.kagu.tus.ac.jp
^d e-mail: nmaitra@hunter.cuny.edu

Received: 28 February 2018
Received in final form: 9 April 2018
Published online: 4 June 2018

Abstract

It was recently shown [Suzuki et al., Phys. Rev. Lett. 119, 263401 (2017)] that peak and valley structures in the exact exchange-correlation potential of time-dependent density functional theory (TDDFT) are crucial for accurately capturing time-resolved dynamics of electron scattering in a model one-dimensional system. Approximate functionals used today miss these structures and consequently underestimate the scattering probability. The dynamics can vary significantly depending on the choice of the initial Kohn-Sham state, and, with a judicious choice, a recently-proposed non-adiabatic approximation provides extremely accurate dynamics on approach to the target but this ultimately also fails to capture reflection accurately. Here we provide more details, using a model of electron-He⁺ as illustration, in both the inelastic and elastic regimes. In the elastic case, the time-resolved picture is contrasted with the time-independent picture of scattering, where the linear response theory of TDDFT can be used to extract transmission and reflection coefficients. Although the exact functional yields identical scattering probabilities when used in this way as it does in the time-resolved picture, we show that the currently-available approximate functionals do not, even when they have the correct asymptotic behavior.