Fournais, Søren; Lampart, Jonas; Lewin, Mathieu; Sørensen, Thomas Østergaard
(2016):
Coulomb potentials and Taylor expansions in timedependent densityfunctional theory.
In: Physical Review A, Vol. 93, No. 6, 62510

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Abstract
We investigate when Taylor expansions can be used to prove the RungeGross theorem, which is at the foundation of timedependent densityfunctional theory (TDDFT). We start with a general analysis of the conditions for the RungeGross argument, especially the time differentiability of the density. The latter should be questioned in the presence of singular (e.g., Coulomb) potentials. Then we show that a singular potential in a onebody operator considerably decreases the class of timedependent external potentials to which the original argument can be applied. A twobody singularity has an even stronger impact and an external potential is essentially incompatible with it. For the Coulomb interaction and all reasonable initial manybody states, the Taylor expansion only exists to a finite order, except for constant external potentials. Therefore, highorder Taylor expansions are not the right tool to study atoms and molecules in TDDFT.