Coulomb potentials and Taylor expansions in Time-Dependent Density Functional Theory
Abstract
We investigate when Taylor expansions can be used to prove the Runge-Gross Theorem, which is at the foundation of Time-Dependent Density Functional Theory (TDDFT). We start with a general analysis of the conditions for the Runge-Gross 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 one-body operator considerably decreases the class of time-dependent external potentials to which the original argument can be applied. A two-body singularity has an even stronger impact and an external potential is essentially incompatible with it. For the Coulomb interaction and all reasonable initial many-body states, the Taylor expansion only exists to a finite order, except for constant external potentials. Therefore, high-order Taylor expansions are not the right tool to study atoms and molecules in TDDFT.
Keywords
Cite
@article{arxiv.1603.02219,
title = {Coulomb potentials and Taylor expansions in Time-Dependent Density Functional Theory},
author = {Søren Fournais and Jonas Lampart and Mathieu Lewin and Thomas Østergaard Sørensen},
journal= {arXiv preprint arXiv:1603.02219},
year = {2016}
}