  The density functional theory (DFT) is a remarkably successful theory of
electronic structure of matter. At the foundation of this theory lies the
Kohn-Sham (KS) equation. In this paper, we describe the long-time behaviour of
the time-dependent KS equation. Assuming weak self-interactions, we prove
global existence and scattering in (almost) the full "short-range" regime. This
is achieved with new and simple techniques, naturally compatible with the
structure of the DFT and involving commutator vector fields and non-abelian
versions of Sobolev-Klainerman-type spaces and inequalities.
