  By reverse-engineering from exact solutions we obtain
Hartree-exchange-correlation (Hxc) potentials for a double quantum dot subject
to generic density-density interactions and Hund's rule coupling. We find
ubiquitous step structures of the Hxc potentials that can be understood and
derived from an analysis of stability diagrams. We further show that a generic
Hxc potential can be decomposed into four basic potentials which allows for a
straight-forward parametrization and paves the road for the construction of Hxc
potentials for interacting multi-orbital systems. Finally we employ our
parametrization of the Hxc potential in density functional theory calculations
of multi-orbital quantum dots and find excellent agreement with exact many-body
calculations.
