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By reverse-engineering from exact solutions we obtainHartree-exchange-correlation (Hxc) potentials for a double quantum dot subjectto generic density-density interactions and Hund's rule coupling. We findubiquitous step structures of the Hxc potentials that can be understood andderived from an analysis of stability diagrams. We further show that a genericHxc potential can be decomposed into four basic potentials which allows for astraight-forward parametrization and paves the road for the construction of Hxcpotentials for interacting multi-orbital systems. Finally we employ ourparametrization of the Hxc potential in density functional theory calculationsof multi-orbital quantum dots and find excellent agreement with exact many-bodycalculations.

Exchange-correlation potentials for multi-orbital quantum dots subject to generic density-density interactions and Hund's rule coupling