  We employ density functional calculated eigenstates as a basis for exact
diagonalization studies of semiconductor double quantum dots, with two
electrons, through the transition from the symmetric bias regime to the regime
where both electrons occupy the same dot. We calculate the singlet-triplet
splitting $J(\epsilon)$ as a function of bias detuning $\epsilon$ and explain
its functional shape with a simple, double anti-crossing model. A voltage noise
suppression "sweet spot," where $dJ(\epsilon)/d\epsilon=0$ with nonzero
$J(\epsilon)$, is predicted and shown to be tunable with a magnetic field $B$.
