The two electron artificial molecule

Exact results for the classical and quantum system of two vertically coupled two-dimensional single electron quantum dots are obtained as a function of the interatomic distance (d) and with perpendicular magnetic field. The classical system exhibits a second order structural transition as a function of d which is smeared out and shifted to lower d values in the quantum case. The spin-singlet - spin-triplet oscillations are shifted to larger magnetic fields with increasing d and are quenched for a sufficiently large interatomic distance.