  We show that electrons in coupled quantum dots characterized by high aspect
ratios undergo abrupt density rotations when the dots are biased into an
asymmetric confinement configuration. Density rotations occur with electron
transfer to a single dot, and give rise to sharp variations of the exchange
coupling between electrons as a function of inter-dot detuning. Our analysis
based on exact diagonalization technique indicates that this unusual behavior
is in agreement with the von Neumann-Wigner theorem that dictates the
variations of the energy spectrum from the symmetries of the molecular states
during the detuning process. It is also shown that the overall effect is
quenched by the presence of magnetic fields, which by adding angular momentum
to the electron motion affects the spatial symmetry of the molecular states.
