  We calculate the exchange energy in two dimensional laterally coupled quantum
dots using Heitler-London, Hund-Mullikan and variational methods. We assess the
quality of these approximations in zero and finite magnetic fields comparing
against numerically exact results. We find that surprisingly, the Hund-Mullikan
method does not offer any significant improvement over the much simpler
Heitler-London method, whether at large or small interdot distances. Contrary
to that, our variational ansatz proves substantially better. In a single dot at
finite magnetic field, all approximate methods fail. This reflects the
qualitative change of the single electron ground state from non-degenerate
(harmonic oscillator) to highly degenerate (Landau level). However, we find
that the magnetically induced failure does not occur in the most important,
double-dot, regime.
