  Orbital modeling of two electron spins confined in a double quantum dot is
revisited. We develop an extended Hund Mulliken approach that includes excited
orbitals, allowing for a triplet configuration with both electrons residing in
a single dot. This model improves the reliability and applicability of the
standard Hund Mulliken approximation, while remaining largely analytical, thus
it enables us to identify the mechanisms behind the exchange coupling dynamics
that we find. In particular, our calculations are in close agreement with
exchange values that were recently measured at a high interdot bias regime,
where the double occupancy triplet configuration is energetically accessible,
demonstrating reduced sensitivity to bias fluctuations, while maintaining the
large exchange needed for fast gating.
