  We derive an accurate molecular orbital based expression for the coherent
time evolution of a two-electron wave function in a quantum dot molecule where
the electrons interact with each other, with external time dependent
electromagnetic fields and with a surrounding nuclear spin reservoir. The
theory allows for direct numerical modeling of the decoherence in quantum dots
due to hyperfine interactions. Calculations result in good agreement with
recent singlet-triplet dephasing experiments by Laird et. al. [Phys. Rev. Lett.
97, 056801 (2006)], as well as analytical model calculations. Furthermore, it
is shown that using a much faster electric switch than applied in these
experiments will transfer the initial state to excited states where the
hyperfine singlet-triplet mixing is negligible.
