  The differences in energy between electronic bands due to valley splitting
are of paramount importance in interpreting transport spectroscopy experiments
on state-of-the-art quantum devices defined by scanning tunneling microscope
lithography. We develop a plane-wave density functional theory description of
these systems which is size-limited due to computational tractability. We then
develop a less resource-intensive alternative via localized basis functions,
retaining the physics of the plane-wave description, and extend this model
beyond the capability of plane-wave methods to determine the ab initio valley
splitting of well-isolated \delta-layers. In obtaining agreement between
plane-wave and delocalized methods, we show that the valley splitting has been
overestimated in previous ab initio calculations by more than 50%.
