can then establish the validity and accuracy of other basis sets, which can be used to extend the system sizes to that beyond what is practical using PW basis set. As seen in Table \[tab:valley\], the valley splitting value converges to 93 meV using 80-layer cladding. The DZP localized basis set gives an excellent agreement at 99.5 meV using 80-layer cladding (representing a 7% difference). On the other hand, the SZP localized basis set (similar to what was used in Refs.  and ) gave a value of 145 meV using the same amount of cladding. This represents a significant difference of 55% over the value obtained using PW basis set, and demonstrates that the SZP basis set is unsuitable for accurate determination of valley splitting in these systems.

Density of states {#sec:eDOS}
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The electronic density of states (eDOS) was calculated for each cell. Figure \[fig:eDOS\] compares the unscaled eDOS for bulk 80-layer cells to that of doped cells varying from 40 to 80 layers. The bulk bandgap is visible, with the conduction band rising sharply to the right of the figure. The doped eDOS exhibits density in the bulk bandgap, although the features of the spectra differ slightly according 