those values were taken from the unfitted, untransformed donor-electron distribution, and represent a $\sim$15% underestimation of the DZP result.

Conclusion {#sec:conclusion}
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In this article, we have studied the valley splitting of monolayer $\delta$-doped Si:P, using a density functional theory model with a plane-wave basis to establish firm grounds for comparison with less computationally-intensive localized basis *ab initio* methods. We found that the best current descriptions of these systems (by density functional theory, using SZP basis functions) overestimate the valley splitting by over 50%, due to an assumption made early in their methodology. We show that DZP basis sets are complete enough to deliver values within 10% of the plane-wave values, and due to their localized nature, are capable of calculating the properties of models twice as large as is tractable with plane-wave methods. These DZP models are converged with respect to size well before their tractable limit, which approaches that of SZP models.

Valley splittings are important in interpreting transport spectroscopy experiment data, where they relate to families of resonances, and in benchmarking other theoretical techniques more capable of actual device modeling. It is therefore pleasing to have an *ab initio* description of this effect which is fully-converged with 