Electronic Structure of donor pairs in Si

We develop an effective mass theory for a pair of substitutional group-V donors in Si. An empirical central cell correction for a single donor, applied to energies and wavefunctions, leads to an accurate description of the $D_2$ ``molecular'' spectrum. No configuration averages simulating an ensemble of pairs are taken: our formalism applies to the single pair regime, including the A1, T and E single donor states in the hydrogenic S-like manifold and a Configuration Interaction approach to account for electron-electron correlations. We also obtain the inter donor distance dependence of experimentally accessible quantities: first ionization $(D_2^0 \to D_2^+)$, second ionization $(D_2^+ \to D_2^{++})$ energies, charging energy and singlet-triplet splitting. All results are consistent with recently performed experiments on As doped Si, suggesting that our approach is reliable down to distances $\sim$ 2 nm, and possibly smaller.