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The wave function and binding energy for shallow donors in GaAs are calculated within the tight binding ͑TB͒ approach, for supercells containing up to two million atoms. The resulting solutions, coupled with a scaling law, allow extrapolation to the bulk limit. A sharp shallow-deep transition is obtained as the impurity perturbation increases. The model allows investigating the quantitative consistency between the effective mass theory and the TB formalism. Although the calculated binding energies are in excellent agreement, anisotropies and the overall decay obtained in the TB envelope function can not be afforded by the hydrogenlike effective mass prediction.