The Pauli approximation for many-electron atoms is derived. This yields an unambiguous expression for the fine-structure splitting and other first-order relativistic corrections to the energy, using nonrelativistic wave functions. A formalism is developed for atoms, based on these results, which is suitable for the evaluation of the fine structure using multiconfiguration wave functions. Fine-structure splittings calculated from Hartree-Fock wave functions are presented for ground states from He through Ar; the remaining energy corrections are also presented. Multiconfiguration results are presented for the lowest ${}_{}{}^2{}_{}{}^{}D$ and ${}_{}{}^2{}_{}{}^{}P$ states of N, accounting for about 80% of the discrepancy between Hartree-Fock values and experimental values.

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