Electronic structures of the tetrahedral transition-metal complexes MnO4- and Ni(CO)4 and square-planar complex CuCl42- have been calculated, from first principles, by the self-consistent-field Xα scattered-wave (“multiple-scattering”) method. The stabilizing electrostatic fields of typical crystalline environments have been approximately included for MnO4- and CuCl42-, and in the latter example spin-polarized calculations have been carried out. Contour maps of the valence-orbital wave functions and charge density are presented for MnO4-, illustrating the importance of both 2pσ-3d and 2pσ-3d ligand-metal bonding. In Ni(CO)4 there is little evidence for the occurrence of “back-bonding” between the Ni 3d electrons and unoccupied CO 2σ orbitals. Electronic excitations between occupied valence levels and unoccupied levels have been calculated, utilizing Slater's transition-state concept, which accurately includes the effects of spin-orbital relaxation. “Ligand-to-metal” excitations are shown to be most important in MnO4- and CuCl42-, while “metal-to-ligand” excitations are most important in Ni(CO)4. The calculated transition energies are in good agreement with observed visible and near-ultraviolet optical properties, in contrast to the poor agreement previously obtained in semiempirical and ab initio LCAO calculations. All of the reported SCF-Xα scattered-wave calculations have required relatively small amounts of computer time.