Configuration irregularities: deviations from the Madelung rule and inversion of orbital energy levels

(a) The electron configurations of many atoms that do not obey the Madelung rule of orbital occupancy can be explained by minimum-energy configurations obtained from the Dirac Hyper Hartree–Fock equations. The resulting non-integral occupation of ns and (n−1)d orbitals (the usual interpretation for energy band calculations in solids) explains eight of the ten `anomalousʹ configurations. (b) All four d- and f-block atoms whose singly charged cations result from the loss of an (n−1)d electron rather than an ns electron are shown to have (n−1)d rather than ns as their highest occupied energy levels.