(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 'anomalous' 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. (C) 2002 Published by Elsevier Science B.V.