The potential energy surface (PES) corresponding to the reaction of the iron cation with ethane, which represents a prototype of the activation of C-C and C-H bonds in alkanes by transition metal cations, has been investigated employing the recently suggested hybrid density functional theory/Hartree-Fock method (B3LYP) combined with reasonably large one-particle basis sets. The performance of this computational approach has been calibrated against experimentally known Fe+-R binding energies of fragments R relevant to the [Fe,C-2,H-6](+) PES and against the relative energies of the possible exit channels. Both the C-C and C-H bond activation branches of the PES are characterized by a low barrier for the first step, the insertion of the iron cation into a C-C and C-H bond, respectively. Rate determining are the second steps which in the C-C bond activation branch corresponds to an [1,3]-H shift leading to a complex between Fe=CH2+ and methane. Along the C-H activation reaction coordinate, no transition state corresponding to a beta-hydrogen shift resulting in a dihydrido species could be located, even though such a step has been often postulated. The decisive step is rather a concerted saddle point connecting the C-H inserted species directly with a complex of Fe+ with molecular hydrogen and ethylene. The mechanistic scenario provided by our calculations is in concert with all experimental information and allows for the first time a detailed and consistent view on the mechanistic details of this import reaction sequence. It further demonstrates the usefulness of the B3LYP approach for describing even complex electronic situations such as present in open-shell transition metal compounds.