We computed electron impact ionisation cross sections (EICSs) of iron hydrogen clusters, FeHn with n = 1,2,...,10, from the ionisation threshold to 10 keV using the Deutsch-Märk (DM) and the binary-encounter-Bethe (BEB) formalisms. The maxima of the cross sections for the iron hydrogen clusters range from 6.13 × 10-16 cm2 at 60 eV to 8.76 × 10-16 cm2 at 76 eV for BEB-AE (BEB method based on quantum-chemical data from all-electron basis sets) calculations, from 4.15 × 10-16 cm2 at 77 eV to 7.61 × 10-16 cm2 at 80 eV for BEB-ECP (BEB method based on quantum-chemical data from effective-core potentials for inner-core electrons) calculations and from 2.49 × 10-16 cm2 at 43.5 eV to 7.04 × 10-16 cm2 at 51 eV for the DM method. Cross sections calculated via the BEB method are substantially higher than the ones obtained via the DM method, up to a factor of about two for FeH and FeH2. The formation of Fe-H bonds depopulates the iron 4s orbital, causing significantly lower cross sections for the small iron hydrides compared to atomic iron. Both the DM and BEB cross sections can be fitted perfectly against a simple expression used in modelling and simulation codes in the framework of nuclear fusion research. The energetics of the iron hydrogen clusters change substantially when exact exchange is present in the density functional, while the cluster geometries do not depend on this choice.
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