The geometric and electronic structures of the title compounds are calculated with scalar relativistic, gradient-corrected density functional theory. The most stable geometry of ThCp4 (Cp = η5-C5H5) and UCp4 is found to be pseudo-tetrahedral (S4), in agreement with experiment, and all the other AnCp4 compounds have been studied in this point group. The metal–Cp centroid distances shorten by 0.06 Å from ThCp4 to NpCp4, in accord with the actinide contraction, but lengthen again from PuCp4 to CmCp4. Examination of the valence molecular orbital structures reveals that the highest-lying Cp π2,3-based orbitals split into three groups of pseudo-e, t2 and t1 symmetry. Above these levels come the predominantly metal-based 5f orbitals, which stabilise across the actinide series, such that in CmCp4, the 5f manifold is at more negative energy than the Cp π2,3-based levels. The stability of the Cm 5f orbitals leads to an intramolecular ligand→metal charge transfer, generating a Cm(III) f7 centre and increased Cm–Cp centroid distance. Mulliken population analysis shows metal d orbital participation in the e and t2 Cp π2,3-based orbitals, which gradually decreases across the actinide series. By contrast, metal 5f character is found in the t1 levels, and this contribution increases four-fold from ThCp4 to AmCp4. Examination of the t1 orbitals suggests that this f orbital involvement arises from a coincidental energy match of metal and ligand orbitals, and does not reflect genuinely increased covalency (in the sense of appreciable overlap between metal and ligand levels). Atoms-in-molecules analysis of the electron densities of the title compounds (together with a series of reference compounds: C2H6, C2H4, Cp−, M(CO)6 (M = Cr, Mo, W), AnF3CO (An = U, Am), FeCp2, LaCp3, LaCl3 and AnCl4 (An = Th, Cm)) indicates that the An–Cp bonding is very ionic, increasingly so as the actinide becomes heavier. Caution is urged when using early actinide/lanthanide comparisons as models for minor actinides/middle lanthanides.