Using density functional theory calculations, we have carried out a broad survey of trigonal bipyramidal iron(III) and manganese(III) oxo, sulfido, selenido, and hydroxo complexes, with tripodal tetradentate "triureidoamine" supporting ligands. The calculations reproduce the experimentally observed high-spin states of these compounds; a multifunctional analysis suggests that the high-spin nature of these species follows largely from their trigonal bipyramidal geometry. In conjunction with earlier calculations, the present study provides a broad overview of spin density profiles in iron-oxo species in general. Iron-oxo d(pi)-p(pi) interactions invariably result in a substantial spin density on the oxygen, which in turn may be significantly tuned by hydrogen bonding interactions. The oxygen spin densities are smaller in analogous manganese-oxo species, indicating that manganese is less adept at pi-bonding than iron, which parallels earlier findings on porphyrin systems. The Fe(III)-S/Se spin density profiles provide one of the first confirmations in a transition metal context of Schleyer's prediction that the heavier p-block elements are as effective as their second-row congeners in terms of their pi-donating ability.