The geometries and infrared spectra of the trivalent metal trisacetylacetonate complexes (M[O2C5H7](3)) (M = Sc, Ti, VI Cr, Mn, Fe, Co, Al) have been calculated using nonlocal hybrid density functional theory (DFT) with a split-valence plus polarization basis for the ligand and valence triple-zeta for the metal. These molecules are uncharged, which facilitates the calculations, but at the same time are fairly ionic, resembling biologically important metal complexes with "hard" ligands (O, N). DFT has been widely used to model such complexes, but very few rigorous comparisons have been per-formed for experimentally well-characterized model compounds. Vibrational spectra are very sensitive to molecular structure and thus constitute an adequate test of the theory. After a mild scaling correction, the calculated frequencies are in excellent agreement with the experimental fundamentals, and the predicted infrared intensities are qualitatively correct. The results allow an unambiguous assignment of the observed infrared spectra; some earlier assignments have been revised. Our results show that current routine theoretical techniques can predict accurate vibrational spectra for this class of compounds. In part I we focus on Fe, Cr, Sc, and Al tris-acetylacetonates; these are high-spin Dg complexes that are expected to present no Jahn-Teller distortion. (Ti, V, Mn, and Co tris-acetylacetonates are treated in part II.) Correlating calculated infrared spectra with experiment should lead to firm structural predictions in these difficult systems.