This paper presents systematic data for 200 neutral diatomic molecules ML (M is it second- or third-row d-block metal and L = H, F, Cl, Br, I, C, N, O, S, or Se) Computed with the density functionals TPSSh and BP86. With experimental Structures and bond enthalpies available for many of these molecules, the computations first document the high accuracy of TPSSh, giving metal-ligand bond lengths with a mean absolute error of similar to 0.01 angstrom for the second row and 0.03 angstrom for the third row. TPSSh provides metal-ligand bond enthalpies with mean absolute errors of 37 and 44 kJ/mol for the second- and third-row molecules, respectively. Pathological cases (e.g., HgC and HgN) have errors of up to 155 kJ/mol, more than thrice the mean (observed with both functionals). Importantly, the systematic error component is negligible as measured by a coefficient of the linear regression line of 0.99. Equally important, TPSSh provides uniform accuracy across all three rows of the d-block, which is unprecedented and due to the 10% exact exchange, which is close to optimal for the d-block as a whole. This work provides an accurate and systematic prediction of electronic ground-state spins, characteristic metal-ligand bond lengths, and bond enthalpies for many as yet uncharacterized diatomics, of interest to researchers in the field of second- and third-row d-block chemistry. We stress that the success of TPSSh cannot be naively extrapolated to other special situations such as, e.g., metal-metal bonds. The high accuracy of the procedure further implies that the effective core functions used to model relativistic effects are necessary and sufficient for obtaining accurate geometries and bond enthalpies of second- and third-row molecular systems.