  The concept of $\pi$ backbonding is widely used to explain the complex
stabilities and CO stretch frequency red shifts of transition metal carbonyls.
We theoretically investigate a non-transition metal 18-electron carbonyl
complex (Mg(CO)$_8$) and find a pronounced CO red shift without metal-carbon
$\pi$ bonds. Moreover, we use truncated basis sets on the "honorary" and true
transition metals Ca and Ti in Ca(CO)$_8$ and [Ti(CO)$_8$]$^{2+}$ complexes to
probe the influence of $d$ functions on carbonyl complex stability, C-O bond
strength, metal-to-ligand charge transfer and bond order compared to
hypothetical complexes without metal-$d$ contributions. We find that the
occurrence of metal-ligand $\pi$ bonds through metal $d$ functions greatly
enhances the complex stabilities on one hand but only slightly affects the CO
red shift on the other hand. This does not correspond to the classical
rationalization of transition metal-CO bonds as synergistic $\sigma$
donation/$\pi$ backdonation.
