There are thousands of stable carbonyl cmplxs of TM. The TM are typically in a zero or low oxdn state (e.g., hexacarbonylchromium(0),Cr(CO)6, is an air-stable, white crystalline solid; ν(CO) = 1984 cm^-1). To rationalize the bonding in these cmplxs we have to look at the HOMO-LUMO interactions.
For the HOMOs and LUMOs on CO we must use the sp mixing MO scheme:
CO: 10 valence e⁻ = σ1(2e⁻)σ2 (2e⁻)π1(4e⁻) σ3(2 e⁻)………..π2*(0e⁻) σ4*(0e⁻)
The HOMO is σ3 and is located mainly on C and is donated to the σ MO on the Cr: O≡C:→Cr.
(hybridization such as sp^3d^2 is not used). The π* MOs have the correct symmetry and energy to overlap with the filled tg Cr AOs and there is π back-donation that gives the M-CO partial double-bond character. It is also called synergic bonding: the buildup of e⁻ density on the metal by the σ donation is offset by the π back-donation. Up until ~20 years ago this was fine; the
ν(CO) of typical metal carbonyl cmplxs come in the 2125 - 1850 cm^-1 range of the IR. Borane carbonyl O≡C:→BH3 exhibits the CO stretch at 2165 cm^-1 some 22 cm^-1 above that of uncoordinated carbon monoxide. [1]
There were then reports of stable binary metal carbonyls [(MCO)6]^n+ where π bonding must be small due to the contraction of the d AOs. These cations have high CO stretching frequencies (e.g., [Ir(CO)6]^3+ ; ν(CO) = 2295 cm^-1) [2].
The most remarkable cmplx of this type is Hg(CO)2]2+ (2(Sb2F11)^-1) where ν(CO) = 2280cm^-1) [3]. In the nonTM Hg (especially Hg^2+) the 5d e⁻ are considered as core electrons that do not participate in bonding. These observations are rationalized that the bonding is mainly σ bonding and the HOMO σ3 on CO is slightly antibonding in character (C 2p AO at higher energy); and donation of electron density therefore increases the CO bond order resulting in the shift to higher frequencies in this and similar cmplxs.
I think there is more to this argument but let me leave it at that.
[1]
https://en.wikipedia.org/wiki/Borane_carbonyl [2] Organometallics 1997, 16, 4807.
[3] (Aubke and co-workers) Inorganic Chem. 1996, 35, 82.