Carbonyl
CO is capable of accepting (d)pi electrons by back-bonding by virtue of the C-O multiple bond. So, it’s an unsaturated, soft ligand, in contrast to hard ligands, which are often pi-donnors.
Frontier orbitals of M and CO regulate the bonding. The relevant electronic structure of CO results from the combination of 1 e- from C(pz) and 1 e- from O(pz). The bonding combination pi (CO) has stronger O character, according to the highest electronegativity of O. Conversely, the antibonding combination pi*(CO) has stronger C character. M bonds to C and not to O as a consequence.
Through M bonding polarization occurs, making C more sensitive to nucleofilic attack, and O more sensitive to electrofilic attack. This polarization is modulated by the electronic effect of other ligands and the charge.
The description of M-CO bond is often explained by means of IR spectroscopy. One can visualize three ideal situations (a) M-C≡O, (b) M=C=O and (c) M≡C-O, to argue an increase on the pi back bonding from (a) to (c). The CO stretching frequency (st.) will range from about 1820 to 1250 cm-1.
CO is small, usually strongly held ligand and its complexes tend to coordinative saturation, showing a tendency for the 18 e- configuration.
CO also has a tendency to bridge two metal atoms. In these cases, st CO frequency falls to 1720-1850 cm-1, consistently with the idea of a nucleofilic attack from a second metal. The bridging CO is more basic at O than a terminal one.
Isonitriles
Replacing the O of CO by the isoelectronic but less electronegative fragment NR gives isonitrile CNR. It is a better e- donnor than CO and stabilizes more cationic and higher oxidation states than does CO, but tends to bridge less efficiently than does CO. I is also more sensitive to nucleofilic attack at carbon to give amino carbenes, and has higher tendency to migratory insertion. Unlike CO, the st.CN in isonitrile is often lower than in the free ligand.
The C lone pair is nearly nonbonding in the case of CO, but is much more antibonding in isonitriles, so depletion of e- density by donation to the metal has little effect on st.CO but raises st.CN. Back bonding lowers both st.CO and st.CN. Depending on the balance of sigma vs pi bonding, st.CN is raised for weak pi-donor metals, such as Pt(II), and lowered for strong pi-donor metals, such as Ni(0).
Phosphines
The wide use on phosphines as ligands is due, in part, to its high tunability: electronic effects can be induced to the metall by choosig the right R on PR3.
In phosphines, pi-acidity extent depends on the nature of R. For R= alkyl, pi-acidity is weak. Aryl, dialkylamino and alkoxy groups are successively more effective in promoting pi-acidity. On the extreme, PF3 is as good promoting pi-acidity as CO.
P-R bonds sigma* orbitals play the role of acceptors. That means the more electronegative is R, the more stable sigma*. Also, P contribution to sigma* increases making sigma* more accessible for back donation.