Why do CO and CN- ligands bind via the Carbon atom?

You are correct: it does depends on H*OMO-LUMO matchups on the metal and CO (CN^-: they're isoelectronic)

A variation of Fukui's frontier orbital concept is that a strong bond will form if the H*OMO on one species matches the approximate energy and symmetry of the LUMO on the other and preferably vice versa.

MO scheme for CO:

CO: 10 valence e- σ1(2e-) σ2 (2e-) π1(4e-) σ3(2e-) π2*(0e-) σ4*(0e-)

σ3 is higher in energy than π1 because of sp mixing. This is the H*OMO and is located mainly on the C atom (confirmed by MO calculations). It has the right symmetry and energy to overlap with an empty metal σ AO (I don't use hybridization) to give the M-C σ bond OC:→M,

But the bond is augmented by back-donation from the filled M d AOs (H*OMOs) into the π2* LUMOs of the CO (oncve agin energy and symmetry match). This makes for a strong bond (synergic bonding) without any need for a charge on the metal unlike classical cmplxs. Metals are typically in low or zero oxidation state (Cr(CO)6, Fe(CO)5, Ni(CO)4 all M(0)).

In CN^- the σ3 is at higher energy that makes it a stronger σ donor but it is a weaker π acceptor than CO and accounts for the difference in binding properties. e.g., [Fe(CN)6]^4-or3- Fe(II) or Fe(III)

the bible besides as all important international religions have a concern-unfastened source we now call Paganism, Egyptian Mythology, Greek Mythology and basically airtight Philosophy. The ancients won't have been as technological as we are (notwithstanding some could argue they the place greater so) yet they actually had a deeper understand-how of the international we adventure and the stars above with the aid of learn of shape, quantity and oneself. instructors of airtight theory right this moment are greater beneficial than many times restricted to memberships and are ridiculed by utilising non secular communities and human beings that don't understand, and are for this reason named "Occult" "Satanic" or "Illuminati". you need to look into Manly P. corridor, John Michell (authors) and Danny Wilten on YouTube.