Solution (source code)

= Solution

Use ionic <electron counting>, counting each ordinary donor atom once and keeping ligand charge distinct from <denticity>. \b[A is 16-electron, B is 14-electron and C is 16-electron], so none is an 18-electron complex under this convention.

A contains a modified, monoanionic PNP pincer: the exocyclic double bond and altered pyridine-ring bond pattern in the drawing matter. Its two phosphines and its central N donor provide six <electrons> altogether, while neutral N$_2$ provides two. Neutrality then gives Co(I), $d^8$, and $8+6+2=16$. Treating the modified pincer as a neutral intact <pyridine> ligand would incorrectly produce Co(0) and a 17-electron count. A four-coordinate approximately <square planar molecular geometry> in a $d^8$ complex can leave the strongly sigma-antibonding orbital empty and be stable at 16 <electrons>. The underlying modified-pincer <chemistry> has been examined using structure, spectroscopy and electronic-structure calculations.<Four-Coordinate Cobalt Pincer Complexes: Electronic Structure Studies and Ligand Modification by Homolytic and Heterolytic Pathways by Scott P. Semproni and others>[JACS 136, 9211–9224; modified PNP framework and dinitrogen derivative]{ref}

B has a neutral tertiary <amine> donor at the centre of its tripod and three anionic amido arms. Their combined charge is $-3$, so Re is Re(III), $d^4$. The four N donors give eight <electrons> and N$_2$ gives two: $4+8+2=14$. Such an <electron> count is not inherently unexpected in an amido-supported complex: strong amido <pi donation> and the imposed five-coordinate geometry alter the orbital energies, and the empty orbitals are not nine equivalent slots that must all be filled. Steric protection and <chelation> also help stabilize this coordinatively restricted structure. The 14-electron figure uses the usual two-electron ionic count for each amido donor; pi bonding should not be appended to it inconsistently.

C has an anionic acyl <carbon> donor and a neutral phosphine in the <chelate>, together with two neutral PMe$_3$ donors. Thus Co(I), $d^8$, receives $2+2+4=8$ ligand <electrons>, giving $8+8=16$. This is again a reasonable four-coordinate $d^8$ structure. The acyl C=O is part of a carbon-bound <acyl ligand>, not an additional free CO donor.