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Molecular $\mathrm{BC}{\mathrm{l}}_3$ has a trigonal-planar sigma framework and ligand-to-boron pi donation. Association energetics differ from those of aluminium chloride.

A coordinated oxide, formally ${\mathrm{O}}^{2-}$. A terminal $\mathrm{M}=\mathrm{O}$ unit is conventionally counted as an $X_2$ ligand giving four electrons in ionic electron counting. Additional oxygen-to-metal pi donation is an orbital-bonding issue and must not be silently mixed with another counting convention.

Use ionic electron counting, counting each ordinary donor atom once and keeping ligand charge distinct from denticity. 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.^[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.

Join three trigonal BO${}_3$ units corner to corner. The resulting alternating six-membered B–O ring has one terminal oxygen on each boron:The superscript records the total charge; the three explicit O${}^{-}$ labels each carry one share of it. Atom counting gives three B, three bridging O and three terminal O. Boron is three-coordinate and approximately trigonal planar. The original structure diagram shows the ring connectivity and terminal atoms.

A planar arrangement permits the perpendicular empty boron p orbitals to accept pi donation from suitable oxygen lone pairs. The terminal oxygens can donate effectively toward one boron, giving their B–O linkages more multiple-bond character and explaining why they are shorter than bridging B–O linkages. A bridging oxygen shares its interactions between two boron centres. An approximately planar ring is therefore expected from the trigonal units and favourable orbital alignment. This reasoning does not require describing the entire anion as benzene-like with an assumed six-electron aromatic ring; the oxygen lone pairs and terminal donations must actually be counted before making an aromaticity claim.

ammonia and cyclohexylamine are sigma-donor ligands; chloride and acetate are sigma- and pi-donor ligands. The nitrogen lone pair of each amine points toward the metal and forms the donor interaction. These saturated amines have no low-lying conjugated acceptor system that would make them conventional pi-acceptor ligands.

chloride uses a lone pair for sigma donation and has additional occupied $p$ orbitals perpendicular to the bond that can donate with pi symmetry. An oxygen-bound acetate similarly has occupied oxygen-centred orbitals available for sigma and pi donation, although its carboxylate resonance in chemistry changes their energies and distribution. Neither should be classified as a pi acceptor merely because its bonding can be drawn with multiple bonds or resonance in chemistry contributors. None of these four is a standard sigma-donor/pi-acceptor ligand.

Dimerization lowers enthalpy by letting the coordinatively unsaturated aluminium centres accept chlorine lone-pair donation. Effective intramolecular Cl-to-Al pi stabilization of the monomer is relatively weak, while aluminium's larger size accommodates four-coordinate geometry and two chloride bridges. At room temperature this bonding gain can outweigh the entropy penalty of associating two molecules.

In boron trichloride, the compact short B–Cl framework supports appreciable ligand-to-boron pi donation, stabilizing the planar monomer. Its smaller boron centre also makes the crowded four-coordinate bridged arrangement less favourable. Thus dimerization must be assessed from the balance of monomer stabilization, bridge-bond formation, structural strain and entropy; merely counting six electrons around each monomeric centre would incorrectly predict identical association for both. orbital overlap depends on radial extent, bond length and energy matching, not just whether two orbitals share the same principal quantum number.

In molecular boron trichloride, boron uses three approximately $s{p}^2$ hybrids to form three equivalent B–Cl sigma bonds in a trigonal plane. Its perpendicular empty $2p$ orbital can accept electron density from the compatible combination of filled chlorine $3p$ lone pairs. The resulting pi donation is delocalized over the three B–Cl connections.

In the elementary model, one net pi bond is distributed over three equivalent sigma bonds, giving formal average B–Cl bond order $1+1/3=4/3$. The corresponding resonance contributors each put a B=Cl connection in a different position, with formal negative boron and positive donating chlorine. They do not mean one experimentally distinct double bond and two single bonds. The $4/3$ value is the idealized sigma-plus-delocalized-pi bookkeeping value; a computed bond index need not equal that exact rational number.

Strong ligand-to-metal pi donation is favoured by an occupied ligand p orbital and a suitable empty metal d orbital of matching symmetry, with reasonably similar energies and good spatial overlap. Small donor atoms such as O or N can supply short bonds and efficient overlap; oxo, imido and nitrido ligands are familiar examples. Early transition metals in high oxidation states, often $d^0$, are particularly favourable because the metal acceptor orbitals are vacant and relatively low in energy. More spatially extended $4d$ and $5d$ orbitals can strengthen the overlap.

Metal-to-ligand pi backbonding is the complementary case: electron-rich, low-oxidation-state metals donate occupied d orbitals into low-lying ligand antibonding orbitals, as for CO. In both directions, filling a metal–ligand pi-antibonding orbital offsets the multiple-bond stabilization. The relevant prediction is orbital occupancy and overlap, rather than the presence of a formal double-bond line in a drawing.

A model in which six donor orbitals of an octahedral complex form $a_{1g}+e_g+t_{1u}$ symmetry-adapted combinations. metal s, p and two d orbitals supply matching symmetry partners; the other three d orbitals remain nonbonding $t_{2g}$ orbitals. The model neglects ligand pi donation, backbonding and departures from octahedral symmetry.