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In the chromium complex, Cr(0) is $d^6$ and receives substantial donation from four carbonyl ligands. Its occupied orbitals can give pi backbonding into the boron-rich acceptor orbitals of the B${}_2$N${}_2$ ring, while the nitrogen-rich occupied ring orbitals donate to the metal. This favors binding across the ring face, approximately ${\eta }^4$, with all four ring atoms participating. A nearly planar ring maintains the p-orbital alignment needed for that interaction and accounts for comparable Cr–B and Cr–N distances. A four-electron ring donor also gives the useful count $6_d+8_{\mathrm{CO}}+4_{\mathrm{ring}}=18$.

Ti(IV) in TiCl${}_4$ is $d^0$ and strongly electron deficient. It is a good acceptor for the two nitrogen lone pairs, but has no filled $d$ set for comparable backbonding into the boron acceptors. chromium therefore favors a face-bound pi complex, while titanium favors N,N sigma coordination. Donation makes the nitrogen environments more nearly tetrahedral and permits the 2,4-Diazadiboretidine ring to pucker. The borons are not directly bound in the same way, explaining $d(\mathrm{Ti}\cdots \mathrm{B})>d(\mathrm{Ti}-\mathrm{N})$. The distinction follows from electron availability, rather than simply calling every short metal–ring contact a separate ordinary sigma bond.

In borazine, each B and N is approximately trigonal planar. The alternating ring contains a sigma framework with perpendicular p orbitals; the nitrogen lone pairs can donate into the boron acceptor orbitals. Six pi electrons can therefore be distributed around the ring, giving partial B–N multiple-bond character rather than six ordinary isolated single bonds. Equal ring distances are compatible with this symmetric delocalization.

The electronegativity difference makes each B–N bond strongly polar, ${\mathrm{B}}^{\delta +}-{\mathrm{N}}^{\delta -}$. The occupied pi orbitals are weighted toward N, and the empty acceptors toward B. In benzene, equivalent carbon centers give much more even pi distribution and strong resistance to addition that destroys the aromatic system. borazine resembles benzene geometrically but has substantially more polarized, more reactive bonding. It presents electrophilic boron sites to nucleophiles and nitrogen donors to Lewis acids. Polar reagents can add across B–N, and water can cleave the ring; benzene ordinarily favors substitution under suitable conditions rather than facile polar addition or hydrolysis. The label “inorganic benzene” should therefore not be interpreted as identical aromatic stabilization or reactivity. nitrogen-bound Lewis-acid adducts and hydrogen-halide additions demonstrate this contrast experimentally.^[ref]

Start from an octahedral molecular geometry with ligands on $\pm x,\pm y,\pm z$, with $e_g=(d_{z^2},d_{x^2-y^2})$ above $t_{2g}=(d_{xy},d_{xz},d_{yz})$. Remove the $-z$ donor while keeping the other five positions. Loss of axial repulsion lowers $d_{z^2}$ substantially; $d_{x^2-y^2}$ still points directly at four basal donors and remains highest. Loss of an axial donor also lowers the orbitals with $z$ dependence relative to $d_{xy}$. The remaining fourfold axis keeps $d_{xz}$ and $d_{yz}$ degenerate.

The usual qualitative square-pyramidal molecular geometry diagram, shown in the last panel above, is thereforeThe corresponding $C_{4v}$ labels are $b_1,a_1,b_2,e$. Energies can be re-zeroed to the new orbital barycenter after ligand removal. Symmetry fixes the degeneracy and labels, but does not universally fix the separation of $d_{z^2}$ and $d_{xy}$: a weak or distant axial donor can reverse this middle pair on approach to the square-planar limit. The displayed ordering assumes an appreciable fifth axial interaction.

For comparable octahedral environments with the same donor set, the expected qualitative order isAcross comparable first-row ions, the increasing effective attraction and changing metal–ligand distances tend to increase octahedral splitting, giving Mn(II) below Fe(II). Raising the charge on the same metal gives Fe(III) above Fe(II), because the ligand interaction generally strengthens and metal–ligand distances contract. Moving from $3d$ to more radially extended $4d$ orbitals gives larger metal–ligand overlap, placing Mo(III) above Fe(III); Rh(III) lies further along the same $4d$ series and typically gives the larger splitting. The $5d$ ion Pt(IV) combines the heavier row with high charge and gives the largest splitting here.

This is a matched-environment trend, not an intrinsic list of constants for bare ions. Actual $\Delta$ also depends strongly on donor identity, geometry and distance. It would be meaningless to compare an unspecified weak-field tetrahedral compound with a strong-field octahedral compound solely through this ordering.

The dimer has two unpaired electrons and a triplet ground state, $S=1$. Its approximately threefold-symmetric Fe${}_2$(CO)${}_3$ core supplies a pair of degenerate frontier molecular orbitals. The last two electrons occupy separate members with parallel spins, favored by exchange, rather than pairing in one. A useful qualitative picture is a sigma bond plus two perpendicular, singly occupied pi half-bonds: together these support a formal Fe–Fe double bond while retaining paramagnetism. The spin-only magnetic moment for $S=1$ is $\sqrt{8}{\mu }_B\simeq 2.83{\mu }_B$; real moments can include orbital and spin–orbit effects.

The formal 18-electron count does not require every molecular orbital to be doubly occupied. It is therefore compatible with an open-shell dimer. The primary structural/magnetic study establishes this unusual triplet state; an isolated-atom high-spin $d^7$ diagram would not describe the coupled metal–ligand system.^[ref]

For the doubly bridged tetracarbonyl, each iron has one terminal carbonyl ligand, two bridging carbonyl ligands and one cyclopentadienyl ligand. Neutral electron counting gives $8+5+2+2=17$ before direct bonding, so a single Fe–Fe bond gives 18 at each iron. For the triply bridged tricarbonyl, each iron instead has $8+5+3=16$ before direct bonding; formal completion to 18 requires a double Fe–Fe bond. Equivalently, the total fragment counts before metal–metal bonding are 34 and 32 respectively.The increased direct bond order explains the substantial contraction. The pentamethylcyclopentadienyl ligands also alter steric and electronic effects, and bridge geometry changes, so this is not a controlled measurement of bond order alone. Nevertheless, the markedly shorter distance in the less carbonyl-saturated dimer is consistent with stronger direct Fe–Fe bonding. The isolated triply bridged compound was characterized structurally and magnetically in the primary work.^[ref]