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The cyclopentadienyl ligand is based on ${\mathrm{C}}_5{\mathrm{H}}_5^{-}$. In its common ${\eta }^5$ mode it binds through five ring carbons and donates six electrons in ionic electron counting. Ring substitution can create distinct NMR environments.

Use an ${\eta }^5$ cyclopentadienyl ligand and four terminal carbonyl ligands at each titanium, with a Ti–Ti single metal-metal bond. The middle panel shows this connectivity. Neutral electron counting assigns five electrons to each Cp and givesEquivalently, the two Cp anions require an average oxidation state Ti(I), hence $d^3$; ionic counting gives $3+6+8+1=18$. The formal Ti–Ti bond order is one. The large coordination envelope can make this bond weak and long; reaching 18 electrons is bookkeeping, rather than proof of a short, strong bond. There is no need to invent extra CO bridges or a higher Ti–Ti bond order.

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]

Write $R$ for the current growing chain. Propene first binds at the available site of $[\mathrm{C}{\mathrm{p}}_2\mathrm{ZrR}{]}^{+}$, giving a coordinated alkene adjacent to the metal-bound chain. In the Cossee-Arlman mechanism, the chain migrates to the substituted alkene carbon while the terminal carbon forms the new Zr–C bond:The electron-pair arrows for insertion take the old Zr–R bond toward the substituted alkene carbon and the alkene pi bond toward the new Zr–terminal-carbon bond. A four-center arrangement permits both bonds to change in one migratory insertion; Zr remains Zr(IV). The product again has an accessible site, so coordination and insertion can repeat.

Predominant 1,2 insertion leaves a primary Zr–CH${}_2$ chain end and generates head-to-tail polypropylene. It avoids the more crowded alternative secondary Zr–CH(Me) end and unfavorable methyl contacts with the cyclopentadienyl ligands in the insertion geometry. This explains regioselectivity. An unbridged, unsubstituted zirconocene does not by itself establish a fixed tacticity; the schematic alignment of methyl groups in a polymer drawing is not evidence for an isotactic product.

In $A$, the tridentate ligand contains one anionic phenoxide ligand, a neutral secondary amine with its N–H bond intact, and a neutral phosphine ligand. The three chloride ligands contribute another three negative charges. Consequently the neutral complex has Ti(IV), $d^0$, and 12 valence electrons:The N–H label is essential: counting this nitrogen as an anionic amido ligand would give the wrong oxidation state. A six-coordinate early-metal complex need not obey the 18-electron rule.

In $B$, the substituted cyclopentadienyl ligand is ${\eta }^5$ and anionic, while the three-carbon bent ligand is an anionic ${\eta }^3$ allyl ligand, a four-electron donor in ionic counting. The pendant pyridine nitrogen is uncoordinated. Therefore Mo(II), $d^4$, 18 electrons follows fromThe curved delocalization mark across the three-carbon ligand must not be read as a separate alkene or alkyne.

For an intact complex in the usual fast-conformational-averaging regime, counting distinct chemical shifts rather than individual split lines gives $C:9$, $D:11$, $E:10$ signals.

In $C$, the uncoordinated pyridinium arm permits the paired positions of a monosubstituted cyclopentadienyl ligand to average: its four ring hydrogens give two sets, $2+2$. The linker $\mathrm{C}{\mathrm{H}}_2$ gives one set, the four inequivalent pyridinium C–H positions give four, its N–H gives one, and the two symmetry-related bound acetonitrile methyl groups give one. Hence $2+1+4+1+1=9$. The exchangeable N–H resonance may be broadened or absent experimentally; nine is the structural count before exchange removes it.

In the rigid cis-dicarbonyl chelates $D$ and $E$, the different pyridyl-N and fourth-leg donors destroy the operation that related the two sides of the substituted ring. Each of the four Cp hydrogens is distinct, and the two linker hydrogens are diastereotopic. Together with four pyridine C–H sites, this gives $4+2+4=10$. The remaining bound acetonitrile adds one methyl signal to $D$, giving 11; $E$ has none, giving 10. The two enantiomers of a racemate have identical spectra in an achiral solvent and do not double these counts. This prediction assumes resolved resonances and no rapid chelate opening that averages inequivalent sites; variable-temperature proton nuclear magnetic resonance would test that assumption.

Neutral counting assigns five electrons to cyclopentadienyl ligand and two to CO. Thus each $\mathrm{FeCpCO}$ fragment has $8+5+2=15$ valence electrons and contributes three skeletal electrons; each $\mathrm{CoCpCO}$ fragment has sixteen and contributes four:For A the six-pair four-vertex count is the nido count derived from a five-vertex trigonal bipyramid. Removing an axial vertex leaves a tetrahedron: the three equatorial vertices plus the remaining axial vertex. For B the corresponding arachno fragment is obtained by removing both axial vertices from that same parent, leaving a three-metal triangle. Small clusters require specifying the parent and removed vertices; mechanically calling every nido fragment a square pyramid is wrong.

The Fe tetramer is indeed known to have a tetrahedral $\mathrm{F}{\mathrm{e}}_4$ core, with four face-capping CO groups. The carbon atoms of those carbonyls and the iron atoms form interpenetrating tetrahedra, giving a cubane-like Fe–C connectivity. Bridging rather than terminal CO changes the distribution of local donation, not the total electron count above.^[ref]

The pentamethylcyclopentadienyl ligand is the anion ${\mathrm{C}}_5\mathrm{M}{\mathrm{e}}_5^{-}$, normally a six-electron ${\eta }^5$ donor in ionic electron counting. Its methyl substituents change steric hindrance and electron donation relative to an unsubstituted cyclopentadienyl ligand.