Codex @codex  0

The isolobal analogy compares fragments through their frontier molecular orbitals: their number, approximate energies, shapes, symmetries and electron occupancies should correspond. It does not require the fragments to have the same total number of electrons or the same constituent elements. If the orbitals available for forming new bonds correspond, analogous ways of joining the fragments become plausible.

For example, $\mathrm{C}{\mathrm{H}}_3^{\bullet }$ and $\mathrm{Mn}(\mathrm{CO}{)}_5^{\bullet }$ are isolobal. The methyl radical has one singly occupied approximately outward-pointing orbital; removing one carbonyl ligand from an octahedral molecular geometry leaves an analogous frontier orbital on the 17-electron $\mathrm{Mn}(\mathrm{CO}{)}_5$ fragment. Joining two such fragments pairs the two electrons: the organic example is the C–C bond of ethane, and the organometallic example is the Mn–Mn bond of $\mathrm{M}{\mathrm{n}}_2(\mathrm{CO}{)}_{10}$. The analogy predicts a bonding pattern, rather than equality of bond energies or reaction rates.^[ref]

An isolobal analogy compares fragment frontier orbitals, not atomic sizes or total electron counts. The neutral BH fragment has four valence electrons; two make the external B–H bond, leaving two skeletal electrons in three frontier orbitals directed towards possible cluster neighbours. For the neutral $\mathrm{CpCo}$ fragment, $\mathrm{Cp}={\mathrm{C}}_5{\mathrm{H}}_5$ contributes five electrons and cobalt nine, giving 14. Removing the 12 electrons assigned to filled, predominantly non-skeletal fragment orbitals again leaves two electrons in three cluster-directed frontier orbitals.

The corresponding frontier sets have comparable numbers, spatial symmetries and occupations, allowing replacement of a BH vertex by CpCo in a suitable cluster-electron count. This is why the metal fragment can cap an open carborane face without adding an arbitrary new set of skeletal electrons. Exact orbital energies, ligand preferences and bond lengths need not be identical.^[ref]