Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 1 / 3 / Solution

Solid $\mathrm{MoC}{\mathrm{l}}_2$ contains octahedral $\mathrm{M}{\mathrm{o}}_6$ clusters, while $\alpha$-$\mathrm{MoC}{\mathrm{l}}_3$ has paired molybdenum centres in a layered chloride lattice. The first material is better represented by $\mathrm{M}{\mathrm{o}}_6\mathrm{C}{\mathrm{l}}_{12}$ than by isolated bent or linear $\mathrm{MoC}{\mathrm{l}}_2$ molecules. Eight inner chlorides cap the triangular faces of an octahedral metal core, giving $[\mathrm{M}{\mathrm{o}}_6({\mu }_3-\mathrm{Cl}{)}_8{]}^{4+}$. Outer chloride coordination completes the solid: one useful connectivity notation is $\mathrm{M}{\mathrm{o}}_6\mathrm{C}{\mathrm{l}}_8\mathrm{C}{\mathrm{l}}_2\mathrm{C}{\mathrm{l}}_{4/2}$, with two terminal outer chlorides and four intercluster-shared outer chlorides per octahedron. The empirical total is $8+2+4/2=12$ chlorides for six metals.

Each Mo(II) is formally $d^4$, giving 24 metal-based electrons. These support extensive Mo–Mo bonding along the 12 octahedral edges; they are not localized as four free spins on each molybdenum. In $\alpha$-$\mathrm{MoC}{\mathrm{l}}_3$, Mo(III) is $d^3$ in edge-sharing $\mathrm{MoC}{\mathrm{l}}_6$ octahedral layers. The metal honeycomb distorts into short Mo–Mo pairs. A localized dimer picture uses the six d electrons to fill one sigma and two pi bonding combinations, producing a formal triple bond and pairing the spins. The bulk crystal remains an extended chloride lattice, rather than a collection of unconnected $\mathrm{M}{\mathrm{o}}_2\mathrm{C}{\mathrm{l}}_6$ molecules.

By comparison, $\mathrm{CrC}{\mathrm{l}}_2$ has predominantly localized high-spin Cr(II), $d^4$, in Jahn–Teller-distorted chloride octahedra; $\mathrm{CrC}{\mathrm{l}}_3$ has layered Cr(III), $d^3$, with three locally unpaired electrons. Their magnetic exchange is not evidence for the same strong short multiple bonds as in the molybdenum solids. The greater radial extent of Mo $4d$ orbitals enables larger metal–metal overlap than the more contracted Cr $3d$ orbitals. Real structure and magnetism still depend on ligand geometry and phase, so the orbital comparison is a trend rather than a prohibition of chromium–chromium bonds in other compounds. Diffraction and magnetic/spectroscopic studies directly distinguish the dimerized $\alpha$-$\mathrm{MoC}{\mathrm{l}}_3$ lattice from $\mathrm{CrC}{\mathrm{l}}_3$.^[ref]