How is the bonding in the [Au6C(PPh3)6]2+ cluster explained?

Question

How can carbon form six bonds in such a compound as $\ce{[Au6C(PPh3)6]^2+}?$ I understand how carbon with five bonds can be formed $(\ce{CH5+},$ for instance), but it shouldn't have enough electrons to form six bonds.

Answer 1

This is by no means a trivial case. You are dealing with a so-called template or interstitial atom placement within a cluster shell. There is a thorough review available [1, pp. 18–20] (reference numbers updated):

An alternative way of satisfying the closed shell electronic requirements and retaining a positive charge on the cluster is possible if an interstitial atom is introduced. For an octahedral gold cluster an additional gold atom is too large to satisfy the steric requirements of the interstitial cavity, but a small main group atom, e.g. C, N or O, is able to satisfy these steric requirements. Figure 11 gives the relevant interaction diagram for octahedral $\ce{[Au6C(PPh3)6]^2+}$ and an interstitial carbon atom, which contributes just the right number of electrons to lead to a $\mathrm{[S^σ]^2[P^σ]^6}$ pseudo-spherical ground state configuration. It is noteworthy that this simple theoretical analysis was first published in 1976 [2], and the existence of $\ce{[Au6C(PPh3)6]^2+}$ was confirmed by Schmidbaur and his coworkers in 1989 [3–5]. This compound had been isolated and structurally characterised previously, but the interstitial carbon had not been identified. The introduction of the interstitial atom strengthens the radial interactions significantly as a result of effective overlaps between the carbon $\mathrm{2s}$ and $\mathrm{2p}$ orbitals and the matching $\mathrm{S^σ}$ and $\mathrm{P^σ}$ cluster molecular orbitals. In broad brush terms the stabilisation of the valence orbitals of the central atom are stabilised by $\mathrm{nβ^σ}$/degeneracy of the molecular orbitals. If $\mathrm{β^σ(s)} = \mathrm{β^σ(p)} = \mathrm{β^σ(d)},$ the relative stabilisations are $\mathrm{6β^σ(s)},$ $\mathrm{2β^σ(p)},$ and $\mathrm{3β^σ(d)}.$ Therefore, the greatest stabilisation involves the $\mathrm{s}$ orbitals of the central atom and increases as the number of metal atoms, $n,$ increases. For filled shells the stabilisation energies are independent of geometry as long as the ligand polyhedron approximates to a sphere. It follows that gold clusters with main group interstitial atoms are characterised by a pec of $12n + 8$ (sec 8) valence electrons, since each $\ce{AuPPh3}$ fragment is associated with a filled $\mathrm{d}$ shell containing $10$ electrons and a bonding $\ce{Au–P}$ bonding molecular orbital.

Fig. 11 Molecular orbital interaction diagram for $\ce{[Au6C(PPh3)6]^2+}.$ Similar analyses may be constructed for trigonal bipyramidal $\ce{[Au5N(PPh3)5]^2+}$ and tetrahedral $\ce{[Au4O(PPh3)4]^2+}$

References

1. Gold Clusters, Colloids and Nanoparticles II; Mingos, D. M. P., Ed.; Structure and Bonding; Springer International Publishing: Cham, 2014; Vol. 162. DOI: 10.1007/978-3-319-07845-8.
2. Mingos, D. M. P. Molecular-Orbital Calculations on Cluster Compounds of Gold. J. Chem. Soc., Dalton Trans. 1976, No. 13, 1163–1169. DOI: 10.1039/DT9760001163.
3. Schmidbaur, H., Grohmann, A., Olmos, M. E.; Organogold chemistry. In: Schmidbaur, H. (ed) Gold progress in chemistry, biochemistry and technology. Wiley, Chichester, 1999. pp 648–731.
4. Steigelmann, O.; Bissinger, P.; Schmidbaur, H. Assembly of the $\ce{[CAu6]^{2⊕}}$ Cluster with a Tailor-Made Diphosphane Spanning the Octahedral Edges. Angewandte Chemie International Edition in English 1990, 29 (12), 1399–1400. DOI: 10.1002/anie.199013991.
5. Schmidbaur, H.; Brachthäuser, B.; Steigelmann, O. Direct Observation of the Central Atom in $\ce{[C\{Au[(C6H5)2(PC6H4NMe2)]\}6](BF4)2}$ by $\ce{^{13}C}$ NMR Spectroscopy. Angewandte Chemie International Edition in English 1991, 30 (11), 1488–1490. DOI: 10.1002/anie.199114881.