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

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.

• Carbon can well be hexacoordinate, or even hepta. This case isn't all that different from methanium you mention. Jan 12, 2020 at 19:47
• Jan 12, 2020 at 19:50
• Mildly related: I explain a (relatively simplistic) model of bonding for $\ce{SF6}$ in Why do compounds like SF6 and SF4 exist but SH6 and SH4 don't?. The discussion following the MO diagram briefly touches on species such as $\ce{CH6^2+}$. Now, if you treat $\ce{Au(PPh3)+}$ as a replacement for a single proton (the proper term is isolobal), then that becomes $\ce{C[Au(PPh3)]6^2+}$. Note the qualitative similarity in the MO diagram there to the one andselisk has drawn. Jan 13, 2020 at 1:26

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.
• I wonder, if the LaTeX advanced editors use any handy reference generator, or if all is written down.. I bet for the former. When I was writing my diploma work, top tech were DOS based editors a latex was rubber. Jan 12, 2020 at 12:44
• @Poutnik I use Zotero (desktop)/Zbib (online) for references as there is no Bib(La)TeX support on any of the SE sites. Jan 12, 2020 at 13:33
• @Poutnik, the references in andselisk's answer are not in LaTeX (apart from the chemical formula in ref 5, which I assume is manually typed in). They are just plain Markdown. See chemistry.meta.stackexchange.com/a/4299/16683 for a tool which generates citations from a DOI. Jan 12, 2020 at 15:38
• @orthocresol I see. I had rather in mind perhaps just generated by LaTex aware word processing software, as I am not familiar with these systems. I will check the link, thanks. Jan 12, 2020 at 16:02
• You beat me to it, +1. Compare with SF6 where the e_g orbitals are occupied. As explained here this orbital pair becomes antibonding if the central spacer atom is too small. But if that level is empty, as in the gold cluster, you want the small central atom to promote ligand-ligand bonding in the still occupied lower orbitals. Jan 12, 2020 at 16:36