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Often called "hypervalent", chemicals like phosphorous pentachloride and sulfur hexafluoride are possible due to the fact that their central atoms form covalent bonds with more than four other atoms, giving rise to uncommon arrangements.

In the case of $\ce{PCl5}$, the phosphorous atom forms 5 bonds, giving rise to trigonal bipyramidal shape according to the VSEPR model. With $\ce{SF6}$, the Sulfur atom forms 6 bonds, giving rise to octahedral shape.

My question is, which central atom can achieve the highest number of bonds through the use of an expanded octet, and what is its shape?

The greatest I can think of is iodine heptafluoride, whose shape is pentagonal bipyramidal due to its fluorine atom of 7 bonds.

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  • $\begingroup$ What you really want to know is what is the highest possible coordination number. It's possible to go quite high; take a look at this Wikipedia article. Also, though it's not completely related, I used to have a great link with all the (theoretical) lowest energy coordination geometries up to massive coordination numbers like 30. I'll see if I can find it. $\endgroup$ – Nicolau Saker Neto Mar 29 '15 at 0:29
  • $\begingroup$ Interesting, I never knew about those. It would seem strange to have one equal to 30, as it would seem that such an arrangement would require the use of electrons from lower principle energy levels, if I'm reading that article correctly, that is. $\endgroup$ – Nerdatope Mar 29 '15 at 0:35
  • $\begingroup$ Oh the thing I said about a coordination number of 30 is purely theoretical, just a mathematical investigation for the fun of it! The highest I know is actually 16 though, from uranocene. Though perhaps one should establish a difference between coordination number for single-atom ligands (i.e. hapticity 1) and for multiple-atom ligands (hapticity greater than 1). $\endgroup$ – Nicolau Saker Neto Mar 29 '15 at 0:40
  • $\begingroup$ as for doubtful octet exp. concept: chemistry.stackexchange.com/questions/13949/…, chemistry.stackexchange.com/questions/19433/… $\endgroup$ – Mithoron Mar 29 '15 at 0:48
  • $\begingroup$ also chemistry.stackexchange.com/questions/444/… $\endgroup$ – Mithoron Mar 29 '15 at 0:50
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I took an interest in this question because it's something I recently wondered myself. First of all, I should clarify that while you mention hypervalency, what you seem interested in is hypercoordination, or even more generally, just compounds with high coordination numbers (hypercoordination is used specifically when the number of ligands in a compound is larger than "normal"). Hypercoordination and high coordination numbers are entirely independent of hypervalency or VSEPR theory altogether. Regardless of the precise electronic structure in a compound, coordination numbers can often be determined far more directly, especially when the compounds can create crystal structures for x-ray crystallography or neutron diffraction.

Usually there is little focus given to compounds with more than six ligands, as the vast majority of compounds will have atoms surrounded by six or less ligands. However, there are some representatives for higher coordination numbers. Some books will mention iodine heptafluoride, $\ce{IF7}$, as a seven-coordinate compound, with its pentagonal bipyramidal structure. It is still possible to add a fluoride and obtain an example of coordination number 8 in the octafluoroiodate(VII) anion, $\ce{IF8^{-}}$, which has an interesting square antiprismatic geometry (take a cube and twist a face by 45°).

For coordination number 9, representatives can be found in the transition metal hydrides, such as the nonahydridorhenate anion, $\ce{ReH_9^{2-}}$, and the lowest energy configuration in this case is a curious tricapped triagonal prism.

Is it possible to go higher than coordination number 9 in coordination compounds? While there are examples, at the present it seems that none of them contain solely monodentate ligands, that is, individual ligands which only bind to the centre once. This is because either there would have to be a lot of crowding over the central atom, creating repulsions between the ligands, or because to allow enough space the ligands would have to stay relatively far from the central atom, making their bonds weak.

However, if a single ligand is allowed to bond to the centre through more than atom simultaneously, then the coordination number can keep increasing without requiring the presence of too many ligands. Actinides have a very rich coordination chemistry and are capable of generating several impressive compounds, such as uranocene with coordination number 16, but it seems the current record is held by actinide elements surrounded by four cyclopentadienyl rings, each with five carbon atoms, reaching an amazing coordination number of 20 in tetrakis(cyclopentadienyl)thorium(IV) ($\ce{Th}\mathrm{(\eta ^5-}\ce{C5H5}\mathrm{)_4}$ or its uranium analogue.

To finalize, it's interesting to note that though there are no examples yet of compounds with coordination number 10 or above containing only monodentate ligands, their expected geometries can be calculated even for much higher coordination numbers (under certain assumptions). For very high coordination numbers, calculations and physical reality will likely diverge, but perhaps a few more coordination numbers with the expected geometry will be unlocked by the study of ultraheavy element chemistry. Of course, the calculations linked here don't help much to study the geometry of coordination compounds with polydentate ligands, as they rely significantly on the geometry of the ligand itself

Edit: This very relevant article raises some interesting points. For example, endohedral fullerene compounds could be thought of as a central atom surrounded by a single ligand in the shape of a cage, so one could possibly make a case for structures with coordination numbers of 60, 70, 80 or even more. The article also calculates the possible existence of a compound containing 15 monodentate ligands, the cation $\ce{PbHe_{15}^{2+}}$, though it would be very weakly bound (as you might expect from a helium compound) and possibly restricted to the gas phase.

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  • $\begingroup$ Additional content very related to this answer (and partially superceding it) can be found in this more recent question. In particular, the coordination number for cyclopentadienide and other cyclopolyene ions arguably is different from what I wrote here. $\endgroup$ – Nicolau Saker Neto Jul 11 '15 at 17:05

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