How many kisses?

Isaac Newton and David Gregory couldn't agree on how many identical spheres can simultaneously touch a central sphere of the same radius: 12, said Newton, 13 Gregory. It was only long after their deaths that Newton was rigorously proved right. In most dimensions higher than three, however, this 'kissing-number' problem is still unsolved, and so is the case, even in three dimensions, in which the to-be-kissed sphere has a different radius from those of the spheres surrounding it. Andreas Hermann and colleagues have considered a related problem in chemistry (Angew. Chem. Int. Edn 46, 2444–2447; 2007), searching for the highest possible coordination number for a given species — that is, the highest number of ligands that can be packed into one shell around a central atom with which they all interact (but without having strong interactions between the ligands).

In many problems, a coordination number, N, of 12 leads to stable configurations, such as clusters with icosahedral structures, or the face-centred cubic and hexagonal close-packed lattices in solids. However, the first-principles quantum-chemical simulations by Hermann et al. indicate that for the case of a single charged lead atom surrounded by helium atoms, up to 15 ligands fit in one coordination sphere. This would make PbHe₁₅²⁺ the first gas-phase molecule that has a coordination number higher than 12. The authors present evidence that the molecule is stable, and expect that the new record holder should be identifiable by mass spectrometry.

Credit: © 2007 Wiley

The series of PbHe_N²⁺ molecules goes through shapes of all kinds as the number of helium atoms is increased (see pictures from top left). Up to N = 6, all of the ligands lie in one half-sphere, but are then equally distributed when the ligands number 8 to 12; (N = 7, however, looks a bit like an umbrella). Hermann et al. found that they can comfortably push further, up to N = 15, and still accommodate all of the helium atoms in one shell. But, for more than 15 ligands, it seems that the central lead atom rejects the intimacy of kissing, preferring to keep further adherers at some distance in a second coordination shell (final picture).