Chemistry with muons

This is my Crucible column for the January issue of Chemistry World.

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The periodic table seems constantly on the verge of expansion. There are of course new superheavy elements being added, literally atom by atom, to its nether reaches by the accelerator-driven synthesis of new nuclei. There’s also talk of systematic organization of new pseudo-atomic building blocks, whether these are polyatomic ‘superatoms’ [1] or nanoparticles assigned a particular ‘valence’ via DNA-based linkers [2]. But one could be forgiven for assuming that the main body of the table that adorns all chemistry lecture theatres will remain largely unchanged, give or take a few arguments over where to put hydrogen.

Yet even that can’t be taken for granted. A preprint [3] by quantum chemists Mohammad Goli and Shant Shahbazian at Shahid Beheshti University in Iran posits two new light elements – although these should formally be considered isotopes. They are muonium (Mu), in which an electron orbits a positively charged muon (μ+), and muonic helium (Heμ), in which an electron orbits a ‘nucleus’ consisting of an alpha particle and a negative muon – the latter in a very tight orbit close to the true nucleus.

Both of these ‘atoms’ can be considered analogues of hydrogen, with a single electron orbiting a nucleus of charge +1. They have, however, quite different masses. Since the muon – a lepton, being a ‘heavy’ cousin of the electron (or of its antiparticle the positron) – has a mass of 0.11 amu, muonium has about a tenth the mass of 1H, while muonic helium has a mass of 4.11 amu.

They have both been made in particle accelerators via high-energy collisions that generate muons, which can then be captured by helium or can themselves capture an electron. Some of these facilities, such as the TRIUMF accelerator in Vancouver, can generate beams of muons which can be thermalized by collisions with a gas, reducing the particle energies sufficiently to make muonic atoms capable of undergoing chemical reactions. True, the muons last for only around 2.2×10**-6 seconds, but that’s a lifetime, so to speak, compared with some superheavy artificial elements. Indeed, their chemistry has been explored already [4]: their reaction rates with molecular hydrogen not only confirm their hydrogen-like behaviour but show isotope effects that are consistent with quantum-chemical theory.

So undoubtedly Mu and Heμ have a chemistry. It seems only reasonable, then, to find a place for them in the periodic table. Indeed, Dick Zare of Stanford University, who probably known more about the classic H+H2 reaction than anyone else, is said to have once commented that if muonium was listed in the table then it would be much better known.

The question, however, is whether these exotic atoms truly behave like other atoms when they form molecules. Do they still look basically hydrogen-like in such a situation, despite the fact that, for example, Mu is so light? After all, conventional quantum-chemical methods rely on the Born-Oppenheimer approximation, predicated on the very different masses of electrons and nuclei, to separate out the electronic and nuclear degrees of freedom. Might the muons perhaps ‘leak’ into other atoms, compromising their own atom-like identity? To explore these questions, Goli and Shahbazian have carried out calculations to look at the electronic configurations of Mu and Heμ compounds using the Quantum Theory of Atoms In Molecules (QTAIM) formalism [5], which classifies chemical bonding according to the topology of the electron density distribution. A recent extension of this theory by the same two authors treats the nuclei as well as the electrons as quantum waves, and so is well placed to relax the Born-Oppenheimer approximation [6].

Goli and Shahbazian have calculated the electronic structures for all the various diatomic permutations of Mu and Heμ with the three conventional isotopes of hydrogen. They find that in all cases the muon-containing species are contained within an ‘atomic basin’ containing only a single positively charged particle – that is, they look like real nuclei, and don’t contaminate the other atoms in the union with any ‘sprinkling of muon’. What’s more, Mu and Heμ fit within the trend observed for heavy hydrogen, whereby the atom’s electronegativity increases as its mass increases. This is particularly the case for Mu-H molecules, which are decidedly polar: Muδ+-Hδ-. That in itself forces the issue of whether Mu is really like light hydrogen or needs its own slot in the periodic table: Goli and Shahbazian raise the latter as an option.

The zoo of fundamental particles might provide yet more opportunities for making unusual atoms. Goli and Shahbazian suggest as candidate constituents the positive and negative pions, which are two-quark mesons rather than leptons. But that will stretch experimentalists to the limit: their mean lifetime is just 26 nanoseconds. Still more exotic would be entire nuclei made of antimatter or containing strange quarks (‘strange matter’)[7]. At any rate, it seems clear that there are more things on heaven and earth than are dreamed of in your periodic table.

1. A. W. Castleman Jr & S. N. Khanna, J. Phys. Chem. C 113, 2662-2675 (2009).
2. R. J. Macfarlane et al., Angew. Chem. Int. Ed. 52, 5688-5698 (2013).
3. M. Goli & Sh. Shahbazian, preprint http://www.arxiv.org/abs/1311.6431 (2013).
4. D. G. Fleming et al., J. Chem. Phys. 135, 184310 (2011).
5. R. F. W. Bader, Atoms in Molecules: A Quantum Theory. Oxford University Press, 1990.
6. M. Goli & Sh. Shahbazian, Theor. Chem. Acc. 129, 235-245 (2011).
7. STAR collaboration, Science 328, 58-62 (2010).