Friday, January 03, 2014

Chemistry with muons

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


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 (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).


John C. Beach said...

During the unique high-energy environment of a supernova, could a muon displace or otherwise substitute for one of the electrons in Argon's outer shell, and could this explain the Herschel Space Observatory's detection of Argon Hydride in the Crab Nebula? What would the spectra look like for a hypothetical muonic-Argon hydride?

This occurred to me after reading your mention of the research suggesting muonic helium bonds with hydrogen.

Reference: Science 13 December 2013, "Detection of a Noble Gas Molecular Ion, 36ArH+, in the Crab Nebula"

Thanks for any insights,

John Beach
just outside of Austin, Texas

John C. Beach said...

Also, what would the spectra look like for a hypothetical
muonic-argon muonic-helium compound?

Since in the previous post I asked about muonic-argon hydride, it occurred to me that your article discussed muonic-helium being a hydrogen analogue. Could a supernova create muonic argon, muonic helium, and provide an environment conducive to the formation of
muonicArgon-muonicHelium ?

John Beach

John C. Beach said...

In continuation of my posts asking what the spectra would look like for a molecule that included muonic-argon, muonic helium, and/or muonic hydrogen (on 2014-01-14 and 2014-01-15).

Is it reasonable to look for a combination of signals for which the composite pattern could uniquely identify muonic atoms in a molecule? In other words, what instrument or combination of instruments would you have to point at the Crab Nebula to detect a molecule based upon muonic atoms?

For example regarding muonic hydrogen, in “Muonic hydrogen and the proton radius puzzle” (A. Antognini and F. Kottmann , 2010)
I see that they induced 2S → 2P transitions in the muonic atom by illuminating it with a short laser pulse tunable to a wavelength around λ ≈ 6 µm
They also describe the 2P → 1S de-excitation via emission of a 2 keV X-ray

Perhaps naively, from that I infer that two of the signals in a composite fingerprint for muonic hydrogen might be
Some amount of absorption of mid-infrared at wavelength around λ ≈ 6 µm
Emission of 2 keV X-rays

The Herschel Space Observatory was sensitive to the far infrared and submillimetre wavebands (55–672 µm per Wikipedia) so it wasn't able to detect Mid-infrared: 30 to 120 THz (10 to 2.5 μm). Could an absorption at λ ≈ 6 µm be inferred by looking in far-infrared wavebands for a lack of constructive or destructive interference that is normally observed in other astronomical light sources (presumably lacking muonic atoms)? Or could the information be both detected and inferred in the Spitzer Telescope’s 3-180 µm imaging of the Crab Nebula? I’m not suggesting there would be an absorption line, but perhaps weaker-than-expected results near 6 µm.

Chandra X-ray Observatory has imaged the Crab Nebula’s X-ray emissions. Would that data be useful in looking for muonic de-excitation emissions?

What other ways might there be to tease out a pattern uniquely identifying molecules that are based upon muonic atoms?
If there is a way to do it, could this technique provide insight into how molecules can form with noble gases bonded to other elements? (e.g. the Argon Hydride detected in the Crab Nebula.)
Could there be other oddities? For example, could you make an analogue of NaCl by using muonic Magnesium (i.e. MuonicMg-Cl)? What would be the effects upon the ionic bond due to the tighter atomic radius of muonic Mg as compared to normal Na?
Is there any way to slow down the muonic decay (and therefore lengthen the existence of the muonic molecule) by bombarding the collision area with a stream of another type of particle? (Especially a particle that would be present in sufficient numbers in the Crab Nebula.)

Out of curiosity I just Bing’d for “muonic magnesium” and got 1 result. From it I see that in Osaka they have detected muonic magnesium in an experiment with MuSIC at RCNP. Now if they’ll just steer the particles into a chlorine cloud… ;-)

I’m sure the excellent Ball article (to which I’ve tacked these comments) draws some bright people. If any of you have a spare minute, I appreciate constructive feedback, suggested resources for further reading to support or dismantle my assumptions, etc.


John Beach
just outside of Austin, Texas
January 30, 2014