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Muonium delivers a fundamental isotope effect in chemical bonding: vibrational binding in BrMuBr

Bond vibrations in molecules could be thought of as the corner stone of molecular spectroscopy but in all such cases these are sustained as bound states in potential wells. Conventional wisdom dictates then that bond vibrations cannot be sustained at a potential maximum or “saddle point” on a potential energy surface unless differences in zero-point energy (ZPE), a purely quantum mechanical phenomenon, can create favourable circumstances to form what is colloquially referred to as a vibrational bound state. In marked contrast to conventional bonding, the stabilization of a vibrational bound state on a repulsive surface is ∝1/√mass and hence is only feasible for the lightest atoms. The quantum concept of vibrational bonding has been known since the early 1980s from calculations carried out at the time on semi-empirical surfaces for the ‘Heavy-Light-Heavy’ systems IHI or BrHBr, but had not heretofore been convincingly demonstrated.

The effect of isotopic mass is most pronounced for hydrogen, and in particular for the range of isotopic mass provided by muon science, from its lightest isotope ‘muonium (Mu = µ+ e​)’, with a mass of 0.114 amu, formed by a positive muon, to its heaviest, ‘muonic He (4Heμ)’, with a mass of 4.11 amu, formed by the capture of a negative muon on helium. Motivated by a recent experimental study suggesting that BrMuBr may have been formed in the Mu + Br2 reaction system [Phys. Chem. Chem. Phys., 14, 10953 (2012)], extensive high-level quantum chemistry calculations have been carried out on a new ab initio surface, reported in [Angewandte Chemie Int’l Ed., doi: 10.1002/anie.201408211], which unequivocally show for the first time that a vibrational bound state can be stabilized at the saddle point of the Br-Mu-Br surface, due to the fact that its ZPE lies sufficiently below that of the MuBr product so this gain in energy more than offsets the loss of potential energy at the barrier. In contrast, all of the heavy isotopomers, including Br4HeμBr, can only be stabilized in van der Walls wells, a twin ‘triumf’ for both muon science and quantum chemistry.

Congratulations to Don Fleming of the Muon Group at TRIUMF.

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Front page photo caption: In the vibrational bond muonium would 'bounce' between the two bromine atoms.