Muon bonding

These observations are supported by the calculations of Estreicher et al. [9], using the the PRDDO method and density functional theory, the semi-empirical calculations of Percival and Wlodek [10] and ab initio ROHF calculations [11]. They confirm that the most stable state of CeoMu results from the muon bonding itself to one of the carbon atoms from outside the cage. 

Figure 6 Polyhedral view (to scale) of structure types ai(a), a2(b) and two orientations of 03(0 and d) for CtqMu. The muon is at the end of the dangling bond and in views (a) and (b) lies in the plane of the paper. For views (a), (b) and (c) four edge carbon atoms are also in the plane of the paper. The other visible atoms are above the paper. Each atom above the paper hides a corresponding atom below the paper except for type 03 where in the region of the muon the undistorted structure below the plane is shown with dashed lines. This is useful since it clearly shows the nature of the distortion. View (d) is an orientation of type 03 to illustrate that the distortion is similar to the other type a structures...

Despite the precise knowledge of the muon hyperfine interaction and a wealth of other complementary information on Mu, no compelling theory emerged until 1986 when Cox and Symons proposed a molecular-orbital bond-center (BC) model to explain the muon hyperfine interaction (Symons, 1984 Cox and Symons, 1986). Since then it has been tested both theoretically (Van de Walle, 1991) and experimentally. 

The muon and 29Si hyperfine parameters provide compelling evidence in support of the BC model. In the simple molecular-orbital model proposed by Cox and Symons (1986) the muon is located at the center of a Si—Si bond near a node in the unpaired electron spin density, which is... 

The close correspondence between the properties of Mu in Si as determined by /u,SR and pLCR and those for the AA9 center produced by implanting hydrogen in silicon shows that Mu in silicon and the AA9 center are isostructural and in fact almost identical. They are neutral isolated bond-centered interstitials. Numerous theoretical studies support this conclusion. The observation of such similar centers for muonium and hydrogen supports the generalization that hydrogen analogs of many of the muonium centers exist. Of course, this assumes that the effects of the larger zero-point vibration of the muon relative to the proton do not make a major contribution to structural differences. The p-SR experiments, reinforced by theory, demonstrate that another structure also exists for muonium in silicon, called normal muonium or Mu. This structure is metastable and almost certainly is isolated neutral muonium at a tetrahedral interstitial site. 

When relaxation is allowed, the global minimum shifts to the bond-center site (Claxton et al., 1986 Estle et al., 1987 Briddon et al., 1988). This is in agreement with the experimental observation that anomalous muonium is the most stable state for muons in diamond (Holzschuh et al., 1982). An expansion of the bond length by 42% is necessary. The bond center was found to be more stable than the interstitial muonium by s 1.9 eV. Displacements of the muon along directions perpendicular to the bond cost little energy (Estle et al., 1987). 

This simple treatment, formulated in a context of molecular bonding, was also what led Cox and Symons (1986) to propose the bond-center site as an explanation for anomalous muonium (Mu ). The location of the muon at the nodal plane of the nonbonding orbital explains the very small hyperfine coupling observed in pSR. Still, the muon is close to the electron, which occupies a nonbonding state on the neighboring semiconductor atoms. 

But one can ask the question why normal muonium is observed at all if the global energy minimum (i.e., the stable site) is really at the bond center (anomalous muonium). On the time scale of the muon lifetime, relaxations of the Si atoms may be sufficiently slow to effectively trap the muon in the low-density regions of the crystal, where relaxation of the host atoms is... 

For instance, the Bohr radius of in muonic Pb is only about 4 fm, whereas the radius of the nucleus is about 7 fm. Finally, the muon may be captured by the nucleus or it may decay as a free particle. The influence of the charge distribution in nuclei on muons is also greater than that on electrons, and X rays emitted by muonic atoms, in particular from inner orbitals, give information about the charge distribution and surface structure of nuclei. The influence of electron densities and chemical bonds has been studied by use of pionic atoms, such as p 7r. ... 

In the presence of unsaturated organic molecules Mu can add to double or triple bonds and form free radicals (R) in which the muon is chemically bound as a polarized spin label, as in ... 

Mu addition to double bonds places the muon two bonds away from the radical center. Mu is thus not normally directly involved in reactions of the radical, and any kinetic isotope effects are secondary and thus small. This makes the muon a non-perturbing radical kinetics probe. Its advantage is the extraordinary sensitivity of the technique which requires only a single muon in the sample at a given time. This eliminates any radical termination reactions. With on the order of 10 muons needed for an experiment the concentration of the reaction partner does not change, and kinetics is of ideal pseudo-first order. This eliminates a munber of sources for serious errors which often affect the accuracy of conventional radical kinetics. 

Mu-substituted free radicals had not been detected by pSR at about 100 G which had been the magnetic field intensity commonly used in the muon facilities, and the first observation was made at high transverse magnetic fields (about 3000 G) in 1978 [11, 45] and this method has sometimes been called high-field pSR . A great number of radicals have been measured since then, e.g. olefins and dienes [46], methyl-, F- and other substituted benzenes [13, 47], and triple bonds [48]. All the observed radicals are derived by Mu addition to unsaturated molecules, and thus p is automatically located at the P-position, i.e. two bond, away from the unpaired electron or delocali system. Although Mu-substituted radicals are typical entities that are created by p" " and their structures and reactivities are probed by p itself, they are not ctealt with here in detail, since they have been fully reviewed [12,49]. 

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