Hyperfine InteractDOI 10.1007/s10751-014-1121-9

Muons as hyperfine interaction probes in chemistry

Khashayar Ghandi ·Amy MacLean

© Springer International Publishing Switzerland 2015

Abstract Spin polarized positive muons injected in matter serve as magnetic probes forthe investigation of physical and chemical properties of free radicals, mechanisms of freeradical reactions and their formations, and radiation effects. All muon techniques rely on theevolution of spin polarization (of the muon) and in that respect are similar to conventionalmagnetic resonance techniques. The applications of the muon as a hyperfine probe in severalfields in chemistry are described.

Keywords Free radicals · Muonium · Muon · Radiation chemistry · Hyperfine interactions

OutlineIn designing new materials and chemical processes, it is of paramount importance to

understand what is happening at an atomic level. Muon techniques provide a unique glanceat such microscopic properties, given the kinetic time window which they can probe, as wellas their extreme sensitivity to local magnetic and electronic environments. The applicationsof muon spectroscopy are far reaching, from nuclear reactor development to targeted can-cer treatments to green industrial processes. Many and more of these applications will bediscussed in this brief review.

This review paper includes the following:

1) A very brief review of the muon with references to muon literature.2) An explanation of the muon as a probe of free radical kinetics.3) The futuristic aspects of the muon as a probe of free radical kinetics.4) The muon as a hyperfine probe of hydrogen atoms in different materials.5) The muon as a probe of the mechanisms of free radical reactions.

Proceedings of the 5th Joint International Conference on Hyperfine Interactions and InternationalSymposium on Nuclear Quadrupole Interactions (HFI/NQI 2014), Canberra, Australia, 21–26September 2014

K. Ghandi (�) · A. MacLeanDepartment of Chemistry & Biochemistry, Mount Allison University, Sackville, NB, Canadae-mail: kghandi@triumf.ca

K. Ghandi, A. MacLean

Fig. 1 Muonium (Mu) from a chemical perspective is considered an isotope of the H atom. Electronicproperties of Mu and the H atom are compared here

This review is by no means all-inclusive and it only summarizes some of the represen-tative recent works in the above list. For a more detailed review of the muon and muontechniques, see ref [1]. Several recent reviews referred to in [1] provide comprehensiveoverviews of other aspects not covered in this review (such as applications to soft matterand surfaces).

1 The positive muon, muonium, and muoniated free radicals

The positive muon, μ+, is an elementary particle that, in the context of this review, is bestregarded as a light proton with one-ninth the proton mass. Like the proton, it is a spin-1/2particle. Its magnetic moment is 3.18334 larger than the magnetic moment of the proton,making it useful as a magnetic probe of matter. Muon spectroscopy techniques are basedon muon spin evolution in the presence of transverse or longitudinal magnetic fields, rel-ative to the direction of the muon beam spin. In this edition of Hyperfine Interactions,Brewer gives a historical review of the muon, its applications as a probe of magnetic andelectronic environments in material, and different muon techniques [1]. We would referthe reader to this review article for a more in-depth examination of the muon techniques.In the chemical probe applications discussed here, information is extracted from the ini-tial amplitude and the spin evolution of the muon in different magnetic and electronicenvironments [1].

After a muon is injected into a material, one of several events can occur. The muon canremain in its diamagnetic state, either as a molecular ion or diamagnetic neutral species[2], but it can also capture an electron from its radiation track to form paramagnetic muo-nium (Mu). Mu can be considered an ultra-light isotope of the H atom (Fig. 1), because

Muons as hyperfine interaction probes in chemistry

within the Born-Oppenheimer approximation, the electronic properties (and hence chemicalproperties) of a single electron atom depend on its reduced mass (1).

mr = mμme

mμ + me≈ me (1)

Mu has one-ninth the mass of H and, therefore, significant isotope effects can be expectedfor different reactions. This will be discussed later in the context of applications forinvestigating chemical dynamics.

The short lifetime of muon, 2.2 μs, makes it useful for studying fast kinetic processesinvolving the H-atom with pseudo first order rate constants on the order of 105 to 107 s−1

[2]. The in situ formation of muonium in the presence of other reactants often leads to theformation of more complicated and interesting free radicals. There are four ways that amuoniated free radical can be formed:

1) Addition of Mu to a molecule with a double bond (2):

C6H6 + Mu → C6H6Mu (2)

2) Reaction of a solvated electron and a muoniated molecular ion (3):

C6H6Mu+ + e(sol)− → C6H6Mu (3)

3) Reaction of Mu and a molecule with carbene or carbene-like functional groups [3].4) Dissociation of a reactive intermediate in its vibrational excited state [4].

In addition to the pathways listed above, muoniated free radicals can go on to react withother reagents in the system; this will be further discussed later.

Positrons from the decay of muons in situ must first be detected to learn about reactionkinetics, free radical formation and related free radical mechanisms using muon techniques,positrons from decay of muons must first be detected. Indeed, the positrons can easilypass through solid walls and be detected external to the reaction vessel. The relevant spin,magnetic precession and hyperfine coupling information carried in the decay products canthen be measured to study materials. The combination of techniques used to study muo-niated free radicals or muon methods in molecular and material science are collectivelycalled μSR [1].

There are three main muon techniques utilized in chemistry. The first, TF-μSR (trans-verse field μSR), involves the application of a magnetic field perpendicular to the directionof spin, and is most useful for studying reaction rates and muon-electron hyperfine interac-tions. The second, LF-μSR (longitudinal field μSR), is often used to study spin dynamics,though it can also identify free radicals formed either in slow reactions or at low precursorconcentration. In both cases, a magnetic field parallel to the muon beam spin is applied.In the case of either low concentration of the precursor or slowly formed free radicals, theTF-μSR spectra is lost due to dephasing of spin polarization [1]. One type of LF methodis Radio Frequency-μSR (RF-μSR), in which radio frequency is applied perpendicular tomuon spin, in addition to the LF. This is a resonance method similar to NMR. Another typeof LF muon method is Avoided Level Crossing Resonance (ALCR) [1], which is also a res-onance technique. In isotropic environments, ALCR provides isotropic hyperfine couplingconstants for spin nuclei other than muon, and in anisotropic environments, it provides infor-mation on free radicals bound anisotropically via hyperfine coupling of muon and electron[1–4]. Finally, in ZF-μSR (zero field -μSR), the only magnetic influences on the muon arisefrom the sample itself; even the earth’s magnetic field is cancelled out. This can be used tostudy the intrinsic magnetic properties of materials [1].

K. Ghandi, A. MacLean

Fig. 2 Splitting of spin states of muonium (Mu) (H) in a magnetic field. The spin states on the left side showthe low field states where mixing of states happens. The spin states on the right side show the high fieldstates. Most Mu studies in the TF use low field conditions. The two transitions typically used to measure thehyperfine coupling constant (HFC) of Mu in TF are also shown

2 Muon as a probe of free radical kinetics

Due to the volume of research that has been done on free radical kinetics using muon meth-ods, this section is divided into two parts. First, we will review muon-based kinetic studiesin the gas phase, followed by a section on condensed phase studies using the same methods.

2.1 Gas phase studies

Hydrogen is the simplest atom in nature. Consequently, the study of its interactions andchemical reaction rate constants (kH ) has been central to the field of reaction dynamicssince the studies of the first potential energy surface (PES) for H + H2 [5, 6]. In the realmof reactive collision dynamics, modern atomic and molecular beam studies of H atom reac-tions produced under near single-collision conditions at epithermal (∼ 1 eV) energies, withtheir ability to probe ro-vibrational cross sections at the state-to-state level, play an everincreasingly important role in assessing reaction rate theories [7, 8]. However, as these col-lision impact energies are well above threshold, the general features of reactive collisionprocesses are often well described by classical (or quasi-classical) dynamics. Therefore, thestudy of chemical kinetics and thermal rate constants, which are generally much more sen-sitive to quantum mass effects in probing the details of the PES at the barrier, continue tobe important. This is all the more true in the case of a sensitive isotopic mass probe, such asMu [9–15].

Kinetic studies of chemical reactions most often require measurements of the Mu decayrate using the (TF-μSR) technique at low magnetic fields (2−10 G) [1]. This can be doneboth at continuous beam facilities, such as TRIUMF (Canada) or PSI (Switzerland) forfaster reactions (equivalent to the first order rate constants in the range of 1 to 4 μs−1), orat pulsed facilities, such as the Rutherford Appleton Laboratory (UK) and JPARC (Japan),for slower reactions (with first order rate constants smaller than 1 μs−1). More details on

Muons as hyperfine interaction probes in chemistry

how to obtain the reaction rate constants can be found elsewhere. [2, 9–11]. Occasionally,studies are done as a combination of TF-μSR and LF-μSR [11] to investigate both finalproducts and kinetics. Much more accurate rate constants can be measured using TF-μSR atlow field (where the two spin precession frequencies of Mu (Fig. 2) are the same). Productcharacterization at small concentration of reactants requires LF-μSR or RF-μSR studies [1,12].

In the general realm of isotopic mass effects, the ultra-light mass of Mu compared to Hoften gives rise to two opposing and dramatic kinetic isotope effects (KIEs) [2]: zero-pointenergy (ZPE) shifts (for vibrational energy), and quantum tunneling effects. With recentdevelopments of muonic helium [9], arguably the heaviest radioisotope of hydrogen at 4.1H,such KIEs have facilitated critical tests of the predictions of reaction rate theories. For exam-ple, Fleming et al. [9] showed that the kinetic isotope effects (= kMu/kH) provide valuableinformation about the nature of reaction potential energy surfaces (PES). These effects aremost easily identified in the case of direct abstraction reactions [2, 9, 10]. In endoergic (late-barrier) reactions (such as Mu+ H2 [9]), ZPE shifts at the transition state (TS) dominate,giving rise to KIE << 1. Fleming et al. showed that variational transition state theory cal-culations (calculations that optimize the (isotope-dependent) location of the barrier) withmultidimensional tunneling performs better overall over a wider temperature range whencompared with the predictions of accurate quantum mechanical (QM) dynamics calcula-tions carried out on a well converged Born-Huang (BH) potential energy surface, based oncomplete configuration interaction calculations and including a Born-Oppenheimer diago-nal correction [9]. The fact that tunnelling plays a role even for such a late barrier reactionis a remarkable finding that is only evident when such a broad range of mass ratio of iso-topes are used for comparison with theory. Other groups have since used computationaltechniques to investigate the intriguing properties of muonic molecules [16]. Attempts havealso been made to better model the contributions of ZPE shift in theoretical calculations,using ex. local mode approximations [17].

However, in the exoergic (early-barrier) reactions of Mu and halogens, quantum tun-neling dominates, giving the opposite limit with KIE >> 1 at the lowest (∼ 100 K)temperatures and with activation energies Ea

Mu << EaH [11]. At higher temperatures, the

reaction of Mu with heavier halogens can result in a new class of bonds (dynamic bond),which form by the most drastic KIEs via vibrational/rotational stabilization of the TS. Thiswas shown for the first time using a combination of experimental longitudinal μSR data anddetailed Born-Oppenheimer molecular dynamics quantum calculations [11] and was laterconfirmed by higher level calculations [13].

Also of interest are Mu (H)-atom addition/association reactions. In these reactions, ratesfor addition and stabilization compete with rates for unimolecular dissociation of the ergodiccomplex (product in its excited state after collision), with the overall rate constant exhibitingdifferent pressure limits. For Mu addition to polyatomic molecules (for example, Mu +C2H4 → MuC2H4) [14, 15, 18], the high-pressure limit is easily realized at moderatorpressures ∼ 1 bar. However, in the case of small molecules with only a few degrees offreedom (e.g. MuNO), much higher pressures (or densities) are required for stabilization[19]. Such studies provide information regarding the effects of intermolecular interactionson such dynamic processes, as well as the PES under low and high pressure limits. Keep inmind that at the low pressure limit, krxn increases almost linearly with pressure, while at thehigh pressure limit, the rate constant only changes given a significant change in the volumealong the reaction coordinate.

Although studies of Mu kinetics have mostly been limited to the investigations of Mureactions with the ground state molecules, recent developments extended such studies to

K. Ghandi, A. MacLean

the realm of excited state kinetics measurements [20, 21]. Cormier et al. [14] developedpump-probe type methods to study reaction kinetics and dynamics of Mu with excited states(a.k.a. pump-probe type methods). Those studies led to the measurement of Mu reactionrate constants for reactions with electronically excited molecules, which were comparedto those same reactions in the ground state. Molecular excitation was achieved by usingthe second harmonic of a Nd-YAG laser pulse, the timing of which (relative to the muonpulse) showed a clear and significant impact on Mu signals. When the laser pulse arrivesbefore the muon pulse, the reactions of Mu with excited state molecules can be studied.When the laser pulse follows the muon pulse, the studies provide information on excitedfree radical states (either electronic structure information or kinetics information). Havingthe laser pulse on at the same time as the muon pulse can be used to study the radiationchemistry involved in Mu formation (reactions close to the end of the muon radiation track[20]). This work opened up the field of Mu reactions with excited state molecules and laserMu chemistry, which led to the recent construction of a permanent laser station for muonstudies at the Rutherford Appleton Laboratory. It also facilitated the studies of Mu + H2

reaction by Bakule et al. [21] did not show such a significant difference between the laseron and off, due to a smaller distribution of molecules in the vibrational excited states atthe time/space of the reaction with Mu with H2; however, theoretical calculations pointedto a large change in the rate constants of Mu with vibrationally excited state molecules[15].

The important point is that these techniques allow researchers to probe reaction kineticsof the H atom with excited state molecules and to study the reaction dynamics of the H atomunder laser excitations. Ghandi et al. [7] and Bakule et al. [21] developed a new type ofmuon spectroscopy that makes it possible to study a) the effects of mass on H atom reactionswith laser-pumped molecules to investigate quantum effects on reactions in exited statesand b) excited-state dynamics of “dyes” used in e.g. photodynamic therapy, in particularthe role of free radical reactions under laser irradiation [20, 21]. This has applications intissue-targeted cancer treatments, among other things. Other applications are in the realm ofdye-based solar cells, where free radical reactions could negatively affect the stability of thematerial used in solar cells [22].The studies of reactions of Mu with vibrationally excitedsimple molecules are, however, more interesting for theoretical chemists as they are easierto investigate computationally [23–25].

Reactions of muoniated free radicals with other molecules can also be studied by muonmethods. Such reactions provide information regarding reactions of free radicals in general(not only the H atom). For example, the reaction of ethyl radical and O2 has been investi-gated over a pressure range of 1.5 to 60 bar using muon spin relaxation [26]. Such studiesof muoniated free radicals with molecules (either experimentally or computationally) arestill very scarce and should be expanded significantly. In addition, there is still a significantneed to study thermal reactions of Mu, as more computational methods to study the reactionrates are being developed. However, experimental studies of Mu kinetics are often amongthe best tests for these reaction rate theories [8–11, 13–15, 18–21, 23, 24].

2.2 Condensed phase studies

Studying Mu reaction kinetics in the condensed phase provides similar informa-tion to studying kinetics in the gas phase. However, in the condensed phase andunder extreme conditions, the role of Mu kinetics is even more important. Exam-ples include experiments under high temperature and/or pressure, or cases where thereaction products cannot be observed optically. Muon methods are the only methods

Muons as hyperfine interaction probes in chemistry

available to study H atom kinetics under many extreme conditions [2, 10, 14, 15, 27–33].Such studies not only have fundamental importance in helping us to establish better reactionrate theories, they also have important applications in e.g. the nuclear industry, where super-critical fluid coolant systems are being investigated for next generation nuclear reactors [10,33]. Therefore, studies of reactive intermediates (such as the H atom) and their reactionsunder extreme conditions are important to the development of efficient energy sources andstorage, including modern nuclear reactors, efficient lithium-ion batteries and solar-powereddye cells [36–38].

Muon spin spectroscopy has a number of advantageous features for the study of extremeconditions, compared to conventional/beam techniques. Muons can be injected into mostmaterials in any phase. The momentum of the backward (high energy/momentum) muonbeams can be adjusted over a wide range for optimum penetration of the sample. Also,optical windows are unnecessary for muon studies, which is a limiting feature of othermethods such as pulse radiolysis and flash photolysis that are commonly used for studiesof reactive intermediates. Spin polarized muons give high sensitivity, making it possible tomeasure the rate of Mu reactions with only one Mu in the sample, i.e. under ideal solutionconditions.

Due to the short lifetime of the muon, µSR is inherently suited to the study of tran-sients/intermediates, and for fast reactions at low reagent concentration (< 1 mM). Asa result of this short lifetime, phase properties are not altered, which is important forstudies done near the critical point [10, 14, 15]. Muon methods do not necessarily needradio-frequency or other radiation, which would otherwise decrease the range of availabletemperatures and pressures. The detectors in muon spectroscopy are simple devices (plasticscintillators) that exist outside the controlled sample environment at atmospheric condi-tions. Therefore, the detection system is not negatively affected by extreme conditions ofexperiments. Indeed, since low energy positrons (one of the muon decay products) wouldnot reach the detectors due to thick sample cell walls, the observed asymmetry is usuallyhigher for such experiments.

Most rate constants for aqueous reactions (krxn) have Arrhenius temperature dependenceat low temperatures [27–33]. However, in many cases the krxn plateaus before the criti-cal point, and in most cases, even decrease again past the critical point, before returningto Arrhenius behavior. This suggests that a decrease of krxn near the critical point mightbe a general phenomenon for aqueous systems. For example, in the addition of Mu tohydroquinone [32] and benzene [30], krxn reaches a maximum at about 250 ◦C. The reac-tion of Mu with methanol has also been studied [29], and was described as an H-atomabstraction reaction, where krxn plateaus at about 350 ◦C, decreases with temperature,and increases again past the critical point. The results of research on Mu kinetics athigh temperatures and pressures have attracted the interest of several research groupsthat are initiating similar studies with other radiation products, especially due to theapplications in nuclear energy. For example, Janik et al. (2007, 2014) studied H react-ing with O2 to form HO2 [14] and H reacting with HO2 to form H2O2 [39] (bothrecombination reactions). They confirmed trends similar to those discovered by muonmethods.

When considering high-temperature reactions in water, Mu kinetic studies [27–33]served as a test for the validity of various models for reaction rate theories used under theseconditions. This led to a proposed new model based on the generalized Troe model [2, 27–33], which includes an efficiency factor to account for the effects of decreased hydrogenbonding on reaction efficiency [27–33]. In addition, the Mu studies showed the effects ofthe water molecules directly on the PES of reactions. This was established by studies of

K. Ghandi, A. MacLean

reactions with formate ion and hydroxide ions, in which the dipole moment would changeinversely along the reaction coordinate [2].

A more recent study investigated the reaction of Mu+H2O experimentally and computa-tionally to predict the rate constants for analogue reactions for the H atom. Alcorn et al. [10,33] reported non-Arrhenius behavior of the reaction rate constant around the critical pointof water. They identified two different temperature-dependent channels for the reactionof Mu (H) with water. Channel one is Mu + H2O ↔ eaq−+ H3O+ (an electron-protontransfer reaction) that dominates below 190◦ (a slightly higher temperature for H atom).At higher temperatures (above 300◦), the H-abstraction reaction Mu+H2O↔OH+MuHdominates (channel 2). Channel 1 starts with an early barrier reaction (prone to quan-tum tunneling effects) while channel 2 occurs as a late barrier reaction [10]. As such,ZPE effects are especially important in channel 2; however, significant competing solventeffects were also observed in this case. Those studies (along with the work of Cormieret al. [14] and Ghandi et al. (2012) for reactions in near critical CO2) established modelsto explain and predict reaction rates near the critical point, which is dominated by criti-cal fluctuations [14, 15]. Alcorn et al. (2010) also computationally studied the cluster sizeeffects of water on this kinetics system (both in a dielectric continuum, as explicit solventmolecules, or as a combination of the two). Comparisons with experimental data helpedto probe solvent and quantum effects separately [33] and predict the corresponding reac-tions for H, which is very important in designing safe, supercritical water-cooled nuclearreactors.

Addition reactions to unsaturated molecules in the condensed phase can also be stud-ied. Ghandi et al. (2012) reported rate constants for Mu addition to vinylidene fluoride inCO2 at 290 to 530 K, 30 to 360 bars [15]. It was found that this reaction exhibits criticalslowing near conditions of maximum solvent isothermal compressibility. The sensitivity ofmuon methods allowed measurements of the largest ever reported activation volume (forany reaction and in any medium) with a magnitude of order ±106 cm3 mol−1. Such verylarge activation volumes are not artificially inflated by the solvent isothermal compress-ibility, but are of physical origin from the sharp divergence in rate constants at points nearcompressibility maxima. This indicates a significant change in the solvation shell betweenthe TS and the reactant, as well as the importance of pressure in tuning monomer reactiv-ity for free radical addition in supercritical CO2 (scCO2). The study also established themost economic and green conditions for free radical addition, which is important in greenchemistry and for industries that use scCO2.

Cormier et al. (2014) later used Mu kinetics and muoniated free radical analysis to reporta means to modify alkene reactivity, and their selectivity towards reactions with non-polarreactants in scCO2 near the critical point [14]. Near carbon dioxide’s critical point, the addi-tion of Mu to ethylene exhibits critical speeding up, while halogenated analogues displaycritical slowing. This suggests that scCO2 as a solvent may be used to tune selective alkenechemistry in near-critical conditions. This is another case where the predictions from Mukinetics data provide information that is of value to synthetic chemists and in industrialapplications.

The most important point from all of this research is that by investigating Mu reactionsin the condensed phase and in combination with computational and theoretical studies, sig-nificant information on H atom chemical dynamics and kinetics, mechanisms of reactions,solvent effects and effects of thermodynamic interactions can be obtained. Applicationscan be far reaching, from industrial development to energy generation and medicinaltreatments.

Muons as hyperfine interaction probes in chemistry

3 Futuristic aspects of muon as a probe of free radical kinetics

Some of the above mentioned studies involved very recent technique developments (forexample, laser μSR [14, 15] and muonic helium techniques [9]). It is expected that in thenear future, additional studies will extend the data set to test and develop better reactiondynamics theories. Studies of reactions of Mu under other excitations are being initiatedin our group, the results of which will be available soon. These studies include the useof microwave excitation and electro-excitation. In 2007, Ghandi et al. demonstrated manytechniques that will be applied to microwave-free radical chemistry work and will havefar reaching impacts on our understanding of the effects of microwaves on free radicalprocesses [20].

Other future studies could involve new theoretical developments that help provide a moreaccurate account of chemical kinetics, in particular KIEs with significant tunnelling, ZPEand even non-Born-Oppenheimer effects. Such studies will make it possible to accuratelypredict H atom kinetics from Mu kinetics data. Because, in general, Mu-based kinetic datahas less systematic error and can be obtained under more ideal conditions than kinetic databased on other isotopes of H, such theoretical calculations will have a very large impacton any applications where H atom reactions are important. Examples of such new devel-opments are demonstrated in the works of Alcorn et al. (2014) and Perez de Tudela et al.[10, 34]. The work of Alcorn et al. (2014) is described in Section 2.2. Perez de Tudelaet al. (2012) studied the ZPE and tunneling effect of the Mu + H2 reaction using the ringpolymer molecular dynamics technique (RPMD) [34]. They found that the effect of tunnel-ing is not overcompensated by ZPE. Their RPMD calculation was in agreement with highlevel and computationally expensive quantum calculations. Considering that RPMD is lessexpensive computationally, it is expected to significantly impact the modelling of accuraterate constants for H atom via Mu studies.

The use of KIEs to study drug actions by enhancing their pharmacokinetic, pharmaco-dynamic, or toxicological properties has recently gained momentum [40, 41]. In the realmof muon methods, studies of KIEs related to biological applications have not been done,although it is likely that such studies will begin soon. These include the study of deuteratedversions of patented and off-patent drugs with claims of increased efficacy, decreased tox-icity, reduced interpatient variability, and decreased drug dose or dosing frequency, as wellas the modelling of biological systems to understand PES data.

4 Muon as a hyperfine probe of the H atom in different materials

In addition to their ability to provide information on the H atom and free radical kinetics(described in the previous sections), muon techniques can also provide information on theelectronic environment of the H atom in different media, where providing such informationby other methods is difficult or impossible. Such information can be obtained via hyperfineinteractions of muon and unpaired electron in muonium (using either TF-μSR or repolar-ization studies using longitudinal magnetic fields [1]). A Breit-Rabi diagram of Mu can beseen in Fig. 2, showing how hyperfine coupling constants are measured. Muon techniquescan be considered ideal for such studies because a) information can be obtained at the sin-gle atom level (only one Mu in the medium at a time), b) no other spin probes or scavengersare needed, c) sample preparation consists only of oxygen removal, and d) the techniquescan be performed under any temperature, pressure or phase of matter.

K. Ghandi, A. MacLean

There are many examples of these studies in the literature, which have been coveredby other review articles [1, 2, 42]. Here, we use representative examples to demonstratewhat can be learned from such studies. Probably the most applied contributions of muonmethods as a hyperfine probe are the studies done on semiconductors to mimic H atom inthese materials [42]. Their significance lies in the fact that that hydrogen is understood tobe a prominent and unavoidable impurity in all electronic grade material. There have beenseveral reviews that described studies of Mu in semiconductors [[1, 42] and review articlesin the list of their references]. Recently, muons have been used to investigate propertiesof nanomaterials, an approach which is expected to become more popular in the future[36, 43].

Muon methods might also predict the effect of H on the electronic properties of othernew materials, such as those envisaged for optoelectronic or dielectric applications [42].An important observation from muon studies in semiconductors is that muons can pickup and bind individual electrons to form Mu in different states or sites within a material[1, 42]. These studies also provide information on chemical fate of H in different states/sites of semiconductors [1, 42]. They further showed that the H atom in semiconductorsmust exhibit metastability, a feature more usually associated with much heavier or complexdefects. This was first shown in Si where Mu states were neutral and paramagnetic, but withfairly different chemical characteristics. One resembles the interstitially trapped atom, whilethe other one has axial symmetry with electron spin distribution over a few surrounding Siatoms [1, 42].

Recently, μSR has been used to study the behaviour of low concentrations of hydrogenin diamond [44]. Natural diamond is highly impure, and these impurities are inconsistentbetween samples, rendering studies of their properties difficult before the discovery of dia-mond synthesis methods. These methods can produce diamond with impurities in the lowpart per billion ranges, and one in particular – chemical vapour deposition (CVD) – allowsfor controlled doping. Diamond has shown promise in electronic applications under extremeconditions, such as high temperature, high power, and high electronic frequency. In lightof this and the excellent charge collection properties of diamond prepared by CVD, thecoherent transport properties of Mu (and, indirectly, hydrogen) in diamond were studied inrecently available pure diamond prepared by high-pressure, high-temperature (HPHT) syn-thesis. In diamond samples with sub-ppm nitrogen concentrations, three muon species wereobserved: 1) Mu at the tetrahedral interstitial site of the diamond crystal structure 2) bond-centered Mu and 3) a muon in a diamagnetic environment. Most of the Mu was found inthe first state, in which its hyperfine coupling constant was 3711 MHz. The results of thiswork were very similar to the results of previous studies of Mu in diamond where two Mustates were found: normal and anomalous. Normal Mu is Mu at the tetrahedral interstitialsite, which has been reported with isotropic hyperfine interaction coupling constant A =3711 ± 21 MHz [38]. The isotropic Mu, therefore, has an HFC – 83 % of that of free Muin vacuum (4463 MHz) [2, 46–48].

The hyperfine coupling constant of bond-centered Mu is much smaller (186 MHz),and indicates that the unpaired electron spin density in this case is mostly localized atits two carbon neighbours, making it somewhat analogous to a muoniated radical. This issimilar to the anomalous Mu in previous studies, which is described by a (111) axiallysymmetric spin Hamiltonian with coupling constants extrapolated to 0 K of Aparallel =167.98 ± 0.06 MHz and Aperpendicular = 392.59 ± 0.06 MHz. The comparison with compu-tational studies provides important insights on the nature of the chemical bond of Mu and itselectronic structure. Based on unrestricted Hartree-Fock calculations, only one site is foundin undistorted cluster, that being the centre of interstitial tetrahedral space. However, by

Muons as hyperfine interaction probes in chemistry

extending C-C bonds, a more stable site is created at the middle of the extended bonds [44,45]. Computational results also indicate a highly repulsive antibonding interaction betweenthe interstitial Mu and the diamond clusters. The experimental results also indicate thatthe fractions of the muon states in the diamond prepared by CVD are close to those inhigh-quality natural type-IIa single crystal diamond [44].

The quantum diffusion of Mu in diamond was also studied using motional narrowing andlifetime broadening TF-μSR and by spin-lattice relaxation using LF-μSR [44]. The quantumcounterpart of the classical random walk, which can be modeled mathematically using aSchrodinger equation with a Markovian time dependent random potential, is quantum diffu-sion. For temperatures larger than 0 K, tunneling occurs on a background of coupling withexcitations of the medium [42, 49]. The results indicate that the diffusion constant of tetra-hedral interstitial Mu is high and not significantly dependent on temperature, whereas itshyperfine coupling follows a power law increase above 300 K, indicating localization of themuon above this temperature [44]. Moreover, the experimental study at very low tempera-ture (below 0.1 K) in different materials strongly suggests that Mu is in a delocalized state[50].

Although relatively old, the experiments on C60 using μSR are classical and instructiveto describe here [46, 51]. They have yielded two very different paramagnetic muoniatedspecies [46, 51]. The hyperfine coupling constant of the paramagnetic centre of one speciesis 4341 ± 24 MHz, which is only slightly less than that of vacuum Mu and indicates thatthe Mu is endohedral in this species. The other species has a coupling constant more typicalof a muoniated radical (325 MHz) at room temperature; the Mu in this species is bondedto the outside of the carbon cage. Using zero-field μSR, it has also been determined thatthe latter species has a completely anisotropic hyperfine interaction in the solid state. Inaddition, such studies have suggested that the properties of this species are dependent uponthe orientation of the radical with respect to the crystalline axes of C60.

Muon studies of clathrate hydrates have yielded interesting results, as well. Natural gashydrates are being considered as a potential energy source. Previous attempts to study freeradical formation in hydrates by ESR required gamma-irradiation of the sample to form theradicals. However, this resulted in multiple transient species being formed. Additionally,as in most cases, the characterization of free radicals is much more definitive, in particu-lar when using combination of μSR techniques. Muonium was detected in clathrates dopedwith cyclopentane and tetrahydrofuran, and its hyperfine coupling constants in these com-pounds were close to that of vacuum Mu, indicating muonium was unbound. Meanwhile,muoniated free radicals were observed in analogous samples containing cyclopentene and2, 5 - dihydrofuran (Scheme 1); more on this later [52]. (Similar results have been found inμSR studies of liquid water and hexagonal ice and in supercritical water [48].)

The studies described are examples of Mu as a probe of the H atom in the solid state,where Mu can be in its own space (such as Mu (H) in the gas phase or liquids), or it cantransfer significant electron density to surrounding nuclei (decreased HFC compared to vac-uum HFC). The s orbital of the Mu (H) could also be squeezed by neighbouring molecules,resulting in a larger HFC compared to the HFC in vacuum.

Similar studies in fluids provide information on the effects of surrounding molecules onthe wave function (electronic structure) of Mu (H) at the infinite dilution limit, which isthe ideal condition to study solvent-solute interactions [47, 48]. These studies are needed todemonstrate the Mu (H) atom is stable and does not react with the fluid molecules in caseswhere the investigations of Mu (H) kinetics is of interest [47, 48]. Studies in supercriticalfluids in particular are very interesting because they allow the gradual tuning of solventproperties [47, 48]. These studies in general showed a smaller HFC compared to the HFC

K. Ghandi, A. MacLean

Scheme 1 Muonium addition to cyclopentene and 2,5-dihydrofuran [52]

in vacuum, a decrease of HFC with density and pressure, and an increase of HFC withtemperature. Interestingly this trend is common in very different fluids, such as CO2 andwater [47, 48], which shows that it is possible to use small changes to the thermodynamicvariables to change the wavefunction of Mu (H) in both systems.

5 Muon as a probe of mechanism of free radical reactions

Free radicals play an important role in many fields of chemistry such as combustion, atmo-spheric chemistry, polymer chemistry, bio and medicinal chemistry, electronic industry,plasma and nuclear chemistry. In the following section, we describe applications of muonas a probe of free radical chemistry within the context of some of these applications, as wellas from a fundamental science perspective.

The studies on muoniated free radicals are mostly based on organic centered radi-cals and can be done in all phases (solid, liquid, gas, supercritical, and liquid crystal) oreven in heterostructures. Indeed, muoniated radicals were recently detected in samples ofclathrate hydrates containing unsaturated guest molecules, such as cyclopentene and 2,5-dihydrofuran (see Scheme 1); the observed hyperfine coupling constants of these radicalswere typical of alkyl radicals [52]. The μSR spectra of these radicals in the presence ofclathrates differed from those of the compounds in liquids, indicating that the clathrate cav-ities restricted the motion of the radicals. Similarly, HFCs of muoniated benzene radicals,both aqueous and in bulk, have also been measured [53]. Examples of other types of radicals(ex. organometallic ferrocene radicals), have also been reported [54].

Other examples of studies in the solid state include formation of anisotropic Mu (indeeda radical) in diamond [45] and in C60 by addition to the outer surface of C60 [46]. Com-paring molecules with similarities and differences in molecular structures would provideinformation on the effect of molecular structure on free radical formation. Hybridization ofcarbon in diamond is sp3, while the hybridization of carbon in C60 is between sp2 and sp3.The HFC in the bond-centered site of diamond is almost half the HFC of the radical fromaddition to C60. This suggests much lower electron density at the muon in the antibonding-trapped state of diamond, despite significant delocalization of unpaired electron density inMu-C60 [46].

Muon methods can be used to explore the mechanism of reactions of the H atom probedby Mu. If different channels lead to different free radicals, the probability of different chan-nels will affect the amplitude of the muoniated free radical signals (the larger the probability,the larger the amplitude of the free radical product). E.g. Brodovitch et al. (2003) studied

Muons as hyperfine interaction probes in chemistry

Scheme 2 Generation of amuoniated silyl radical fromaddition to silylene andsubsequent silylradical-to-silylene coupling [61]

the product of Mu added to fluoranthene [55]. In their study, five muoniated radicals wereformed (out of a possible nine). Like most recent works on muoniated free radicals, theHFCs of muon and selected protons in various radicals were obtained by comparison ofDensity Functional Theory (DFT) calculations and spectroscopic data. They showed that thelowest energy isomer of the five has the greatest spread of unpaired π-spin density, which isconsistent with a general notion of resonance stabilization. Theoretical studies of kinetics inthis system have not been performed but are of interest since the five different isomers havedifferent enough free energies of formation, to do not expect some of them. This may besuggestive of quantum tunneling for some of these channels or another mechanism for freeradical formation. The research also showed that Planar Aromatic Hydrocarbons (PAHs)are not good models to investigate the reactivity of a fullerene fragment, because the reac-tivity pattern is very different from what is observed in fullerenes. Such studies are valuableas they provide information on the effect of the strain on reactivity towards free radicaladdition.

There are many other studies of organic free radicals by muon methods that providesimilar mechanistic information under ordinary conditions, in addition to some works doneunder supercritical conditions. For example, Cormier et al. (2008, 2009) studied free radicalformation between Mu and ethene in scCO2 [56, 57]. In the presence of a low concentrationof ethene in scCO2, the addition of Mu to ethene is the only reaction channel, and indeed,the muoniated ethyl radical is observed. At high temperature, there is a significant and largedensity dependence of the HFC of the ethyl radical. This suggests that small changes to thethermodynamic conditions in scCO2 have a significant effect on the electronic structure offree radicals. Interestingly, although at a density close to 0.2 g/cm3, both rotational motionof the methyl R-group and the electronic structure of the radical are similar to those in thegas phase, at a slightly higher density (close to 0.4 g/cm3) CO2 molecules cluster around theethyl radical, and this increases the local density around the ethyl radical. These results wereobtained from studies of muon and proton hyperfine coupling constants (using TF-μSR andavoided level crossing (ALCR)) over the temperature of range 305 to 475 K. The studiesshowed a decrease in muon HFCs as a function of density due to the interaction betweenthe CO2 molecules and the ethyl radical p-orbital, which contains the unpaired electron.In these studies, the density dependence of the hyperfine coupling constant increased asthe temperature increased, as a result of an increased collision rate between the ethyl rad-ical and CO2. This allows a transient donation of electron density from ethyl radical toCO2. These results were similar to the observations of Mu HFC in supercritical water[48].

Until recently, μSR studies of free radicals have focused almost exclusively on addingMu to carbon compounds with multiple bonds. Some recent μSR studies of free radicals,

K. Ghandi, A. MacLean

Scheme 3 Example of Mu addition to a C=Si bond [62]

Scheme 4 Observed additions of Mu to a multifunctional cyclic silylene-NHC complex. Additions to theuncomplexed silylene are analogous

however, have dealt with organosilicon compounds [58]. The first study of muoniated silylradicals led to the discovery of silyl radical-to-silylene coupling, an example of which isshown in Scheme 2. This study was also the first in which TF-μSR spectroscopy was usedto directly detect the free radical product of a radical reaction. This finding sparked moreinterest in μSR studies of silyl radicals. A C = Si compound was examined as well, pro-ducing radicals as shown in Scheme 3. Many other such compounds were also tested andsuccessfully transformed to free radicals, but as of now, no μSR spectra have been obtainedfrom Si=Si, Si=N, or Si=O species.

The free radical reactivities of a multifunctional cyclic silylene and its N-heterocyclicCarbene (NHC) complex have also recently been investigated using TF and ALCR meth-ods. The radical formed in this fashion from the NHC complex, are shown in Scheme 4.Although Mu was found to attack the same sites on the silylene regardless of complexa-tion, the HFCs of the free radical species differed significantly between the complexed anduncomplexed silyl compounds. In particular, when Mu was added to the Si atom, the Muhad a much higher HFC in the uncomplexed radical (716 MHz) than it did in the com-plexed radical (19 Hz). This suggests that the spin density of Si in the complexed radical istransferred to the carbenic carbon.

Recent μSR studies of germanium radicals have yielded similar results to those of sil-icon radicals. In one study, TF-μSR spectra were obtained from nine different divalent

Muons as hyperfine interaction probes in chemistry

Scheme 5 Divalent germaniumcompounds studied using μSR.[60]

Scheme 6 Proposed formation of a digermyl radical from a germanium compound studied by μSR. [60]

germanium compounds (shown in Scheme 5) irradiated with muons [60]. The HFCs of Mubound to compounds containing N–Ge bonds were generally large (593-942 MHz), indi-cating strong muon-electron interactions in these radicals. One of the observed radicalsexhibited a much lower coupling constant, suggesting the reaction shown in Scheme 6; thiswould be analogous to the formation of the disilyl radical in Scheme 2. Interestingly, thisdigermyl radical formation was not observed when an extra tert-butyl group was present inthe starting material, though this may have been due to a slowing of the reaction beyondthe microsecond timescale of TF-μSR. Despite the apparent group trend present in radicalformation from divalent silicon and germanium compounds, tin compounds with similarstructures have not been found to react with Mu; this difference in reactivity likely arisesfrom the general unreactivity of divalent tin compounds.

K. Ghandi, A. MacLean

6 Conclusion

In summary, muon spectroscopy methods have a variety of uses and applications in chem-istry, mainly due to a) the muon’s extreme sensitivity to local and applied magnetic fields,b) the short muon lifetime, and c) the muon’s ability to act as a radioisotopic probe ofatomic hydrogen. Many chemically relevant studies have been performed with muon meth-ods, such as those discussed in this paper. Dynamic processes and material properties canbe examined using spin-polarized muons. The nature of reaction potential energy surfacecan be extracted from studies of Mu kinetics with reactants in both the gas phase and con-densed phase systems. The identity and formation mechanism of free radicals can be studiedin situ using muon methods, and single-molecule studies of H in different systems are alsopossible.

Acknowledgments This research was financially supported by Natural Sciences and Engineering ResearchCouncil of Canada, the Generation IV Energy Technologies Program, Natural Resources Canada and AtomicEnergy of Canada Limited.

References

1. Brewer, J.: μSR HOW TO. Hyperfine Interactions. in press (2014)2. Ghandi, K., Miyake, Y.: Muon Interactions with Matter. In: Mozumder, A., Hatano, Y. (eds.): Charged

Particle and Photon Interactions with Matter, Advances, Applications, and Interfaces, pp. Taylor &Francis (2011)

3. McKenzie, I., Ghandi, K., Kecman, S., Percival, P.W.: Formation and spectroscopy of alpha-muoniatedradicals. Phys. B 326, 76 (2003)

4. McKenzie, I., Brodovitch, J.-C., Ghandi, K.: Hyperfine coupling in methyl radical Isotopomers. J. Phys.Chem. A 42, 10625 (2007)

5. Johnson, H.S.: Reaction Theory. Ronald Press (1965)6. Kleinekathofer, U., Tang, K.T., Toennies, J.P., Yie, C.L.: The generalized Heitler-London theory for the

H-3 potential energy surface. J. Chem. Phys. 111, 3377 (1999)7. Yang, X.: Probing state-to-state reaction dynamics using H-atom Rydberg tagging time-of-flight

spectroscopy. PCCP 13, 8112 (2011)8. Wang, X., Bowman, J.M.: Mode-specific tunneling in the unimolecular dissociation of cis-HOCO to

H+CO2. J. Phys. Chem. A 118, 684 (2014)9. Fleming, D.G., Arseneau, D.J., Sukhorukov, O., Brewer, J.H., Mielke, S.L., Schatz, G.C., Truhlar, D.G.:

Kinetic isotope effects for the reactions of muonic helium and muonium with H2. Science 331, 448(2011)

10. Alcorn, C.D., Brodovitch, J.-C., Percival, P.W., Smith, M., Ghandi, K.: Kinetics of the reaction betweenH· and superheated water probed with muonium. J. Chem. Phys. 435, 29 (2014)

11. Ghandi, K., Cottrell, S.P., Fleming, D.G., Johnson, C.: The first report of a muoniated free radical formedfrom reaction of Mu with Br2. Phys. B 374, 303–306 (2006)

12. Johnson, C., Cottrell, S.P., Ghandi, K., Fleming, D.G.: Muonium and muon molecular ions in inert gasesstudied by ?SR. J. Phys. B: At. Mol. Opt. Phys. 38, 119–134 (2005)

13. Fleming, D.G., Manz, J., Sato, K., Takayanagi, T.: Fundamental change in the natureof chemical bonding by isotopic substitution. Angewandte Chemie International Edition,doi:10.1002/anie.201408211/abstract (2014)

14. Cormier, P., Clarke, R., McFadden, R., Ghandi, K.: Selective free radical reactions using supercriticalcarbon dioxide. JACS 136(6), 2200–2203 (2014)

15. Ghandi, K., McFadden, R., Satija, P., Cormier, P., Smith, M.: Radical kinetics in sub- and supercriticalcarbon dioxide: thermodynamic rate tuning. Phys. Chem. Chem. Phys. 14, 8502–8505 (2012)

16. Flores-Moreno, R. et al.: The any particle molecular orbital code. Int. J. Quantum Chem. 114(1), 50–56(2014)

17. Hudson et al.: Zero-point corrections for isotropic coupling constants for cyclohexadienyl radical, C6H7and C6H6Mu: beyond the bond length change approximation. Molecules 18, 4906–4916 (2013)

Muons as hyperfine interaction probes in chemistry

18. Albu, T., Espinosa-Garcia, J., Truhlar, D.G.: Computational chemistry of polyatomic reaction kineticsand dynamics. Chem. Inform. 4, 39 (2008)

19. Pan, J.J., Arseneau, D.J., Senba, M., Fleming, D.G., Himmer, U., Suzuki, Y.: Measurements of Mu+NOtermolecular kinetics up to 520 bar: isotope effects and the Troe theory. Phys. Chem. Chem. Phys. 2,621 (2000)

20. Ghandi, K., Clark, I.P., Lord, J.S., Cottrell, S.P.: Laser-muon spin spectroscopy in liquids—A techniqueto study the excited state chemistry of transients. Phys. Chem. Chem. Phys. 9, 353–359 (2007)

21. Bakule, P., Fleming, D.G., Sukhorukov, O., Ishida, K., Pratt, F., Momose, T., Truhlar, D.G.: State-selected reaction of muonium with vibrationally excited H2. J. Phys. Chem. Let. 3.19, 2755–2760(2012)

22. Grossiord, N. et al.: Degradation mechanisms in organic photovoltaic devices. Org. Electron. 13.3, 432–456 (2012)

23. Jambrina, P., Garcia, E.: Dynamics of the reactions of muonium and deuterium atoms with vibrationallyexcited hydrogen molecules: tunneling and vibrational adiabaticity. J. Phys. Chem. A 14(42), 14596–604 (2012)

24. Jambrina, P.G., Garcıa, E., Herrero, V.J., Saez-Rabanos, V., Aoiz, F.J.: Can quasiclassical trajectorycalculations reproduce the extreme kinetic isotope effect observed in the muonic isotopologues of theH = H2 reaction? J. Chem. Phys. 135(3), 034310 (2011)

25. Aldegunde, J., Jambrina, P.G., Garcıa, E., Herrero, V.J., Saez-Rabanos, V., Aoiz, F.J.: Understanding thereaction between muonium atoms and hydrogen molecules: zero point energy, tunnelling, and vibrationaladiabaticity. Mol. Phys. 111(21), 3169–3181 (2013)

26. Stephanie, M.V., Huynh, L.K., Carstensen, H.H., Dean, A.M.: High-pressure rate rules for alkyl + O2reactions. J. Phys. Chem. A 115, 13425–13442 (2011)

27. LeBlanc, R., Hackman, B., Liu, G., Ghandi, K.: Extrapolation of rate constants of reactions producingH2 and O2 in radiolysis of water at high temperatures, PBNC (In press)

28. Ghandi, K., Alcorn, C.D., Legate, G., Percival, P.W., Brodovitch, J.-C.: Chemical Kinetics in H2O andD2O under Hydrothermal Conditions. In: Proceedings of the second Canada-China Joint Conference onSupercritical Water-Cooled Reactors, 88–103 (2010)

29. Percival, P.W., Brodovitch, J.-C., Ghandi, K., McCollum, B., McKenzie, I.: H atom kinetics insuperheated water studied by muon spin spectroscopy. Radiat. Phys. Chem. 76, 1231–1235 (2007)

30. Ghandi, K., Addison-Jones, B., Brodovitch, J.-C., Kecman, S., McKenzie, I., Percival, P.W.: Muoniumkinetics in sub- and supercritical water. Phys. B 326, 76–80 (2003)

31. Ghandi, K., Percival, P.W.: Prediction of rate constants for reactions of the hydroxyl radical in water athigh temperatures and pressures. J. Phys. Chem. A 107, 3005–3009 (2003)

32. Ghandi, K., Brodovitch, J.-C., Addison-Jones, B., McKenzie, I., Percival, P.W., Schuth, J.: Neardiffusion-controlled reactions of muonium in supercritical water. Phys. Chem. Chem. Phys. 4, 586–595(2002)

33. Alcorn, C., Smith, M., Kennedy, A., Brodovitch, J.-C., Ghandi, K., Percival, P.W.: Kinetics of theReaction between H· and Superheated Water Probed with Muonium. In: Proceedings of InternationalSymposium of the Supercritical Water Reactors (ISSCWR-5), pp. 130–131 (2011)

34. Perez de Tudela, R., Aoiz, F.J., Suleimanov, Y.V., Manolopoulos, D.E.: Chemical reaction rates fromring polymer molecular dynamics: Zero point energy conservation in Mu +H2 → MuH+ H. J. Phys.Chem. Lett. 3(4), 493–497 (2012)

35. Duffey, R.B.: Sustainable futures using nuclear energy. Prog. Nucl. Energy 47(1–4), 535–543 (2005)36. Ashton, T.E. et al.: Muon studies of Li+ diffusion in LiFePO4 nanoparticles of different polymorphs. J.

Mater. Chem. A 2, 6238–6245 (2014)37. Sugiyama, J. et al.: Reactive surface area of the Lix(Co1/3Ni1/3Mn1/3)O2 electrode determined by μ+SR

and electrochemical measurements. Phys. Chem. Chem. Phys. 15, 10402–10412 (2013)38. Safriani, L. et al.: Charge carrier dynamics of active material solar cell P3HT:ZnO nanoparticles studied

by muon spin relaxation (μSR). Adv. Mat. Res. 896, 477–480 (2014)39. Janik, I., Bartels, D.M., Marin, T.W., Jonah, C.D.: Reaction of O2 with the hydrogen atom in water up

to 350 degrees C. J. Phys. Chem. A 111(1), 79–88 (2007)40. Korzekwa, K.: Enzyme kinetics of oxidative metabolism: Cytochromes P450. Methods Mol. Biol.

113(4), 149–166 (2014)41. Gao, Y. et al.: Drug enterohepatic circulation and disposition: constituents of systems pharmacokinetics.

Drug Discov. Today 19(3), 326 (2014)42. Cox, S.F.J. et al.: The first 25 years of semiconductor muonics at ISIS, modelling the electrical activity

of hydrogen in inorganic semiconductors and high-κ dielectrics. Phys. Scr. 88(6), 068503 (2013)43. Farren-Dai, M. et al.: A novel gold nanoparticle stability and its muon chemistry. Chem. Phys. Lett. 610,

331–334 (2014)

K. Ghandi, A. MacLean

44. Connell, S.H., Bharuth-Ram, K., Cox, S.F.J., Keartland, J.M.: μSR in diamond. Hyperfine Interact. 198,117 (2010)

45. Meier, P.F.: Muonium in diamond. Phys. Rev. A 25, 3 (2001)46. Duty, T.L., Brewer, J.H., Chow, K., Kiefl, R.F., MacFarlane, A.W., Morris, G.D., Schneider, J.W.,

Hitti, B., Lichti, R., Brard, L., Fischer, J.E., Smith III, A.B., Strongin, R.M.: Zero-field μSR in crystallineC60. Hyperfine Interact. 86, 789 (1994)

47. Ghandi, K., Arseneau, D.J., Bridges, M., Fleming, D.: Muonium formation as a probe of radiationchemistry in supercritical CO2. J. Phys. Chem. A 52, 11613 (2004)

48. Ghandi, K., Brodovitch, J.-C., Addison-Jones, B., Percival, P.W.: Hyperfine coupling constant ofmuonium in sub- and supercritical water. Phys. B 289, 476 (2004)

49. Prokof’ev, N.V.: Inhomogeneous quantum diffusion of muons in solids. Hyperfine Interact. 85(1), 3(1994)

50. Kadono, R.: Quantum diffusion of positive muons and muonium atoms. Curr. Opinion Solid State Mater.Sci. 6, 141 (2002)

51. Percival, P.W., Addison-Jones, B., Brodovitch, J.-C., Sun-Mack, S.: Radio-frequency muon spin reso-nance studies of endohedral and exohedral muonium adducts of fullerenes. Appl. Magn. Reson. 11(2),315 (1996)

52. Percival, P.W., Mozafari, M., Brodovitch, J.-C., Chandrasena, L.: Organic free radicals in clathratehydrates investigated by muon spin spectroscopy. J. Phys. Chem. A 118, 1162 (2014)

53. McKenzie, I. et al.: Hyperfine coupling constants of the cyclohexadienyl radical in benzene and diluteaqueous solution. J. Phys. Chem. B 117, 13614–13618 (2013)

54. McKenzie, I. et al.: Muon spin spectroscopy of ferrocene: characterization of muoniated ferrocenylradicals. Phys. Chem. Chem. Phys. 16, 10600–10606 (2014)

55. Brodovitch, J.-C., Addison-Jones, B., Ghandi, K., McKenzie, I., Percival, P.W., Schuth, J.: Free radicalsformed by H(Mu) addition to fluoranthene. Can. J. Chem. 81(1), 1 (2003)

56. Cormier, P., Arseneau, D.J., Brodovitch, K.C., Lauzon, J.M., Taylor, B.A., Ghandi, K.: Free radicalformation in supercritical CO2, using muonium as a probe and implication for H atom reaction withethene. J. Phys. Chem. A 112(20), 4593–4600 (2008)

57. Cormier, P., Taylor, B., Ghandi, K.: Hyperfine interactions of a muoniated ethyl radical in supercriticalCO2. Phys. B Condens. Matter 404(5–7), 930–932 (2009)

58. West, R., Samedov, K., Percival, P.W.: Silicon meets cyclotron: muon spin resonance of organosiliconradicals. Chem. Eur. J. 20, 9184 (2014)

59. Percival, P.W., McCollum, B.M., Brodovitch, J.-C., Driess, M., Mitra, A., Mozafari, M., West, R.,Xiong, Y., Yao, S.: Dual reactivity of a stable zwitterionic N-heterocyclic silylene and its carbenecomplex probed with muonium. Organometallics 31, 2709 (2012)

60. West, R. et al.: Germanium-centered free radicals studied by muon spin spectroscopy. Can. J. Chem. 92,508–513 (2014)

61. McCollum, B.M., Brodovitch, J.-C., Clyburne, J.A.C., Percival, P.W., West R: Physica B 404, 940–942(2009)

62. McCollum, B.M., Abe, T., Brodovitch, J.-C., Clyburne, J.A.C., Iwamoto, T., Kira, M., Percival, P.W.,West, R.: Angew. Chem. 120, 9918–9920 (2008); Angew. Chem. Int. Ed. 47, 9772–9774 (2008)