New results for the formation of a muoniated radical in the Mu + Br2 system: a van der Waals complex or evidence for vibrational bonding in Br-Mu-Br?

New evidence is presented for the observation of a muoniated radical in the Mu + Br(2) system, from μSR longitudinal field (LF) repolarisation studies in the gas phase, at Br(2) concentrations of 0.1 bar in a Br(2)/N(2) mixture at 300 K and at 10 bar total pressure. The LF repolarisation curve, up to a field of 4.5 kG, reveals two paramagnetic components, one for the Mu atom, formed promptly during the slowing-down process of the positive muon, with a known Mu hyperfine coupling constant (hfcc) of 4463 MHz, and one for a muoniated radical formed by fast Mu addition. From model fits to the Br(2)/N(2) data, the radical component is found to have an unusually high muon hfcc, assessed to be ～3300 MHz with an overall error due to systematics expected to exceed 10%. This high muon hfcc is taken as evidence for the observation of either the Br-Mu-Br radical, and hence of vibrational bonding in this H[combining low line]-L[combining low line]-H[combining low line] system, or of a MuBr(2) van der Waals complex formed in the entrance channel. Preliminary ab initio electronic structure calculations suggest the latter is more likely but fully rigorous calculations of the effect of dynamics on the hfcc for either system have yet to be carried out.     

Radical anions of flavonoids

Several representatives of natural flavonoids and their synthetic nitro‐derivatives have been investigated by polarography and electron paramagnetic resonance (EPR) spectroscopy under electrochemical reduction in acetonitrile, dimethylformamide (DMF), dimethylsulfoxide (DMSO) or 1,2‐dimethoxyethane. All the compounds studied are reduced in the first stage by one‐electron transfer, apart from flavanone, which accepts two electrons simultaneously. However, the primary radical anions were detected by EPR spectroscopy only for 4′‐nitroflavone. It was shown that radical anions of other flavonoids quickly dimerized. The analysis of the temperature dependence of the hyperfine interaction constants and broadening of lines in EPR spectra of 4′‐nitroflavone radical anions has shown that the distribution of spin density is due to both the change of polarity of the medium and rotation of the nitrophenyl moiety. The assignment of hyperfine structure constants for the 4′‐nitroflavone radical anion was confirmed by density functional theory (DFT) calculations. Copyright © 2011 John Wiley & Sons, Ltd.     

The magnetic behaviour of [NnBu4]4[Ni16Pd16(CO)40]: an even-electron homoleptic carbonyl-metal cluster anion displaying a J = 2 ground state

The magnetic behaviour of the even-electron [Ni16Pd16(CO)40]4- cluster, in its [NnBu4]+ salt, has been investigated by magnetometry and muon spin rotation/relaxation (muSR) spectroscopy. The susceptibility measurements show an exceptionally high magnetic moment corresponding to a total spin value J=2. This suggests a Hund filling of a quadruplet ground state, quite unique in carbonyl-metal clusters. SQUID magnetometry shows a departure from the Curie-Weiss law, for T>150 K, and strong deviation from a Brillouin behaviour of the magnetisation curves. muSR spectroscopy in zero applied field shows a temperature independent decay of the muon spin polarisation, similar to that of a purely paramagnetic system. The observed muon spin repolarisation in a moderate external longitudinal field, however, invalidates this simple picture and suggests the presence of a local anisotropy field acting on the cluster's magnetic moment. A consistent interpretation of magnetometry and muSR results implies the occurrence of an additional interaction of the cluster spin with an effective crystalline field. The inclusion of this interaction in a model Hamiltonian allows us to successfully reproduce both the susceptibility and magnetisation data.     

DFT study of paramagnetic adducts of tris-(8-hydroxyquinoline)aluminum (III)

Radicals formed by the addition of hydrogen (H) or muonium (Mu) to tris(8-hydroxyquinoline)aluminum(III) (Alq(3)) have been studied using density functional theory (DFT) calculations. Drew et al. (Phys. Rev. Lett. 2008, 100, 116601) studied Alq(3) using the longitudinal field muon spin relaxation technique and assumed the formation of muoniated radicals and rapid intermolecular electron hopping with a rate of (1.4 ± 0.2) × 10(12) s(-1). In this work, the results of DFT calculations on Alq(3), the H/Mu adducts of Alq(3), and the corresponding anions and cations are reported. The energy required to transfer an electron to or from the H/Mu adducts of Alq(3) is prohibitively large, ranging from 4.09 to 5.68 eV, which suggests that the unpaired electron does not hop onto neighboring molecules and that there is no long-range diffusion of the unpaired electron. The hyperfine coupling constants for the muoniated radicals were calculated and used to predict avoided level crossing resonance fields, which will allow experimenters to confirm that the unpaired electron is localized in close proximity to the muon.     

Theoretical studies of alkyl radicals in the NaY and HY zeolites

Interplay of quantum mechanical calculations and experimental data on hyperfine coupling constants of ethyl radical in zeolites at several temperatures was engaged to study the geometries and binding energies and to predict the temperature dependence of hyperfine splitting of a series of alkyl radicals in zeolites for the first time. The main focus is on the hyperfine interaction of alkyl radicals in the NaY and HY zeolites. The hyperfine splitting for neutral free radicals and free radical cations is predicted for different zeolite environments. This information can be used to establish the nature of the muoniated alkyl radicals in the NaY and HY zeolites via muSR experiments. The muon hyperfine coupling constants of the ethane radical cation in these zeolites are very large with relatively little dependence on temperature. It was found that the intramolecular dynamics of alkyl free radicals are only weakly affected by their strong binding to zeolites. In contrast, the substrate binding has a significant effect on their intermolecular dynamics.     

Resonance effect of a high-frequency magnetic field on the recombination probability of radical pairs in a liquid

Expressions for a resonance dependence of geminate recombination probability of radical pairs on the intensity of an external steady magnetic field in the presence of a high-frequency magnetic field normal to it have been obtained Numerical calculations of the above dependence have been performed for the cases involving Δg and hyperfine coupling mechanisms of spin conversion.     

The reactions of imidazol-2-ylidenes with the hydrogen atom: a theoretical study and experimental confirmation with muonium

The possible radicals resulting from hydrogen atom addition to the imidazole rings of 1,3-bis(isopropyl)-4,5-dimethylimidazol-2-ylidene (1) and 1,3-bis(2,4,6-trimethylphenyl)imidazol-2-ylidene (2) have been studied by means of density functional calculations (B3LYP). The calculations included solvent effects estimated via the polarized continuum model (PCM) and an empirical treatment of vibrational averaging of hyperfine constants. Addition of a hydrogen (or muonium) atom to the carbeneic carbon of 1,3-bis(isopropyl)-4,5-dimethylimidazol-2-ylidene was found to give a radical 60.46 kJ mol(-)(1) more stable than the radical resulting from addition to the double bond. Estimation of the activation barriers for reaction at the two sites shows that addition at the carbeneic carbon is favored. The site of addition was confirmed experimentally using muonium (Mu), which can be considered a light isotope of hydrogen. Muon spin rotation and muon level-crossing spectroscopy were used to determine muon, (13)C, and (14)N hyperfine coupling constants (hfc's) for the radical products of addition to the two carbenes. Good agreement between the experimental and calculated hfc's confirms that Mu (and hence H) adds exclusively to the carbeneic carbon. The radicals that are produced have nonplanar radical centers with most of the unpaired electron spin density localized on the alpha-carbon.     

ESR and electrochemical studies of 2-acylpyridines and 6,6'-diacyl-2,2'-bipyridines

The ESR spectra of radicals obtained by electrolytic reduction of 2-acylpyridines and 6,6'-diacyl-2,2'-bipyridines were measured in dimethylsulfoxide (DMSO) and analyzed by quantum chemical calculations. The electrochemistry of these compounds was characterized using cyclic voltammetry, in DMSO solvent. The results showed a two step reduction mechanism, first wave was assigned to the generation of the correspondent free radical species, and the second wave was assigned to the dianion derivatives. AM1 and DFT calculations were performed to obtain the optimized geometries, theoretical hyperfine constants, and spin distributions, respectively. The theoretical results are in complete agreement with the experimental ones.     

How do strain and steric interactions affect the reactions of aromatic compounds with free radicals? Characterization of the radicals formed by muonium addition to p-xylene and [2.2]paracyclophane by DFT calculations and muon spin spectroscopy

Muoniated radicals were produced by the addition of muonium (Mu) to the aromatic compound p-xylene (1) in the solid and liquid states and to the strained aromatic compound [2.2]paracyclophane (2) in the solid state. The radicals were characterized by avoided level crossing muon spin resonance spectroscopy and identified by comparing the experimentally determined muon hyperfine coupling constants with values obtained from DFT calculations. Mu was observed to add to both the secondary and tertiary carbons of 1, with the relative yield of the Mu adduct of the tertiary carbons estimated to be ～10% in the liquid phase. The relative yield of the tertiary adduct is much higher in the solid state although this cannot be calculated exactly due to the overlap of resonances and the apparent nonuniform distribution of the radical orientations. There are three possible addition sites in 2 due to the lower symmetry of the six-membered ring compared with 1. Mu can add to the secondary carbons either from the outside of 2, generating the "exo" adduct, or from the inside, generating the "endo" adduct. The relative yields of the exo, endo, and tertiary carbon adducts are 67.1(1), 21.8(1), and 11.1(1)%, respectively. The barriers to Mu addition at the different sites of isolated molecules were determined from DFT calculations. The barriers for Mu addition to 2 are lower than the barriers for Mu addition to 1, except for addition to the "endo" position, where the unfavorable steric interactions with the second ring of 2 raise the addition barrier considerably. The measured relative yields do not reflect the distribution of products calculated using the activation energies obtained from the DFT calculations due to strong steric interactions with neighboring molecules.     

Positive muons in condensed phase ammonia

The chemical behavior of positive muons in condensed phase ammonia has been investigated in order to elucidate the phase and temperature effects on the chemical and physical behavior of the muon and muonium formation in a simple binary compound. Diamagnetic muon yield (P_D) was constant at 0.67±0.01 in both solid and liquid above 125 K. Muonium formation in solids were observed above 100 K with slow muonium spin relaxation. In liquids, the muonium yield and its spin relaxation rate showed temperature dependence. Addition of metallic sodium increased P_D in liquids.     

Observation of muonium substituted free radicals in a durene single crystal

Two chemically inequivalent 2,3,5,6-tetramethyl cyclohexadienyl radicals are observed in a durene single crystal by means of the muon spin rotation technique. Orientations and anisotropies of the muon hyperfine interactions are determined.     

Diketone radical cations: ketonic and enolic forms as revealed by matrix EPR studies and DFT calculations

Radical cations of 2,3-butanedione, 2,4-pentanedione, 3-methylpentane-2,4-dione, 2,5-hexanedione, and 2,3-pentanedione were investigated by electron paramagnetic resonance (EPR) spectroscopy in a solid Freon matrix and density functional theory (DFT) quantum chemical calculations. All the diketone radical cations in ketonic form show small proton hyperfine couplings (typically unresolved in the EPR spectra). In the cases of 2,4-pentanedione and 3-methylpentane-2,4-dione, enolic forms of the radical cations (pi-type species with main spin population at carbon atom) were characterized. Preferential stabilization of the enolic form of 3-methylpentane-2,4-dione radical cation was explained by trap-to-trap positive hole migration rather than monomolecular relaxation of the ionized ketonic form through H atom transfer.     

Solvation of a hydrogen isotope in aqueous methanol, NaCl, and KCl solutions

The muon hyperfine coupling constant (hfc) of the light hydrogen isotope muonium (Mu) was measured in aqueous methanol, NaCl, and KCl solutions with varying concentrations, in deuterated water, and in deuterated methanol. The muon hfc is shown to be sensitive to the size and composition of the primary solvation shell, and the three-dimensional harmonic oscillator model of Roduner et al. (J. Chem. Phys. 1995, 102, 5989) has been modified to account for dependence of the muon hfc on the methanol or salt concentration. The muon hfc of Mu in the aqueous methanol solutions decreases with increasing methanol concentration up to a mole fraction (chiMeOH) of approximately 0.4, above which the muon hfc is approximately constant. The concentration dependence of the muon hfc is due to hydrophobic nature of Mu. It is preferentially solvated by the methyl group of methanol, and the proportion of methanol molecules in the primary solvation shell is greater than that in the bulk solution. Above chiMeOH approximately 0.4, Mu is completely surrounded by methanol. The muon hfc decreases with increasing methanol concentration because more unpaired electron spin density is transferred from Mu to methanol than to water. The unpaired electron spin density is transferred from Mu to the solvent by collisions that stretch one of the solvents bonds. The amount of spin density transferred is likely inversely related to the activation barrier for abstraction from the solvent, which accounts for the larger muon hfc in the deuterated solvents. The muon hfc of Mu in electrolyte solution decreases with increasing concentration of NaCl or KCl. We suggest that the decrease of the muon hfc is due to the amount of spin density transferred from Mu to its surroundings being dependent on the average orientation of the water molecules in the primary solvation shell, which is influenced by both Mu and the ions in solution, and spin density transfer to the ions themselves.     

Understanding solvent effects on hyperfine coupling constants of cyclohexadienyl radicals

Quantum chemical calculations have been carried out to understand better solvent effects on the isotropic muon and proton hyperfine coupling constants in the C₆H₆Mu^• radical. Both polarizable continuum solvent models and explicit inclusion of water molecules into supermolecular complexes were used. Changes in the hyperfine couplings of in-plane hydrogen atoms are very small and difficult to discuss, partly due to relatively large experimental error bars. In contrast, the out-of-plane proton and muon hyperfine couplings exhibit more pronounced changes. These are partly due to structural changes of the radical and partly due to direct electronic polarization effects. Polarizable continuum solvent models agree well with experimental changes for benzene but overshoot the enhancement of the hyperfine couplings for water. Explicit inclusion of water molecules reduces this overestimated spin density increase and thereby tends to bring theory and experiment into closer agreement. The enhancement of the spin density on the out-of-plane hydrogen or muon atoms by the solvent environment is mainly due to an increased polarization of the singly occupied MO towards this side. Electronic Supplementary Material: Supplementary material is available in the online version of this article at dx.doi.org/10.1007/s00214-005-0680-x     

Isolation and Characterization of Radical Anions Derived from a Boryl‐Substituted Diphosphene

Radical anions of a diphosphene with two boryl substituents were isolated and characterized by single‐crystal X‐ray diffraction, electron spin resonance (ESR), and UV/Vis absorption spectroscopy as well as DFT calculations. Structural analysis of the radical anions revealed an elongation of the P=P bond and a contraction of the B−P bonds relative to the neutral diphosphene. The UV/Vis spectra of these radical anions showed a strong absorption in the visible region, which was assigned to SOMO‐related transitions on the basis of DFT calculations. The ESR spectra revealed that the hyperfine coupling constant with the phosphorus nuclei is the smallest that has been reported thus far. The results of the DFT calculations furthermore suggest that this should be attributed to a soaking of electron spin to the vacant p orbitals of the boryl substituents.     

Über ESR-spektroskopische untersuchungen am radikaldianion des lophins und seine cyclisierung zu 2-phenyl-phenanthroimidazol

Treating lophine with potassium at ?50° in an inert solvent yields the radical dianion 6 of this compound. The solution being warmed to room temperature, the radical rearranges to a red diamagnetic intermediate 7. In presence of potassium then the radical dianion 3 of 2-phenyl-4,5,(9′,10′)-phenanthrimidazole is formed which has been described earlier.ESR-spectroscopical investigations show, that the spin density in the 2-phenyl ring of radical 6 vanishes. According to spin density calculations 2-phenyl residue and heterocycle are strongly distorted.     

Isotropic hyperfine interaction and spin-lattice relaxation for radicals in the solid state. Part 4

Spin-lattice relaxation is discussed for radicals in a solid with isotropic hyperfine interaction; various models are used for the interaction between the vibrations in the radical and the lattice vibrations. The formulas relate the relaxation time to temperature, magnetic field, and the parameters of the spin hamiltonian.     

硫氧分子阴离子的QCISD方法研究

使用二次组态相互作用（QCISD）方法和6－311G（d),6-311+G(d),6-311G(2d) 及6－311＋G(2d)基组研究了SO2^-和SO3^-的分子结构，超精细偶数常数（hfcc)及 其对应的分子的绝热电子亲合势（AEA）。发现在QCISD／6－311＋G（2d)水平上计 算的两个分子离子的结构，hfcc值（在^33S和^17O上的）和AEA值与实验值符合得 都很好（除SO^3-中的在^33S上的hfcc值比实验值小23％）。作为比较，我们使用 相同基组作了B3LYP方法计算，得到的超精细偶合常数和AEA值却都与实验符合得不 好。     

Muon implantation of metallocenes: ferrocene

Muon Spin Relaxation and Avoided Level Crossing (ALC) measurements of ferrocene are reported. The main features observed are five high field resonances in the ALC spectrum at about 3.26, 2.44, 2.04, 1.19 and 1.17 T, for the low-temperature phase at 18 K. The high-temperature phase at 295 K shows that only the last feature shifted down to about 0.49 T and a muon spin relaxation peak at about 0.106 T which approaches zero field when reaching the phase transition temperature of 164 K. A model involving three muoniated radicals, two with muonium addition to the cyclopentadienyl ring and the other to the metal atom, is postulated to rationalise these observations. A theoretical treatment involving spin-orbit coupling is found to be required to understand the Fe-Mu adduct, where an interesting interplay between the ferrocene ring dynamics and the spin-orbit coupling of the unpaired electron is shown to be important. The limiting temperature above which the full effect of spin-orbit interaction is observable in the muSR spectra of ferrocene was estimated to be 584 K. Correlation time for the ring rotation dynamics of the Fe-Mu radical at this temperature is 3.2 ps. Estimated electron g values and the changes in zero-field splittings for this temperature range are also reported.     

Pulsed EPR characterization of encapsulated atomic hydrogen in octasilsesquioxane cages

Hydrogen atoms encapsulated in molecular cages are potential candidates for quantum computing applications. They provide the simplest two-spin system where the 1s electron spin, S = 1/2, is hyperfine-coupled to the proton nuclear spin, I = 1/2, with a large isotropic hyperfine coupling (A = 1420.40575 MHz for a free atom). While hydrogen atoms can be trapped in many matrices at cryogenic temperatures, it has been found that they are exceptionally stable in octasilsesquioxane cages even at room temperature [Sasamori et al., Science, 1994, 256, 1691]. Here we present a detailed spin-lattice and spin-spin relaxation study of atomic hydrogen encapsulated in Si(8)O(12)(OSiMe(2)H)(8) using X-band pulsed EPR spectroscopy. The spin-lattice relaxation times T(1) range between 1.2 s at 20 K and 41.8 μs at room temperature. The temperature dependence of the relaxation rate shows that for T < 60 K the spin-lattice relaxation is best described by a Raman process with a Debye temperature of θ(D) = 135 K, whereas for T > 100 K a thermally activated process with activation energy E(a) = 753 K (523 cm(-1)) prevails. The phase memory time T(M) = 13.9 μs remains practically constant between 200 and 300 K and is determined by nuclear spin diffusion. At lower temperatures T(M) decreases by an order of magnitude and exhibits two minima at T = 140 K and T = 60 K. The temperature dependence of T(M) between 20 and 200 K is attributed to dynamic processes that average inequivalent hyperfine couplings, e.g. rotation of the methyl groups of the cage organic substituents. The hyperfine couplings of the encapsulated proton and the cage (29)Si nuclei are obtained through numerical simulations of field-swept FID-detected EPR spectra and HYSCORE experiments, respectively. The results are discussed in terms of existing phenomenological models based on the spherical harmonic oscillator and compared to those of endohedral fullerenes.