Vibrationally averaged spin densities on muons and protons in the hydroxyl and ethyl radicals

Claxton, T. A.; Graham, Alison M.; Cox, S. F. J.; Maric, Dj. M.; Meier, P. F.; Vogel, Stefan

doi:10.1007/bf02397743

Cited by 32 publications

(23 citation statements)

References 8 publications

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“…A larger effect by about a factor of 2 is seen in the case of the B3LYP/EPR-III calculation, which provides another argument in favor of the MP2/EPR-III results for muon HFCC in the absence of lattice interaction effects. Though a case could be made that a smaller scale factor of 1.05 (for MP2/EPR-III) would be in better agreement with the experimental result for A μ ′ (0) = 151 ± 2 MHz, consistent with calculated results reported for Mu−ethyl in ref or refs and , it is important to remember here that these smaller scale factors around 1.05 were determined phenomonologically, in contrast to the factor of 1.076 we have utilized, found from the quantum Monte Carlo calculations of ref .…”

Section: Methodology and Resultssupporting

confidence: 89%

“…Besides the pure electronic structure effect, the importance of incorporating vibrational corrections in HFCC calculations is well-known, as discussed in a recent review article . As already mentioned, vibrational corrections are particularly important for C−Mu bonds in muoniated radicals, , and of particular relevance here are earlier studies of the muoniated ethyl radical. − Though the HFCCs of several small radicals have been calculated in Barone’s group with the inclusion of vibrational corrections by a fully automated second-order perturbative approach implemented locally in Gaussian03, this implementation is generally not available to other Gaussian03 users. In the current study of muoniated butyl radicals, lacking a direct analytical first-principles evaluation of the dynamical effect of vibrational averaging, the C−Mu bond has been intentionally elongated to 1.076 times the corresponding equilibrium C−H bond length and calculations have been carried out on this modified (static) geometry to account for contributions to HFCCs from averaging over vibrational anharmonicity in the C−Mu bond stretch.…”

Section: Methodology and Resultsmentioning

confidence: 99%

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Theoretical Calculations of Hyperfine Coupling Constants for Muoniated Butyl Radicals

2011

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The hyperfine coupling constants (HFCCs) of all the butyl radicals that can be produced by muonium (Mu) addition to butene isomers (1- and 2-butene and isobutene) have been calculated, to compare with the experimental results for the muon and proton HFFCs for these radicals reported in paper II (Fleming, D. G.; et al. J. Phys. Chem. A 2011, 10.1021/jp109676b) that follows. The equilibrium geometries and HFCCs of these muoniated butyl radicals as well as their unsubstituted isotopomers were treated at both the spin-unrestricted MP2/EPR-III and B3LYP/EPR-III levels of theory. Comparisons with calculations carried out for the EPR-II basis set have also been made. All calculations were carried out in vacuo at 0 K only. A C-Mu bond elongation scheme that lengthens the equilibrium C-H bond by a factor of 1.076, on the basis of recent quantum calculations of the muon HFCCs of the ethyl radical, has been exploited to determine the vibrationally corrected muon HFCCs. The sensitivity of the results to small variations around this scale factor was also investigated. The computational methodology employed was "benchmarked" in comparisons with the ethyl radical, both with higher level calculations and with experiment. For the β-HFCCs of interest, compared to B3LYP, the MP2 calculations agree better with higher level theories and with experiment in the case of the eclipsed C-Mu bond and are generally deemed to be more reliable in predicting the equilibrium conformations and muon HFCCs near 0 K, in the absence of environmental effects. In some cases though, the experimental results in paper II demonstrate that environmental effects enhance the muon HFCC in the solid phase, where much better agreement with the experimental muon HFCCs near 0 K is found from B3LYP than from MP2. This seemingly better level of agreement is probably fortuitous, due to error cancellations in the DFT calculations, which appear to mimic these environmental effects. For the staggered proton HFCCs of the butyl radicals exhibiting no environmental effect in paper II, the best agreement with experiment is consistently found from the B3LYP calculations, in agreement also with benchmark calculations carried out for the ethyl radical.

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Section: Methodology and Resultssupporting

confidence: 89%

Section: Methodology and Resultsmentioning

confidence: 99%

Theoretical Calculations of Hyperfine Coupling Constants for Muoniated Butyl Radicals

2011

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“…Reference wavefunctions were calculated using a post hoc SCF method,as described above, and compared to those calculated using the HFQ1 approach with a quantum hydrogenlike nucleus, obtained by the diagonalization of the Hamiltonian described by equation (2). The hydrogen-like nucleus (p or µ + ) basis set used in these calculations (and throughout this paper) consisted of a set of six Gaussians with exponents ranging from 0.4 to 25 centred on two sites along the C-X (X = H, Mu) bond, which was found to yield energies converged to 0.01 eV [8].…”

Section: Approaches To Predicting Quantum Behaviourmentioning

confidence: 99%

“…Here S λσ is an overlap matrix element, and V p replaces V eµ in equation (2). Note that, in equation (6b), r µ represents the position at which the basis function is centred, and is not integrated over.…”

Section: Improving the Correlation Of The Hydrogen-like Nucleus With mentioning

confidence: 99%

Quantum behaviour of hydrogen and muonium in vacancy-containing complexes in diamond

Kerridge¹,

Harker²,

Stoneham³

2004

J. Phys.: Condens. Matter

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Most solid-state electronic structure calculations are based on quantum electrons and classical nuclei. These calculations either omit quantum zeropoint motion and tunnelling, or estimate it in an extra step. Such quantum effects are especially significant for light nuclei, such as the proton or its analogue, µ + . We propose a simple approach to including such quantum behaviour, in a form readily integrated with standard electronic structure calculations. This approach is demonstrated for a number of vacancy-containing defect complexes in diamond. Our results suggest that for the NHV − complex, quantum motion of the proton between three equivalent potential energy minima is sufficiently rapid to time-average measurements at X-band frequencies.

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“…1.2 for more rigid systems like cyclohexadienyl. These deviations are rooted 143,144 in the differing vibrational frequencies and amplitudes conferred upon molecules which have, in effect, had a proton replaced by a particle with a mass of only 1 9 th of that of a proton. Many radicals have been characterised, mainly by TF-MuSR, and I will end the review with just a few relatively recent examples.…”

Section: Organometallic Complexesmentioning

confidence: 99%

8 Muon spectroscopy

Rhodes

2001

Annu. Rep. Prog. Chem., Sect. C

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The elusiveness of reactive free radicals poses great challenges for their investigation per se in most processes in which they have an intermediary role; this is true particularly in heterogeneous media. There are, however, methods available for the detection of radicals with enormous sensitivity and specificity which are given the collective acronym mSR (MuSR). All the MuSR methods rely upon the addition of the light hydrogen atom 'muonium' -a hydrogen atom with a radioactive positive muon as its nucleus, having a mass 1 9 that of a protium atom -to an organic substrate. In addition to its property of radioactive decay, the muon also has spin, and therefore experiments akin to those of conventional magnetic resonance experiments may be undertaken. Among the suite of methods thus encompassed is transverse-field MuSR (TF-MuSR), which is equivalent to ENDOR and yields the nucleus (muon) coupling directly, while the avoided level crossing (ALC) approach yields the magnitudes of the couplings from other nuclei present in a given radical, and also their relative signs (like TRIPLE does). Although these are resonance experiments, they do not require the application of external radiofrequency fields; however, radiofrequency experiments are possible, in which the analogies with more conventional magnetic resonance experiments are more direct. However, the experiments which are rendered possible by muons are unique, and have no practicable counterpart in more conventional techniques. In particular, the feature of single-particle-counting methods being used in combination with nuclear spins which are 100% polarised (i.e. vastly in excess of the Boltzmann factor!) permits unparalleled sensitivity regarding reactive radicals. Through the incisiveness of these methods, knowledge in the field of free radical chemistry has been gained that would be unachievable using the more established methods of EPR and its relatives.In consequence of these benefits, although my own background is in EPR (a topic which I have reviewed previously in this series), 1-3 my research group has become increasingly involved in the techniques of MuSR, especially in regard to determining the behaviour of radicals in catalytic systems and in heterogeneous environmental processes, and for the measurement of free radical reaction rates pertinent to biological membrane damage and repair. These are all topics whose investigation we could not have attempted without muons.

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Vibrationally averaged spin densities on muons and protons in the hydroxyl and ethyl radicals

Cited by 32 publications

References 8 publications

Theoretical Calculations of Hyperfine Coupling Constants for Muoniated Butyl Radicals

Theoretical Calculations of Hyperfine Coupling Constants for Muoniated Butyl Radicals

Quantum behaviour of hydrogen and muonium in vacancy-containing complexes in diamond

8 Muon spectroscopy

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