EPR hyperfine coupling constants

Free radicals are generally short-lived, highly reactive species, usually characterized experimentally by their magnetic properties only. Thus a successful theoretical approach must be able to provide at the same time reliable structural and magnetic properties. Here we have chosen as representative models the methyl, aUyl and formaldehyde cation radicals. The isotropic hyperfine coupling constant (hcc) of a magnetically active nucleus N (a(N)) is related to the spin densities at the nucleus by [69] 

The methyl radical is well characterized by both ejqwrimental and theoretical points of view [e.g. 70-72] thus providing the most natural benchmark for the smdy of 7t-radicals. Some results are shown in table 3. 

CH bond length (A) and isotropic hcc s (G) computed for the methyl radical by different 

It is quite apparent that the PBEO approach provides the most accurate results, even with respect to the B3LYP model. Note, furthermore, that conventional density functionals provide comparable hyperfine splittings for the hydrogen atom, but disappointing results for carbon [73]. 

The allyl radical is of particular theoretical interest as a small molecule which exhibits the phenomenon of doublet instability, or symmetry breaking. As a consequence, the restricted open-shell HF (ROHF) method fails to reproduce the C2v equilibrium structure predicted by experimental smdies [74]. One must, therefore, resort to unrestricted (UHF or UKS) or multiconfigurational (MCSCF) methods. The results obtained using different functionals are reported in table 4. As for the methyl radical, a good agreement is found between the 

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Type II copper enzymes generally have more positive reduction potentials, weaker electronic absorption signals, and larger EPR hyperfine coupling constants. They adopt trigonal, square-planar, five-coordinate, or tetragonally distorted octahedral geometries. Usually, type II copper enzymes are involved in catalytic oxidations of substrate molecules and may be found in combination with both Type I and Type III copper centers. Laccase and ascorbate oxidase are typical examples. Information on these enzymes is found in Tables 5.1, 5.2, and 5.3. Superoxide dismutase, discussed in more detail below, contains a lone Type II copper center in each of two subunits of its quaternary structure. 

EPR hyperfine coupling constants for (NO2-C6H5) in CH3CN for various electrolyte cations (0.1 M). 

Spin densities (p) are theoretical quantities, defined as the sum of the squared atomic orbital coefficients in the nonbonding semi-occupied molecular orbital (SOMO) of the radical species (Hiickel theory). For monoradical species, the spin density is connected to the experimental EPR hyperfine coupling constant a through the McConnell equation [38]. This relation provides the opportunity to test the spin density dependence of the D parameter [Eq. (8)] for the cyclopentane-1,3-diyl triplet diradicals 10 by comparing them with the known experimental hyperfine coupling constants (ap) of the corresponding substituted cumyl radicals 14 [39]. The good semiquadratic correlation (Fig. 9) between these two EPR spectral quantities demonstrates unequivocally that the localized triplet 1,3-diradicals 9-11 constitute an excellent model system to assess electronic substituent effects on the spin density in cumyl-type monoradicals. 

Actually, our mixed discrete-continuum model is not limited to the study of UV-vis spectra, but it has been already successfully employed to model solvent effects on several different spectral properties, such as electron paramagnetic resonance (EPR) hyperfine coupling constants, nuclear magnetic resonance (NMR) chemical shifts, and so on [45, 121]. 

Moon S, Patchkovskii S, Salahub DR (2003) QM/MM calculations of EPR hyperfine coupling constants in blue copper proteins. J Mol Struct-Theochem 632 287-295... 

Munzarova M, Kaupp M (1999) A critical validation of density functional and coupled-cluster approaches for the calculation of EPR hyperfine coupling constants in transition metal... 

For example, if the molecular structure of one or both members of the RP is unknown, the hyperfine coupling constants and -factors can be measured from the spectrum and used to characterize them, in a fashion similar to steady-state EPR. Sometimes there is a marked difference in spin relaxation times between two radicals, and this can be measured by collecting the time dependence of the CIDEP signal and fitting it to a kinetic model using modified Bloch equations [64]. 

Barone also introduces two new basis sets, EPR-Il and EPR-llI. These are optimized for the calculation of hyperfine coupling constants by density functional methods. EPR-Il is a double zeta basis set with a single set of polarization functions and an enhanced s part. EPR-III is a triple zeta set including diffuse functions, double d polarization functions and a single set off functions. 

In the following, all isotropic hyperfine coupling constants were calculated using the BLYP functional and the EPR-II basis set. A full geometry optimization was done in all cases. 

Summary of EPR -Values, Fg-Hyperfine Coupling Constants, Isomer Shifts, and Quadrupole Splittings for Some Representative [Fg3S4] Clusters... 

Munzarova, M., Kaupp, M., 1999, A Critical Validation of Density Functional and Coupled Cluster Approaches for the Calculation for EPR Hyperfine Couphng Constants in Transition Metal Complexes , J. Phys. Chem. A, 103, 9966. 

Pietrzyk, P., Piskorz, W., Sojka, Z. et al. (2003) Molecular structure, spin density distribution, and hyperfine coupling constants of the i7l CuNO n adduct in the ZSM-5 zeolite DFT calculations and comparison with EPR data, J. Phys. Chem. B., 107, 6105. 

Table 4 Hyperfine coupling constants obtained from EPR spectra of frozen solution and unpaired electron distribution of phosphaquinoid compounds3...

Since the phenoxyls possess an S = ground state, they have been carefully studied by electron paramagnetic spectroscopy (EPR) and related techniques such as electron nuclear double resonance (ENDOR), and electron spin-echo envelope modulation (ESEEM). These powerful and very sensitive techniques are ideally suited to study the occurrence of tyrosyl radicals in a protein matrix (1, 27-30). Careful analysis of the experimental data (hyperfine coupling constants) provides experimental spin densities at a high level of precision and, in addition, the positions of these tyrosyls relative to other neighboring groups in the protein matrix. 

Figure 25. X-Band EPR spectra of electrochemically generated [Com(L BuMel )(Ph2acac)]2+ (top) and its at the benzylic methylene deuterated analogue (bottom) the hyperfine coupling constants are given in millitesla (mT). [Adapted from (152).]...

The resonance expression relating the magnetic field and energy (frequency) as seen in equation 3.40, A =/iv=gP5ij, has its analog for hyperfine interactions written as equation 3.43, where A is the hyperfine coupling constant in Hz and a is the hyperfine splitting constant—that is, the distance between the split lines in the EPR spectrum ... 

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