Hyperfine coupling coefficients

When several magnetically equivalent nuclei are present in a radical, some of the multiplet lines appear at exactly the same field position, i.e., are degenerate , resulting in variations in component intensity. Equivalent spin-1/2 nuclei such as 1H, 19F, or 31P result in multiplets with intensities given by binomial coefficients (1 1 for one nucleus, 1 2 1 for two, 1 3 3 1 for three, 1 4 6 4 1 for four, etc.). One of the first aromatic organic radical anions studied by ESR spectroscopy was the naphthalene anion radical,1 the spectrum of which is shown in Figure 2.2. The spectrum consists of 25 lines, a quintet of quintets as expected for hyperfine coupling to two sets of four equivalent protons. 

Coefficients relating the hyperfine coupling of an Si or S2 spin system in a monomer to that in a coupled system, for each 5,- spin level [3]... 

The hyperfine coupling constants of protons attached to a re-center can be determined by EPR/ENDOR spectroscopic measurements [15, 16] these coupling constants are proportional to the local spin densities at the re-centers as predicted by the corresponding atomic orbital coefficients of the... 

Here, the spin-spin interaction between an electron spin and a nuclear spin can be represented by the isotropic term (AS I ) when the radical rotates very fast in solution. This term is called the hyperfine coupling (HFC) and the coefficient (A) the (isotropic) HFC constant. When it is fixed in a crystal or solid matrix, however, the interaction becomes anisotropic, but the latter case is not considered in this section. 

To date the mercurated arene radical cation is known for biphenylene [87], ace-naphthene, pyracene, hexahydropyrene, triptycene, p-terphenyl, tetramethylnaph-thopyran, anthracene, dibenzodioxin [89], and 4-tert-butylanisole [88]. In certain cases multiple mercuration is observed, for example in case of diphenylene [87] and dibenzodioxin [89]. Mercuration causes a decrease in -value and always occurs at the site where the local coefficient of the Huckel HOMO of the hydrocarbon is greatest, and there is a constant ratio of about 20.6 between the hyperfine couplings by the Hg [l, abundance 16.84 %) which has been introduced, and by the proton which has been displaced [89]. EPR spectroscopic evidence is reported for 8, 9, 10, 11, 12, 13, 14, 15 and 16 as new examples of recently recognized alternative mechanism of arene mercuration in which collapse of ArH +Hg(TFA)2 radical ion pair leads to arylmercury trifluoroacetate ArHg(TFA) + [90]. 

Blue copper proteins have a single Cu atom at the active site, and three characteristic properties (1) an intense blue color at —600 nm, with absorption coefficients of 2000-6000 M cm arising from S(Cys) ()u(II) charge transfer (b) an unusually narrow hyperfine coupling (A values of 0.0035-0.0063 cm ) in the EPR spectrum of the Cu(II) protein due to asymmetry at the metal and (3) high reduction potentials (range 184-680 mV) as compared to the aqua Cu(II/I)... 

Fig. 3-15 ESR of the benzyl radical the numbers on 67 are the hyperfine couplings to the corresponding nucleus in gauss,9 and the numbers on 68 are the coefficients of i//4 derived from these numbers using the McConnell equation (p. 22) (ignoring the negative spin density)...

This ability of ESR to quantify hyperconjugation showed that the magnitude of the effect is subject to symmetry control, and can be enhanced or forbidden when the CH group is bonded to both ends of a conjugated system which carries the unpaired electron, in what is known as the Whiffen effect (3-5).10-11 The hyperfine coupling is now given by the equation 3-29, where ca and ca are the coefficients at the two flanking ends of the n system. 

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. 

Anisotropic Hyperfine Interaction. The anisotropic component of the hyperfine coupling has two contributions a local anisotropy owing to spin density in p- or type orbitals on the atom of observation, and nonlocal dipolar coupling with spin on other atoms. The first type of interaction is proportioned to the orbital coefficient (squared) of the pid orbiteds. To a first approximation the second term can be considered as a classic point dipolar interaction between the nucleus and the electron spin on a nearby atom. This depends on the total electron spin density at the neighbor (p ), the distance between the spins (r,2), and the orientation of the vector between them with respect to the external magnetic field (denoted by angle 0). In the point dipole approximation,... 

The solid effect (SE) is a DNP mechanism which requires states mixing caused by the nonsecular component KpsE of the hyperfine coupling [16]. The pseudosecular term /i psE contains the form EzN and EzN (E Electron spin operator, N Nucleus spin operator), which leads to a mixing of the states of the system. In SE polarization, the new mix states are generated from the original states with a coefficient p, which can be calculated by the first order perturbation theory and is given by... 

---