Nuclear hyperfine interaction

The origin of postulate (iii) lies in the electron-nuclear hyperfine interaction. If the energy separation between the T and S states of the radical pair is of the same order of magnitude as then the hyperfine interaction can represent a driving force for T-S mixing and this depends on the nuclear spin state. Only a relatively small preference for one spin-state compared with the other is necessary in the T-S mixing process in order to overcome the Boltzmann polarization (1 in 10 ). The effect is to make n.m.r. spectroscopy a much more sensitive technique in systems displaying CIDNP than in systems where only Boltzmann distributions of nuclear spin states obtain. More detailed consideration of postulate (iii) is deferred until Section II,D. 

Here and H describe radicals A and B of the radical pair and He the interaction of their electrons. The other terms in equation (15) are H g, the spin orbit coupling term, H g and Hgj, representing the interaction of the externally applied magnetic field with the electron spin and nuclear spin, respectively Hgg is the electron spin-spin interaction and Hgi the electron-nuclear hyperfine interaction. 

OIDEP usually results from Tq-S mixing in radical pairs, although T i-S mixing has also been considered (Atkins et al., 1971, 1973). The time development of electron-spin state populations is a function of the electron Zeeman interaction, the electron-nuclear hyperfine interaction, the electron-electron exchange interaction, together with spin-rotational and orientation dependent terms (Pedersen and Freed, 1972). Electron spin lattice relaxation Ti = 10 to 10 sec) is normally slower than the polarizing process. 

In Equation (6) ge is the electronic g tensor, yn is the nuclear g factor (dimensionless), fln is the nuclear magneton in erg/G (or J/T), In is the nuclear spin angular momentum operator, An is the electron-nuclear hyperfine tensor in Hz, and Qn (non-zero for fn > 1) is the quadrupole interaction tensor in Hz. The first two terms in the Hamiltonian are the electron and nuclear Zeeman interactions, respectively the third term is the electron-nuclear hyperfine interaction and the last term is the nuclear quadrupole interaction. For the usual systems with an odd number of unpaired electrons, the transition moment is finite only for a magnetic dipole moment operator oriented perpendicular to the static magnetic field direction. In an ESR resonator in which the sample is placed, the microwave magnetic field must be therefore perpendicular to the external static magnetic field. The selection rules for the electron spin transitions are given in Equation (7)... 

In eqn (4.1), g and A-t are 3x3 matrices representing the anisotropic Zeeman and nuclear hyperfine interactions. In general, a coordinate system can be found - the g-matrix principal axes - in which g is diagonal. If g and A, are diagonal in the same coordinate system, we say that their principal axes are coincident. 

Consider for example the simplest possible system consisting of the muon, an electron, and a single spin nucleus labelled i = n. Take the muon and nuclear hyperfine interactions to be istoropic. The level crossing of interest occurs near the field... 

Electron nuclear double resonance (ENDOR) and electron spin-echo envelope modulation (ESEEM) are two of a variety of pulsed EPR techniques that are used to study paramagnetic metal centers in metalloenzymes. The techniques are discussed in Chapter 4 of reference la and will not be discussed in any detail here. The techniques can define electron-nuclear hyperfine interactions too small to be resolved within the natural width of the EPR line. For instance, as a paramagnetic transition metal center in a metalloprotein interacts with magnetic nuclei such as H, H, P, or these... 

The characteristic shape of the ESR spectrum of the trapped hole in the different systems is not caused by nuclear hyperfine interaction since Cl35 37 (I = 3/2), S32 (I = 0) and P31 (I = 1/2) have different nuclear spins, yet the spectra are almost identical in all the three cases (Figure 8). Also, photobleached specimens of H3PO4 in H20 and D3PO4 in D20 exhibit identical ESR spectra, and hence there is no hyperfine interaction with the H or D nuclei. The shapes can be attributed to randomly oriented species with g-factor anisotropy. 

Assuming four water molecules to be coordinated to the 0 ions, eight protons can interact with the unpaired electron of T . Nuclear hyperfine interaction with eight equivalent protons should result in nine hyperfine components with an intensity distribution of 1 8 28 56 70 -... 

There have been two additional experiments which verified this basic picture of the nuclear hyperfine interaction in hemins. Johnson (78) increased the spin-lattice relaxation time by performing the Mossbauer experiment under field and temperature conditions which provide a large value of H/T. At 1.6 °K and in an applied field of 30 kG, a magnetic hyperfine interaction corresponding to that expected for high spin Fe(III) and for the g-values is measured experimentally. Recently, Lang et al. have found that a portion of hemin chloride dissolved in tetrahydro-furan at 1 mM concentration displays a hyperfine interaction at 4 °K in zero applied magnetic field. Their conclusion is that a portion of the hemin is present in a monomeric form in this solvent, a situation which is not apparent to any extent in water, acetic acid, chloroform, or dimethyl sulfoxide (77) at any concentrations used. 

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