Magnetic electron-nuclear

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. 

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)... 

The physical interpretation of the anisotropic principal values is based on the classical magnetic dipole interaction between the electron and nuclear spin angular momenta, and depends on the electron-nuclear distance, rn. Assuming that both spins can be described as point dipoles, the interaction energy is given by Equation (8), where 6 is the angle between the external magnetic field and the direction of rn. 

In Chapter 2, ENDOR (electron-nuclear double resonance) was briefly described. To perform an ENDOR experiment it is necessary to apply both a radiofrequency and a microwave frequency, effectively performing simultaneous NMR and ESR, respectively, on the sample. The experiment is performed at a fixed magnetic field, with the ESR saturating frequency centered on a... 

Solutions of alkali metals in liquid ammonia have been studied by many techniques. These include electrical conductivity, magnetic susceptibility, nuclear magnetic resonance (NMR), volume expansion, spectroscopy (visible and infrared), and other techniques. The data obtained indicate that the metals dissolve with ionization and that the metal ion and electron are solvated. Several simultaneous equilibria have been postulated to explain the unique properties of the solutions. These are generally represented as follows ... 

Electron-nuclear double resonance (ENDOR) Nuclear magnetic resonance (NMR)... 

B. Nuclear Magnetic Resonance — nuclear-electronic interactions Molecular conformations, solute-solvent interactions, chemical reactions... 

Electron-nuclear double resonance (ENDOR) spectroscopy A magnetic resonance spectroscopic technique for the determination of hyperfine interactions between electrons and nuclear spins. There are two principal techniques. In continuous-wave ENDOR the intensity of an electron paramagnetic resonance signal, partially saturated with microwave power, is measured as radio frequency is applied. In pulsed ENDOR the radio frequency is applied as pulses and the EPR signal is detected as a spin-echo. In each case an enhancement of the EPR signal is observed when the radiofrequency is in resonance with the coupled nuclei. 

The new techniques of phosphorescence-microwave multiplet resonance spectroscopy with optical detection have been reviewed by El-Sayed and Kwiram Such exciting experiments as the optical detection on electron-nuclear double resonance (ENDOR) and of electron-electron double resonance (EEDOR) in zero magnetic field have been achieved, and it is certain that much detailed knowledge concerning the phosphorescent states will evolve from this 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... 

Spectroscopic studies on the Fe-Mo protein by EPR and Mossbauer spectroscopy have shown six iron atoms each in a distinctive magnetic environment coupled to an overall S=3/2 spin system (6,7,8) and electron nuclear double resonance (ENDOR) studies suggest one molybdenum per spin system (8). The 5 Fe signals (five or six doublets) observed in the ENDOR spectra (8) indicate a rather asymmetric structure for the Fe/Mo/S aggregate in which the iron atoms roughly can be grouped into two sets of trios, each set having very similar hyperfme parameters. 

For an elementary proton r )p = 0, g = 2, and only the first term in the square brackets survives. This term leads to the well known local Darwin term in the electron-nuclear effective potential (see, e.g., [1]) and generates the contribution proportional to the factor Sio in (3.4). As was pointed out in [2], in addition to this correction, there exists an additional contribution of the same order produced by the term proportional to the anomalous magnetic moment in (6.6). 

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