Electron-nuclear hyperfine interactions

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)... 

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... 

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 -... 

The work which is reviewed here provides accurate structural data from micro-wave and radiofrequency spectroscopy of relatively small molecule, hydrogen bonded complexes. Its role has been to provide information concerning the stereochemistry and electronic properties — electric dipole moments and nuclear hyperfine interactions — characteristic of hydrogen bonds. The experiments are done on gas phase samples, often in molecular beams, which eliminates environmental perturbations of the hydrogen bonds. In addition, the small molecules used are amenable to ab initio calculations 7 9) and thus the results are extremely useful as criteria for the accuracy of these calculations. Finally, the results are useful to construct models of more complex systems in chemistry and biology involving hydrogen bonds 4). 

In a classic paper, Frosch and Foley [117] derived an elFective Hamiltonian to describe the magnetic nuclear hyperfine interactions of a diatomic molecule in an open shell electronic state. Their Hamiltonian was expressed in the following form ... 

We have chosen to use the hyperfine-coupled representation, where for 12CH, F is equal to J 1 /2. An appropriate basis set is therefore t], A N, A S, J, /, F), with MF also important when discussing Zeeman effects. As usual the effective zero-field Hamiltonian will be, at the least, a sum of terms representing the spin-orbit coupling, rigid body rotation, electron spin-rotation coupling and nuclear hyperfine interactions, i.e. 

Between the A and B regions, a radioffequency field was applied to induce fine-structure transitions within the v" = 1 level of the ground electronic state, split by the nuclear hyperfine interaction. The selection rules for these transitions, which ranged in frequency from 360 to 7700 MHz, were A J = 1, AF = 0, 1. They were detected through resonant changes in the fluorescence intensity an example of a radioffequency double resonance line is shown in figure 11.53. The observed spectrum involved N values from 1 to 27. 

The g-value is used to characterize the position of a resonance. It is a measure of the local magnetic field experienced by the electron. The g-value is a unique property of the molecule as a whole, and is independent of any electron-nuclear hyperfine interactions that may be present. The g-value is defined as... 

Nuclei of ligands in paramagnetic complexes are coupled to the electronic spin of the central ion by the electron-nuclear hyperfine interaction. As a result of this interaction,... 

If a molecule contains an atom with a nucleus having nuclear spin I > 1/2 (e.g., N or Cl), the observed micro-wave spectrum will be more complex due to the electron-nuclear hyperfine interaction as well as nuclear qua-drupole interactions (23,24). For each of the three electron-spin directions, there are a number of different nuclear spin quantization directions. For nitrogen,... 

The nuclear hyperfine interaction splits the paramagnetic states of an electron when it is close to a nucleus with a magnetic moment. For a random orientation of spins and nuclei, the tensor quantities in Eq. (4.11) are replaced by scalar distributions, and the resonance magnetic field is shifted from the Zeeman field // by... 

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