Magnetic hyperfine coupling

The leading term in T nuc is usually the magnetic hyperfine coupling IAS which connects the electron spin S and the nuclear spin 1. It is parameterized by the hyperfine coupling tensor A. The /-dependent nuclear Zeeman interaction and the electric quadrupole interaction are included as 2nd and 3rd terms. Their detailed description for Fe is provided in Sects. 4.3 and 4.4. The total spin Hamiltonian for electronic and nuclear spin variables is then ... 

The different magnetic hyperfine coupling of the spins a and b in this example as heuristically derived for the coupled presentation from above can also be expressed by using the hyperfine coupling constants... 

It is well-known that the hyperfine interaction for a given nucleus A consists of three contributions (a) the isotropic Fermi contact term, (b) the spin-dipolar interaction, and (c) the spin-orbit correction. One finds for the three parts of the magnetic hyperfine coupling (HFC), the following expressions [3, 9] ... 

Conversion of magnetic hyperfine coupling constants A into internal fields for Fe When the nuclear spin is decoupled from the electronic spin by application of an external field, the hyperfine coupling, according to (4.76), is defined as... 

In addition, the93 Nb magnetic hyperfine coupling was large enough to be readily observed, even in the electronic spectrum. It was fitted to the normal Frosch and Foley Hamiltonian for a L state,... 

D. M. Chipman, Magnetic Hyperfine Coupling Constants in Free Radicals. In Quantum Mechanical Electronic Structure Calculations with Chemical Accuracy... 

The magnetic hyperfine coupling constant. A, is in principle measurable in both ESR and Mossbauer effect, but will be observed only in the case of 57Fe which has a nuclear magnetic moment. Since 57Fe is only 2% naturally abundant the ESR spectrum with unenriched samples... 

The magnetic hyperfine coupling is now chosen to represent the first-... 

In equation (61), /ly is the magnetic dipole moment of the nucleus V, is the position of the electron relative to nucleus v, and k denotes the three Cartesian components. The expression for the magnetic hyperfine coupling then becomes... 

Charge distributions were derived from ab initio GVB wave functions for the lowest two states X and a Bi. The positive charge Is essentially located at the heavy atom (contrary to the NHJ Ion) [10]. Atomic charges, the dipole moment, and the magnetic hyperfine coupling constants were also calculated with an MO-SCF method (for a ground state, however) [17]. 

The electric field gradients at P and H, the anisotropic (dipolar) magnetic hyperfine coupling... 

For polyatomic radicals in the gaseous phase the above spin-Hamiltonian does not apply. Here, the presence of unquenchend orbital and rotational angular momenta necessitates the introduction of several magnetic hyperfine coupling constants to describe the interaction between one nucleus and the free electron. These are defined and explained in the introduction to the tables on inorganic radicals. 

The presence of unquenched orbital and rotational components of angular momentum in a free radical necessitates the introduction of several additional terms into the Hamiltonian for the energy of the molecule in a magnetic field. In the case of diatomic free radicals, Frosch and Foley have shown that four magnetic hyperfine coupling constants a, b, c and d are needed to describe the interaction between a nucleus and the electron, where... 

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