Fermi-contact term

The spin Hamiltonian operates only on spin wavefunctions, and all details of the electronic wavefunction are absorbed into the coupling constant a. If we treat the Fermi contact term as a perturbation on the wavefunction theR use of standard perturbation theory gives a first-order energy... 

The only term surviving the Bom-Oppenheimer approximation is the direct spin-spin coupling, as all the others involve nuclear masses. Furthermore, there is no Fermi-contact term since nuclei cannot occupy the same position. Note that the direct spin-spin coupling is independent of the electronic wave function, it depends only on the molecular geometry. 

The complete Hamiltonian of the molecular system can be wrihen as H +H or H =H +H for the commutator being linear, where is the Hamiltonian corresponding to the spin contribution(s) such as, Fermi contact term, dipolar term, spin-orbit coupling, etc. (5). As a result, H ° would correspond to the spin free part of the Hamiltonian, which is usually employed in the electron propagator implementation. Accordingly, the k -th pole associated with the complete Hamiltonian H is , so that El is the A -th pole of the electron propagator for the spin free Hamiltonian H . 

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] ... 

In contrast to the EFG analyzed before, aU of these expectations from ligand field theory are largely confirmed by the DFT calculations. Despite the fact that the S = 2 state has a smaller prefactor for the isotropic Fermi contact term, the core polarization in the presence of four unpaired electrons is much larger and, consequently, the isotropic Fe-HFC is predicted to be roughly a factor of two larger in magnitude for as compared to 2g. Similarly, the dipolar MFCs are comparable for both spin states, which must be due to a considerable contribution from anisotropic covalency in the 5 = 2 species which partially compensates for the smaller prefactor. 

The interpretation of the results was hindered to some extent by the inability to observe more than the gz absorption, except in the Kr matrix, but it was found that although the Fermi contact term, k0, showed some lattice dependence, the main feature of the results was that whilst A ranged from 286 cm-1 in Ne to 668 cm-1 in Kr, the vibronic overlap term varied only between 0.30 and 0.25, thus bearing out the authors predictions concerning the origin of the static distortion, A. 

The correlation between the X-ray crystallographic data of the W—CN bond lengths and the first-order coupling constants between the 183W and 13C in the equatorial cyano ligands, as predicted by the Fermi-contact term (51), is fairly good (see Table III). This illustrates the increase in cis W—CN bond length induced by increased donor... 

Fermi contact interaction. The coupling constant of the Fermi contact term for the nucleus N has the form127 ... 

The one-bond couplings, which are determined almost exclusively by the Fermi contact term, have been treated in some detail, and they have been used to good effect to reveal details of the structural situation particularly at the 15N centre, as discussed in Section V. 

Values of one-bond coupling ( N H) are the largest in magnitude of all 15N couplings to the proton and are generally regarded as being dominated by the Fermi contact term. 

The electron-nucleus interaction, or Fermi contact term, arises from ... 

This empiricism (which concerns the concept of trans-influence) [93] is derived from theory and the Fermi contact term. Since the s-component of the M-L bond determines the magnitude of ij(M,L), bonding considerations which decrease the s-component, e. g., a relatively strong a-bond in the trans-position, decrease j(M,L). In Wilkinson s catalyst, RhCl(PPh3)3, (and the p-tolyl analog) the two j( ° Rh,3ip) values are quite different 189 Hz (P trans to Cl) and 142 Hz (P trans to P) [94]. The larger i [-value arises from the P-atom trans to the weaker donor. 

The coupling interaction between directly bonded N—H is generally dominated by the Fermi contact term, as evidenced by the dependence of 7( N—H) on the amount of s character in the bond. Table 15 lists some illustrative N—H coupling constants, determined under comparable solvent conditions, as a function of the s character in the bonding orbitals. 

It was noted that for 78b and 79b, 7hf and 7cf are dependent on the molecular conformation, but this is not the case with 7nf. which is independent of the conformation. It is well known that the internuclear couplings are electron coupled interactions for which there are three possible mechanisms (1) the nuclear moments interact with the electronic currents produced by the orbiting electrons (2) there is a dipolar interaction between the nuclear and electronic magnetic moments (3) there is an interaction between the nuclear moments and the electronic spins in i-orbitals, the so-called Fermi contact term. ... 

For all couplings involving hydrogen the Fermi contact term is dominant, and the other terms may be neglected. Hence this term is dependent on the molecular conformation. Recent studies using ab initio and DFT techniques to calculate the various... 

This introduces, besides zN(s) (the direct Fermi contact term from the... 

This term is called the Fermi contact term. That part of the electron-nucleus magnetic-dipole interaction represented by (8.104) depends on the angular coordinates of the electron and is therefore anisotropic in contrast, the Fermi contact energy (8.108) is isotropic. The contact term plays an important role in the electron-coupled nuclear spin-spin interactions seen in the NMR spectra of liquids. 

The Fermi contact term is often stated to be a purely quantum-mechanical interaction, having no classical analog. This is not so. The preceding derivation shows the contact interaction to be readily understandable within the framework of classical electromagnetism. 

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