Contact term

Gas-Solids Contacting Terms used in this section to describe the method by which gas may contact a bed of solids are the following ... 

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 113Cd Ti values estimated for the various peaks varied from 10 to 50 ms and obeyed the qualitative dependence upon 1/R6 (R = Mn-Cd distance) of the dipolar relaxation mechanism expected to be operative. The broad line widths were also shown to have significant contributions from the T2 relaxation induced by Mn++, with both dipolar and contact terms contributing. The 113Cd shifts of the peaks assigned to different shells were measured as a function of temperature, and observed to follow a linear 1/T dependence characteristic of the Curie-Weiss law, with slopes proportional to the transferred hyperfine interaction constant 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 ... 

Following [31], we distinguish between temporal and spatial derivatives. Chiral loops are suppressed by powers of p/AirIF, and higher-order contact terms are suppressed by p/A where p is the momentum. Thus, chiral loops are parametrically small compared to contact terms when the chemical potential is large. 

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. 

In summary, VH F demonstrates the same pattern of solvent dependence as does 2/h h. However, all the subtleties seem to be enhanced. Usually 2/H F decreases in solvents of higher dielectric strength, but an appropriate dipole orientation with respect to the H—C—F group can lead to the opposite result as is observed in vinyl fluoride. This situation is perhaps most likely to occur in mono-fluoro compounds where the fluorine is the principal contributor to the molecular dipole. In either case the electric field effect as postulated with the Pople expression for the contact term produces the correct prediction. 

Since the geminal F—F coupling constant is positive and the dipole moment is oriented towards the fluorines the observed increase in 2/F F is expected from the simple contact term variation postulated earlier for 2/H H and 2/h.f The situation is entirely analogous to that of VH-f n vinyl fluoride. 

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

For nuclei other than protons the dipolar term is smaller, due to the smaller value of yjv, a.nd the contact term may be larger, in case of directly coordinated nuclei. Therefore, contact relaxation may more often be the dominant contribution to nuclear relaxation. 

---