The Fermi contact coupling

Since the s orbitals do not have orbital magnetic moment, g — ge — 2.0023. A is an eneigy, which in SI units is expressed in joule. Sometimes it is convenient to have it expressed in frequency units, i.e. in hertz or in radians per second, and then we have to divide A by h or by h (ft = h/2n). In magnetic resonance there often is a factor 2jt which complicates life. The frequency which we refer to is the angular frequency or the Larmor precession frequency. Such frequency co is 

The magnetic nucleus—unpaired electron interaction the hyperfine shift 

In order to express the energy in wavenumbers, we should remember that E = hc/k, and then E is proportional to the inverse of a length. 

In quantum mechanical terms, the Hamiltonian for the contact interaction is 

M/)- In the high field approximation (ge/xsBo -4), which always holds for high field NMR experiments, the contact contribution to the chemical shift is (Appendix III) [1] 

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The Fermi Contact Coupling Mechanism Gauge-Invariant Atomic Orbitals (GIAOs) (4<1))... 

There are no simple rules, but usually the most important contribution to Jab comes from the Fermi contact term (7jg), the next most important is paramagnetic spin-orbit term J, other terms, including the mixed contributions 7 , are of little importance. Let us consider the Fermi contact coupling mechanism between two protons through a single bond (the coupling constant Jab denoted qs Jhh)- The proton and the electron close to it prefer to have opposite spins. Fig. 12.17. Then the other electron of the bond (being closer to the other nucleus) shows the other nucleus the spin of first nucleus, so the second nucleus prefers to have the opposite... 

The Fermi-contact coupling density, Eq. (7.57), for vicinal protons in the eclipsed and staggered conformations of ethane is shown in Fig. 7.45. Analogous... 

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 and operators determine the isotropic and anisotropic parts of the hyperfine coupling constant (eq. (10.11)), respectively. The latter contribution averages out for rapidly tumbling molecules (solution or gas phase), and the (isotropic) hyperfine coupling constant is therefore determined by the Fermi-Contact contribution, i.e. the electron density at the nucleus. 

Evaluation of trends in /pp coupling constants in solid-state 31P NMR spectra of P-phospholyl-NHPs allowed one to establish an inverse relation between the magnitude ofM and P-P bond distances [45], The distance dependence of. /pp is in line with the dominance of the Fermi contact contribution, and is presumably also of importance for other diphosphine derivatives. At the same time, large deviations between lJvv in solid-state and solution spectra of individual compounds and a temperature dependence of lJ77 in solution were also detected (Fig. 1) both effects... 

Since 3dyz/4s admixture is symmetry-forbidden for these radicals, the Fermi contact contribution to the isotropic coupling, As, must be entirely from spin polarization,... 

From the isotropic coupling constant one may calculate C12, the fractional occupancy of the nitrogen s orbital, which is equal to AUo/Ao. The term Ao is the Fermi contact interaction for an unpaired electron in a pure nitrogen 2s orbital. For NO2 the value of ci2 = 56.5/550 = 0.103. The fraction of the unpaired electron associated with the N nucleus is then... 

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 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. 

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... 

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