Nuclear Fermi contact term

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. 

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. ... 

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. 

This interaction leads to hyperfine splittings in atomic and molecular spectra. One particular term for this interaction is the Fermi contact term, which dominates chemical shifts in nuclear magnetic spectra and splittings in electron paramagnetic spectra ... 

Chemical Shifts in NMR. The first effect is very useful in chemical analysis The nuclear spin transitions are affected by the "hyperfine" I S coupling between electron spin S (for any single electron in the molecule that has density at the nuclear position) and nuclear spin I this is due to the isotropic Fermi contact term ... 

In these expressions the index i runs over electrons and a runs over nuclei. The Fermi contact term describes the magnetic interaction between the electron spin and nuclear spin magnetic moments when there is electron spin density at the nucleus. This condition is imposed by the presence of the Dirac delta function S(rai) in the expression. The dipole-dipole coupling term describes the classical interaction between the magnetic dipole moments associated with the electron and nuclear spins. It depends on the relative orientations of the two moments described in equation (7.145) and falls off as the inverse cube of the separations of the two dipoles. The cartesian form of the dipole-dipole interaction to some extent masks the simplicity of this term. Using the results of spherical tensor algebra from the previous chapter, we can bring this into the open as... 

There are three separate contributions to the total magnetic hyperfine interaction, namely, the Fermi contact term, the orbital hyperfine term, and the electron spin-nuclear spin dipolar term ... 

Tables XXXIII to XXXVI). One reason for interest in 7( C— H) is Eq. (11), which is based on the Fermi contact term, Eq. (7) and has been used to calculate the s characters of carbon orbitals in the C—H and C—X bonds 120,206), as described earlier (Section V, A). This approach has been severely criticized 11, 97). The equation was modified to allow for the effective nuclear charge eff [Eq- (14)].

Bally and Rablen ° followed up their important study of the appropriate basis sets and density functional needed to compute NMR chemical shifts with an examination of procedures for computing proton-proton coupling constants." They performed a comparison of 165 experimental with computed proton-proton coupling constants from 66 small, rigid molecules. They tested a variety of basis sets and functionals, along with questioning whether all four components that lead to nuclear-nuclear spin coupling constants are required, or if just the Fermi contact term would suffice. 

The first term is the interaction of the nuclear magnetic moment (spin I) with the current loops made by the orbiting electrons with angular momentum I. The second term is the dipole-dipole interaction between the nuclear (I) and electronic (st) spin magnetic moments. The last term is the Fermi contact term which describes the interaction of the nuclear... 

A few of the most studied physical properties in the CHA are the Fermi contact term A, the nuclear magnetic shielding a, the pressure P and the polarizability a. In the case of impenetrable confinement, the first three quantities grow boundlessly as r —> 0, while the polarizability approaches zero. By contrast, when soft (penetrable) boxes are involved A, a and P become vanishingly small as r —> 0, while the polarizability increases very rapidly and no upper bound is apparently found. 

As mentioned above there are four main contributions to the nuclear spin-spin coupling constants the Fermi contact (FC), the paramagnetic spin-orbit (PSO), the spin-dipolar (SD) and the diamagnetic spin-orbit (DSO) contributions. The Fermi contact term is usually the most important of these and also the most sensitive to geometry changes [8]. The Fermi contact contribution arises from the interactions between the terms containing S(riM) and < (riN) in the operators Hon for nuclei N and M (see Eqn. (12)). 

We only briefly mention that a similar modification, i.e., a change from a Dirac delta distribution to an extended distribution, would be required for the spin-dependent electron-nucleus contact term, known as Fermi contact term, if the usual point-like nuclear magnetization distribution (the pointlike nuclear magnetic dipole approximation) is replaced by an extended nuclear magnetization distribution. 

For a vanishing electron-nuclear distance we would expect an appearance of the Fermi contact term. However, due to the presence of k0, such a term disappears... 

The terms 7 2, 3, H4 (crucial for the NMR experiment) correspond to the magnetic dipole-dipole interaction involving nuclear spins (the term H5 of the Breit Hamiltonian) the classical electronic spin - nuclear spin interaction (7 2) plus the corresponding Fermi contact term (Tia) and the classical interaction of the nuclear spin magnetic dipoles... 

Nuclear spin coupling takes place through the induction mechanism in the chemical bond (cf. Fig. 12.14). Of key importance for this induction is a high electron density at the position of the nuclei (the so-called Fermi contact term see Fig. 12.14). 

The magnetic hyperfine field is composed of three contributions the Fermi contact, the dipolar, and the orbital contributions. The Fermi contact term, which in most iron-containing materials is dominant, results from the interaction between the nuclear magnetic moment and the unpaired electron spin density at the nucleus. The dipolar and orbital terms represent the dipolar interaction between the nuclear magnetic moment and the electronic spin and orbital moments of their... 

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