Hyperfine coupling Fermi contact term

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] ... 

This hyperfine coupling is of two kinds An isotropic interaction arises from the possibility that the electronic wave-function, x , be non-zero at the nucleus, N. This is the Fermi contact term and the hyperfine coupling constant is given by ... 

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 ... 

The contact interaction is also referred to as the Fermi contact term. In a given atomic orbital basis -0, the isotropic hyperfine coupling constant (hfcc) for a particular nucleus N,, is given by the expression,... 

The occurrence of hyperfine coupling for a particular isotope indicates non-zero spin density at that nucleus in accordance with the Fermi contact term (which includes the electron wave function evaluated at the nucleus) [1]. The analysis in terms of spin density then requires at least a comparison with the (calculated [5]) isotropic hyperfine splitting constant ao, ideally, results from increasingly available open-shell quantum-chemical calculation procedures [64] are employed. 

Consequently, although the conclusion that the spin density is located essentially in the 7r-framework of the ring is in accordance with the established experimental data, it is necessary to reserve final judgement upon the subject until values of the anisotropic susceptibilities are known experimentally. Similarly, the conclusion that the extent of covalent interaction in U(Me4Cot)2 is somewhat greater than in Np(Me4Cot)2 is not unequivocably established since it depends upon the approximate identity of the hyperfine coupling constants in the two species (as deduced from the calculated Fermi contact terms), which contain respectively two and three unpaired electrons. 

The hyperfine coupling constants (by the reduction of the Fermi contact term) substantiate this view. 

The nuclear spin-electron spin interactions may be of either sign and then determine the sign of the spin coupling constant. In order to assess the sign of the Fermi contact term we follow the discussion of Jameson and Gutowsky [215] and consider the interactions to be analogous to that between an electron and the nucleus in atoms or ions with unpaired electrons. As in the case of these atomic hyperfine interactions there are three important types of contributions to the spin density at the nucleus from bonding electrons ... 

The spin-density p") obtained in KSCED calculations is used to derive the hyperfine interaction tensor employing the conventional formulas for the isotropic coupling constant (Fermi contact term, Aiao) and the magnetic dipolar tensor (Ay) ... 

One of the unique spectroscopic features of flie T1 site, as mentioned above, is the small compared to that of the normal Cu(II) centers. There are three contributions to account for the metal hyperfine coupling, which are flie Fermi contact (. f), the spin dipolar (.4s), and the orbital dipolar (4l) terms. The Fermi contact term is isotropic (A = 1) and associated wifli unpaired electron spin density at flie nucleus. In a Cu(II) center, this contribution involves the unpaired 3d electron spin polarizing the inner Is, 2s, and 3s core electron pairs (mostly 2s) to produce a net negative spin density at the nucleus. The spin dipolar term is anisotropic (A = -1/24 ) and involves the electron spin, averaged over flie shape of its 3d orbital... 

In addition to the isomer shift and the quadrupole splitting, it is possible to obtain the hyperfine coupling tensor from a Mossbauer experiment if a magnetic field is applied. This additional parameter describes the interactions between impaired electrons and the nuclear magnetic moment. Three terms contribute to the hyperfine coupling (i) the isotropic Fermi contact, (ii) the spin—dipole... 

The hyperfine coupling tensor (A) describes the interaction between the electronic spin density and the nuclear magnetic momentum, and can be split into two terms. The first term, usually referred to as Fermi contact interaction, is an isotropic contribution also known as hyperfine coupling constant (HCC), and is related to the spin density at the corresponding nucleus n by [25]... 

The hyperfine coupling frequency in the hydrogen ground state is given to the leading term by the Fermi contact interaction, yielding... 

Freund, Herbst, Mariella and Klemperer [112] expressed their magnetic hyperfine constants in the form originally given by Frosch and Foley [117]. As discussed elsewhere in this book, particularly in chapters 9, 10 and 11, we prefer to separate the different physical interactions, particularly the Fermi contact and dipolar interactions, in our effective Hamiltonian. This separation is usually made by other authors even when the effective Hamiltonian is expressed in terms of Frosch and Foley constants, because it is the natural route if the molecular physics of a problem is to be understood. Nevertheless since so many authors, particularly of the earlier papers, use the magnetic hyperfine theory presented by Frosch and Foley, we present in appendix 8.5 a detailed comparison of their effective Hamiltonian with that adopted in this book. The merit of the Frosch and Foley parameters is that they form the linear combination of parameters which is best determined (i.e. with least correlation) for a molecule which conforms to Hund s case (a) coupling. The values of the constants determined experimentally from the 7 LiO spectrum were therefore, in our notation (in MHz) ... 

As we have shown in Appendix 8.5, and elsewhere, to is the axial component of the dipolar interaction obtained from the fourth term in equation (11.2). The large value of the Fermi contact constant is consistent with a model in which the unpaired electron occupies a a-type molecular orbital which has 45% N atom, v character. Radford produced convincing arguments to show that the model is also consistent with the small dipolar hyperfine constant, and also the electric quadrupole coupling constant. 

Some confusion has arisen because of the result for HS radicals in the gas-phase. The proton hyperfine coupling of about 5 gauss (67) has been taken by both groups to be the Fermi contact value, whereas, in fact, it does not relate directly to the contact term. 

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