Hyperfine contact coupling

These two coupling mechanisms have effects both on the chemical shifts and on the relaxation rates. The contact contribution to the shift is proportional to the electron spin multiplicity and to the hyperfine contact coupling constant (McConnell and Chesnut, 1958),... 

The observed hyperfine shifts could come from contact coupling or pseudocontact interactions between the electrons and the protons. Contact shifts arise when a finite amount of unpaired electron density is transferred to the observed protons. The contact shifts of the proton resonances for isotropic systems are given by Bloembergen s (9) expression... 

The spin densities on the ring carbon atoms next to the four ring methyl groups and the four mesoprotons were derived with the assumption that the observed hyperfine shifts came entirely from contact coupling. Eq. (4) and (11) were used, with QH = —6.3 107 cps, and QCH3 = 3.0 107 cps. g is given in percent of one electron. For meso-H g may be much smaller than the upper limits given here. 

Fig. 3.8. Energy levels, transition frequencies and transition probabilities per unit time (Wo. W and W2) in a magnetically coupled I-S system ((A) dipolar coupling (B) contact coupling). A is the contact hyperfine coupling constant The order of the levels is for g, < 0.

The coupling of the unpaired electrons with the nucleus being observed generally results in a shift in resonance frequency that is referred to as a hyperfine isotropic or simply isotropic shift. This shift is usually dissected into two principal components. One, the hyperfine contact, Fermi contact or contact shift derives from a transfer of spin density from the unpaired electrons to the nucleus being observed. The other, the dipolar or pseudocontact shift, derives from a classical dipole-dipole interaction between the electron magnetic moment and the nuclear magnetic moment and is geometry dependent. 

The Fermi contact, or isotropic contact or isotropic hyperfine contact mechanism applies when there is finite unpaired electron density at the nucleus. This either adds to, or subtracts from the external field, depending upon the sign and magnitude of (the hyperfine coupling constant). 

ENDOR measurements of isotropic hyperfine couplings are extensively used to obtain the spin density with the aim to clarify the electronic and geometric structures of paramagnetic species.The isotropic or contact hyperfine (hfc) coupling, atso, is proportional to the unpaired electron density p(N) at a nucleus (N) with 1 0 [17a], see [17b] for a nearly classical treatment. 

The isotropic or Fermi contact hyperfine (hf) coupling constant ap was first obtained for both nuclei ip and from ESR spectra of ground-state PHg isolated at low temperature in rare-gas matrices (see the second table below). Anisotropic or dipolar features were first detected for 3 P with PHg anchored by H bonding in a frozen aqueous solution of sulfuric acid [1 ]. Complete sets of ap and the anisotropic components Tqq (q = inertial axes a, b, c XTqq=0) for both nuclei of ground-state PHg were later determined by far-IR laser magnetic resonance (FIR, LMR) [2] and microwave (MW) [3, 4] spectra. The latter [3, 4] also yielded data for the interaction constants Cqq(3ip). Interaction constants were also obtained for the electronically... 

Gas Phase. The isotropic or Fermi contact hyperfine (hf) coupling constant Ajgo and the anisotropic or dipole hf tensor elements Agg, A b, and A c of NH2 in the X Bi(0,0,0) and A Ai(0,V2,0) states are compiled in Table 9. The experimentally determined constants were derived from microwave optical double resonance (MODR), microwave absorption (MWA), laser magnetic resonance (LMR), infrared optical double resonance (lODR), optical optical double resonance (OODR), saturation, and magnetic level-crossing spectra. 

Fermi-contact coupling. The through-bond coupling between the average electron spin and a nuclear spin 7 has a rank-0, isotropic component A (hyperfine Fermi constant) which is proportional to the spin density in the i orbital of the atom carrying the I spin ... 

Gaussian computes isotropic hyperfine coupling constants as part of the population analysis, given in the section labeled "Fermi contact analysis the values are in atomic-units. It is necessary to convert these values to other units in order to compare with experiment we will be converting from atomic units to MHz, using the following expressions ri6ltYg ... 

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. 

Contact shifts give information on the electronic structure of the iron atoms, particularly on the valence distribution and on the magnetic coupling within polymetallic systems. The magnetic coupling scheme, which is considered later, fully accounts for the variety of observed hyperfine shifts and the temperature dependence. Thus, through the analysis of the hyperfine shifts, NMR provides detailed information on the metal site(s) of iron-sulfur proteins, and, thanks to the progress in NMR spectroscopy, also the solution structure 23, 24 ). 

By assuming that the hyperfine shifts are contact shifts in origin, it is possible to evaluate the hyperfine coupling constant from the following equation (50) ... 

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] ... 

Combines sensitivity of EPR and high resolution of NMR to probe ligand super-hyperfine interactions For paramagnetic proteins enhanced chemical shift resolution, contact and dipolar shifts, spin delocalization, magnetic coupling from temperature dependence of shifts Identification of ligands coordinated to a metal centre... 

This mechanism is identical to the one arising from the contact interaction between an unpaired electron and a nuclear spin (41). In that case, the hyperfine coupling (generally denoted by Asc or A and exists only if the electron density is non-zero at the considered nucleus, hence the terminology of contact ) replaces the J coupling and the earlier statement (i) may be untrue because it so happens that T becomes very short. In that case, dispersion curves provide some information about electronic relaxation. These points are discussed in detail in Section II.B of Chapter 2 and I.A.l of Chapter 3. 

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