Contact coupling constant

The functional form of the nuclear longitudinal relaxation immediately suggests that the contact contribution can provide the values of the contact coupling constant and of 72e = Tso, provided that the lifetime, xm, is longer than T e- No information on the field dependence of electron relaxation can be achieved. On the contrary the functional form of transverse nuclear relaxation contains a non-dispersive term, Tig. The latter, as we have seen for the dipolar contribution, increases with increasing the field (Fig. 3), and therefore the nuclear contact transverse relaxation also increases with increasing the field. Its measurement is thus informative on the t value. 

Table II reports the contact coupling constant for different aqua ion systems at room temperature. The contact coupling constant is a measure of the unpaired spin density delocalized at the coordinated protons. The values were calculated from the analysis of the contact contribution to the paramagnetic enhancements of relaxation rates in all cases where the correlation time for dipolar relaxation is dominated by x and Tig > x. In fact, in such cases the dispersion due to contact relaxation occurs earlier in frequency than the dispersion due to dipolar relaxation. In metalloproteins the contact contribution is usually negligible, even for metal ions characterized by a large contact contribution in aqua ion systems. This is due to the fact that the dipolar contribution is much larger because the correlation time increases by orders of magnitude, and x becomes longer than Tig. Under...

In hemes and hemoproteins contact shifts arise if finite amounts of unpaired electron spin density are delocalized from the iron orbitals into the jr-orbital systems of the porphyrin and the axial ligands, as indicated by the arrows in Fig. 25. Electron density is then further transferred from the aromatic ring carbon atoms to the protons (Fig. 2), thus giving rise to contact interactions. The measured isotropic contact coupling constants for the protons, A in Eq. (4), can be related to the integrated spin density on the neighboring ring carbon atom by (McConnell (73)] Bersohn (5) Weissman (107). 

Eq. (4), which relates the observed contact shifts of the proton resonances to their isotropic contact coupling constants, and hence to the spin densities on the ring carbon atoms, is valid only for systems with isotropic g-tensors. To obtain an estimate of the errors which might arise from its application to low spin ferric heme compounds, we shall briefly consider a more general form of the equation, which was given by Jesson (46) for tetragonal systems with more than one populated electronic state. 

We should note that if g = ge, the contact shift is isotropic (independent of orientation). If g is different from ge and anisotropic (see Section 1.4), then the contact shift is also anisotropic. The anisotropy of the shift is due to the fact that (1) the energy spreading of the Zeeman levels is different for each orientation (see Fig. 1.16), and therefore the value of (Sz) will be orientation dependent and (2) the values of (5, A/s Sz S, Ms) of Eq. (1.31) are orientation dependent as the result of efficient spin-orbit coupling. On the contrary, the contact coupling constant A is a constant whose value does not depend on the molecular orientation. 

The presence of contact relaxation indicates that a given moiety is covalently bound to a paramagnetic metal ion and provides an estimate of the absolute value of A (Eqs. (3.26) and (3.27)). Sometimes the contact coupling constant can be evaluated by chemical shift measurements, and it is therefore possible to predict whether the contact relaxation contributions to R m, Rim or both, are negligible or sizable. 

Kurland and McGarvey approach [43] and an angular dependence of the contact coupling constant (as provided by the following Eq. (5.2)), by taking into account the contributions of the various electronic levels [44]. 

Eq. (8.7), which provides the scalar coupling constant due to the interaction between nuclei, is analogous to Eq. (2.29), used to describe the dihedral angle dependence of the contact coupling constant due to the interaction between nuclei and electrons. 

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 isotropic (Fermi contact) coupling constant is defined in terms of the unpaired spin density at a nucleus ... 

The simplest system exliibiting a nuclear hyperfme interaction is the hydrogen atom with a coupling constant of 1420 MHz. If different isotopes of the same element exhibit hyperfme couplings, their ratio is detemiined by the ratio of the nuclear g-values. Small deviations from this ratio may occur for the Femii contact interaction, since the electron spin probes the inner stmcture of the nucleus if it is in an s orbital. However, this so-called hyperfme anomaly is usually smaller than 1 %. 

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 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. 

A completely different type of property is for example spin-spin coupling constants, which contain interactions of electronic and nuclear spins. One of the operators is a delta function (Fermi-Contact, eq. (10.78)), which measures the quality of the wave function at a single point, the nuclear position. Since Gaussian functions have an incorrect behaviour at the nucleus (zero derivative compared with the cusp displayed by an exponential function), this requires addition of a number of very tight functions (large exponents) in order to predict coupling constants accurately. ... 

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) ... 

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... 

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... 

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