Contact coupling

Das, N. C., Elastohydrodynamic Lubrication Theory of Line [39] Contacts Couple Stress Fluid Model, Tribal. Trans., Vol. 40, No.2,1997,pp.353-359. 

Figure 3. Photovoltage from n-CdTe etched with an oxidizing etch ( ) or an oxidizing etch followed by a reducing treatment (NaOH/StOf ) ( J as a function of E,/t of a contacting couple. Key to redox couples 1, Ru(bipy),0/ 2, Rufbipy), 0 3, Ru(bipy), 4, TQt/0 5, TQ > 6, Fe(r)5-CsMes)t m 7, Fe(-f-CsHs)t "> 8, TMPEF /.. 9 TMPD 0 10, MV2t/ and 11, MV 10. (Reproduced from Ref. 18.)...

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...

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... 

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. 

S is an effective electronic spin (S = 1/2), / is a function which depends on the averaging conditions in the solution, g is the electronic g-tensor for the jth state, and A the contact coupling tensor which describes the interactions of the ith proton with the electronic spin in the jth state. The summations are over the populated states, and Ej are the state energies (Fig. 24). Under the averaging conditions in solutions of hemoproteins, with rr <=> 10 8 sec, and gn — gx >0.01 at 220 Me / is... 

The anisotropy of the contact coupling tensor was estimated from the relations (Abragam and Pryce (2) Jesson (46))... 

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. 

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. 

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.

NUCLEAR RELAXATION DUE TO CONTACT COUPLING WITH UNPAIRED ELECTRONS... 

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. 

The spin Hamiltonian for two contact coupled S = V2,1 = lh spins is given by... 

To test our method, we have analyzed the CB stability diagrams for a SSJ and a DSJ. Our results are all consistent with the results of experiments and the master-equation approach. We showed, that the improved lesser Green function gives better results for weak molecule-to-contact couplings, where a comparison with the master equation approach is possible. 

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