Nuclear electron coupling parameter

In the case of dipolar coupling, the transitions Wq, W2 and are all allowed. However it can be shown that the nuclear—electron coupling parameter p is always positive. Under optimum conditions (white spectrum) the ratios of lUo lUi 11 2 are and thus p has a value... 

When both dipolar and scalar interactions are present, p, the nuclear-electron coupling parameter, has to be calculated as a function of Because p depends also on the spectral density near the electron Larmor frequency, p can be plotted as a function of frequency for various values of In practice, it proves to be convenient to present p as a function of (cDsT,) where t,, the diffusional correlation time, is given by—... 

As discussed in Chapter 6, in systems with more than one unpaired electron the ESR spectrum contains features that involve electron-electron coupling parameters analogous to the nuclear hyperfine parameters. In those types of samples the advantages of double resonance are carried out by employing the use of two different microwave frequencies, one fixed and saturating, and one variable frequency that searches for transitions. This technique is known as ELDOR (electron-electron double resonance).38,40,41,44 It has been used much less than ENDOR and usually requires custom-built equipment. 

In the high temperature limit where all the nuclear motions coupled to the process can be described classically, the nuclear factor is expressed in terms of only two parameters the driving force of the reaction AG°, and the whole reorganization energy X (expressions (13) and (14)). Detailed calculations carried out in the case of cytochrome c have demonstrated that AG° is a complex quantity, which depends not only on the electronic properties of the redox centers but also on those of the protein and of the surrounding solvent [100]. Usually, AG can be evaluated from measurements of redox potentials and of eventual interaction energies between the different parts of the systems (Appendix). 

Johnson and Messmer expanded the interpretation of the bonding overlap integral to a Jahn-Teller coupling parameter fi via the relation Sbond(EF) (m/My, where m, M are the electron and nuclear masses, respectively. According to this expression, there are two derived trends (1) for physically realistic values of d (d > 0.05 nm), Tc drops as d increases and (2) at constant d, Tc increases as S increases. 

In these studies, the parameters that could provide the most interesting information are likely to be the electric field gradient (nuclear quadrupole coupling constant) at the 33S nucleus and its asymmetry parameter. Indeed, modifications of the lattice structure in different cement matrixes are expected to influence the symmetry of the electronic distribution around the sulphur nucleus more than the chemical environment of sulphur. 

The experiments of Vos and eo-workers raise the question of whether the coherent nuclear motion associated with the P state that persists on the time-scale of eleetron transfer is coupled to the primary electron transfer reaction. In particular, do any of the nuclear vibrations coupled to the P state facilitate the transfer of electrons from P to Ba The observation of coherent nuclear motion that persists on the time-scale of primary electron transfer raises the possibility that this nuclear motion may be an important parameter that governs the characteristics of this reaction, which would place this process in a near-adiabatic regime. Of obvious importance is the question of whether it is possible to observe coherence in the formation of a produet state such as P Ba". A number of recent studies have addressed this difficult problem with conflicting conclusions (Sp"rlein et al., 1998 Streltsov et al., 1998 Vos et al., 1998 Streltsov et al., 1996) and, as discussed in reeent review (Vos and Martin, 1999) at present this question remains to be answered. 

The parameters of the electronic Hamiltonian are calculated by performing extensive ab initio calculations [21]. Results of calculations of static aspects of the electronic PESs, viz, the equilibrium minimum of the states and energetic minimum of the seam of the CIs within a LVC mo l summarized in Table 1. It can be seen from the data that the minimum of the X—A CIs occurs 0.02 eV above the equilibrium minimum of the A state. The same for the B CIs occurs at 0.84 eV and 0.06eV above the equilibrium minimum of the A and B states, respectively. The minimum of B-C CIs occurs 1.10eV above the equilibrium minimum of the C state. The minimum of the X—B CIs occurs 2.5eV above the equilibrium minimum of B state. The X and C CIs occur at much higher energy and are not considered here. Analysis of the coupling parameters of all 36 vibrational modes revealed the importance of 9 ai (vi3 — V5), 9 2 (r 36 — r zv), 2 az (vie and 4 bi (vzo - V17) vibrational modes in the nuclear dynamics in the X—A—B—C electronic states of PA + [21]. 

Uie rate of electron transfer (ET) from a donor (D) to an acceptor (A) held at fixed distance and orientation depends on of temperature (7), reaction driving force (-AG°) a nuclear reorganization parameter (X), and an electronic coupling matrix element The reorganization parameter... 

Under anisotropic conditions, NMR lineshapes for a quadrupolar nucleus are dominated by chemical shielding and (first and second order) quadrupolar interactions. Dipolar interaction is usually a minor contribution only. First-order quadrupole interaction lifts the degeneracy of the allowed 21 (i.e. seven in the case of V / = V2) Zeeman transitions as shown in Figure 3.7, giving rise to seven equidistant lines, viz. a central line (mj = + V2 -V2. unaffected by quadrupole interaction) and six satellite lines. The overall breadth of the spectrum is determined by the size of the nuclear quadrupole coupling constant Cq the deviations from axial symmetry and hence the shape of the spectral envelope are governed by the asymmetry parameter. Static solid-state NMR thus provides additional parameters, in particular the quadrupole coupling constant, which correlates with the electronic situation in a vanadium compound. [ 1 The central component reflects the anisotropy of the chemical shift. 

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