Nuclear fluctuation coupling

If the paramagnetic center is part of a solid matrix, the nature of the fluctuations in the electron nuclear dipolar coupling change, and the relaxation dispersion profile depends on the nature of the paramagnetic center and the trajectory of the nuclear spin in the vicinity of the paramagnetic center that is permitted by the spatial constraints of the matrix. The paramagnetic contribution to the relaxation equation rate constant may be generally written as... 

The surrounding medium and its relaxation time determine the time for the nuclear fluctuations that are to couple with the electron and to capture it, anulling the charged state of H30+. 

If quantum nuclear fluctuations are sought, from eq.(8) one only needs the first term, H c = Kn + He(L ). These fluctuations include rotations as a whole of a frame rigidly bound to the stationary external Coulomb sources. The coupling terms in W, involving the momenta operators of electrons and nuclei, have no diagonal components they will contribute to changes in the populations of stationary levels related to the hamiltonian Ham. Integrating over electronic coordinates with a particular Hn(p cc°n). the collective nuclear motion can be obtained as a solution to... 

The neglect of the electronic coupling in the calculation of the ECWD (assumption 1) was adopted in the original Marcus and Elush formulation. " Within this framework, the ET matrix element does not strongly affect the nuclear fluctuations, although a nonzero value of Hab is required for electronic transitions to occur. In other words, the transferred electron is assumed to be fully localized in the calculation of the ECWD. To classify electronic delocalization, Robin and Day distinguished between three classes of symmetrical (APo = 0) systems. 

The only way the electron can be locahsed on this model acceptor site is if some perturbation makes it lower in energy than the resonantly coupled atomic sites of the lattice. This perturbation is the nuclear fluctuation of the dielectric medium that displace the nuclear configurations towards position C in Fig. 2.24 where the charge-... 

Often the electronic spin states are not stationary with respect to the Mossbauer time scale but fluctuate and show transitions due to coupling to the vibrational states of the chemical environment (the lattice vibrations or phonons). The rate l/Tj of this spin-lattice relaxation depends among other variables on temperature and energy splitting (see also Appendix H). Alternatively, spin transitions can be caused by spin-spin interactions with rates 1/T2 that depend on the distance between the paramagnetic centers. In densely packed solids of inorganic compounds or concentrated solutions, the spin-spin relaxation may dominate the total spin relaxation 1/r = l/Ti + 1/+2 [104]. Whenever the relaxation time is comparable to the nuclear Larmor frequency S)A/h) or the rate of the nuclear decay ( 10 s ), the stationary solutions above do not apply and a dynamic model has to be invoked... 

In general, fluctuations in any electron Hamiltonian terms, due to Brownian motions, can induce relaxation. Fluctuations of anisotropic g, ZFS, or anisotropic A tensors may provide relaxation mechanisms. The g tensor is in fact introduced to describe the interaction energy between the magnetic field and the electron spin, in the presence of spin orbit coupling, which also causes static ZFS in S > 1/2 systems. The A tensor describes the hyperfine coupling of the unpaired electron(s) with the metal nuclear-spin. Stochastic fluctuations can arise from molecular reorientation (with correlation time Tji) and/or from molecular distortions, e.g., due to collisions (with correlation time t ) (18), the latter mechanism being usually dominant. The electron relaxation time is obtained (15) as a function of the squared anisotropies of the tensors and of the correlation time, with a field dependence due to the term x /(l + x ). 

The relaxivity enhancement of water protons in the aqueous solutions of paramagnetic complexes arises from time fluctuation of the dipolar coupling between the electron magnetic moment of the metal ion and the nuclear magnetic moment of the solvent nuclei (13,14). The dipolar interaction... 

Ms value but on different positions in space. This random motion of the electron around the nucleus is again seen as a fluctuating magnetic field that causes nuclear relaxation through dipolar coupling. 

In situ STM of metalloproteins with localized low-lying redox levels can be expected to follow ET patterns similar to metalloprotein ET in homogeneous solution and at electrochemical surfaces. The redox level is thus strongly coupled to the protein and solvent environment. A key notion is that the vacant local level (oxidized form) at equilibrium with the environmental nuclear motion is located well above the Fermi levels of both the substrate and tip, whereas, the occupied level (reduced form) at equilibrium is located well below the Fermi levels. Another central notion is that the local redox level at the transition metal centre is still much lower than environmental protein or solvent electronic levels. The redox level therefore constitutes a pronounced indentation in the tunnel barrier. This alone would strongly enhance tunnelling. Configurational fluctuations in the environment can, secondly take the redox level to such low values that temporary physical population occurs. This requires nuclear activation but can still be favourable due to the much shorter electron tunnel distances... 

---