Nuclear frequencies

The stimulated (tln-ee-pulse) echo decay may also be modulated, but only by the nuclear frequencies (0,2 and... 

HYSCORE, is a 2D four-pulse ESEEM technique which provides correlation between nuclear frequencies originating from different electron manifolds. The sequence of four microwave pulses is tx/2—x—tx/2—/tx— t2-nl2-x-echo where the echo amplitude is measured as a function of tx and t2 at fixed x. The a-proton anisotropic couplings can be detected by this technique (Konovalova et al. 2001a, Focsan et al. 2008). 

Nuclear frequency factors are calculated directly from the calculated molecular vibrational frequencies and the reorganizational energies, and these, in conjunction with the calculated Hab values lead to values for the electronic transmission coefficient, Kep... 

The Effective Nuclear Frequency. When nuclear tunneling is important we suggest that the individual frequencies should be weighted by their effective barriers, that is, instead of eq 8 it may be more appropriate to use eq 14... 

The reason for the absence of the nuclear frequency from eq 17 is that the slowest process in a nonadiabatic reaction is, by definition, the electron transfer that is, ve v n for a nonadiabatic reaction. 

So-called multidimensional NMR techniques can provide important information about macromolecular conformation. In these cases, the sequence of a protein is aheady known, and establishing covalent connectivity between atoms is not the goal. Rather, one seeks through-space information that can reveal the solution conformation of a protein or other macromolecule. Two-or three-dimensional techniques use pulses of radiation at different nuclear frequencies, and the response of the spin system is then recorded as a free-induction decay (FID). Techniques like COSY and NOESY allow one to deduce the structure of proteins with molecular weights less than 20,000-25,000. 

Where AG is the activation energy of the process, and T are the Boltzmann constant and the absolute temperature, respectively, v is the nuclear frequency factor, and is the transmission coefficient, a parameter that expresses the probability of the system to evolve from the reactant to the product configuration once the crossing of the potential energy curves along the reaction coordinate has been reached (Fig. 17.5). 

A question that arises in consideration of the annihilation pathways is why the reactions between radical ions lead preferentially to the formation of excited state species rather than directly forming products in the ground state. The phenomenon can be explained in the context of electron transfer theory [34-38], Since electron transfer occurs on the Franck-Condon time scale, the reactants have to achieve a structural configuration that is along the path to product formation. The transition state of the electron transfer corresponds to the area of intersection of the reactant and product potential energy surfaces in a multidimensional configuration space. Electron transfer rates are then proportional to the nuclear frequency and probability that a pair of reactants reaches the energy in which they have a common conformation with the products and electron transfer can occur. The electron transfer rate constant can then be expressed as... 

The remaining two terms in equation (1), vn and rel are, respectively, the nuclear frequency factor and the electronic transmission coefficient. The frequency factor gives the frequency with which reaction trajectories reach the avoided crossing region, and rel gives the probability that, once a trajectory has reached the avoided crossing region, it will pass into the product well, rather than be deflected back into the reactant well. 

For adiabatic reaction pathways (i.e. Kel = 1) the nuclear frequency factor, vn (s 1), represents the rate at which reacting species in the vicinity of the transition state is transformed into products. This frequency will be influenced by a combination of the various motions associated with the passage of the system over the barrier, approximately weighted according to their relative contributions to the activation energy. These motions usually involve bond vibrations and solvent motion, associated with the characteristic inner- and outer-shell frequencies, vis and vos, respectively. A simple formula for vn which has been employed recently is [la, 7]... 

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