Intramolecular energy transfer equations

P. Brumer and J. W. Duff, A variational equations approach to the onset of statistical intramolecular energy transfer, J. Chem. Phys. 65 3566 (1976). 

Selective excitation experiments on unimolecular reactions have two main aims. First, to test the proposition, inherent in the statistical theories of unimolecular reactions, that intramolecular energy transfer is extremely rapid and therefore the random lifetime assumption [see equation (1.52)] is valid. Secondly, to measure specific rate constants, k e and compare them with theoretical predictions. In the rest of this section, some of the experimental studies which have had greatest success in fulfilling these objectives are reviewed. 

Intramolecular photoaddition of tertiary amine and styrene moieties has been extensively studied by Aoyama29 and Lewis group28,30,31 (equations 4-8). Equations 4 and 5 show that if the intramolecular additions result in the formation of a five- or six-membered ring, the product yields are excellent. Highly regioselective intramolecular proton transfer is proposed to occur via least motion pathways from the lowest energy... 

The extension of DET to reversible energy transfer was intuitively made only once [7,64] and for the particular case of the resonance intramolecular transfer (AG = 0), when Wa = Wg = W. The set of equations that substituted for Eq. (3.91) assumed the following form ... 

We have used trajectory calculations to calculate this quantity [26]. Our method distinguishes between effective trajectories that contribute to P(E ,E) and those with very large impact parameter which do not. The P(E ,E) thus found, obeys conservation of probability and detailed balance and is independent of the impact parameter. The method is demonstrated for benzene-Ar collisions at various temperatures and internal energies. With this method, it is possible to combine ab initio inter and intramolecular potentials with trajectory calculations, obtain P(E ,E) and use that in master equation calculations to obtain rate coefficients and population distributions without resorting to any a priori assumptions and energy transfer models. 

Figure 3. Plot of ln(l yhj vs. the free energy for the intramolecular electron transfer reactions of the H39C C102T variant of yeast cytochrome c. The solid curve is a plot of equation 1 with Hab = 0.06 cm and A = 1 eV. The data points can be identified by using Table I. The rate constant kj, are indicated by and...

The intramolecular proton transfer from bound H2 to sulfide or other Lewis-basic sites is a key step in the function of active sites in the metalloenzymes hydrogenase (H-ase) and possibly nitrogenase. H-ases are redox enzymes in microorganisms that catalyze interconversion of H2 and protons to either utilize H2 as an energy source or dispose excess electrons as H2 (Equation (17)). ... 

The intramolecular distance r can be estimated by measuring singlet-singlet energy transfer using the Foster equation ... 

The classical Morse curve model of intramolecular dissociative electron transfer, leading to equations (3.23) to (3.27), involves the following free energy surfaces for the reactant (Grx-) and product (Gr +x ) systems, respectively ... 

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