Electrons exchange integral

In Fig. 4, nucleus is coupled to the electron on R and nucleus Hj is coupled to the electron on R by the hyperfine terms and Oj, respectively. The inter-radical separation is denoted by X, and J e is the electron exchange integral. The two radicals move relative to each other and, as shown above, this changes the values of Jee-... 

Mossin S, Weihe H (2003) Average One-Center Two-Electron Exchange Integrals and Exchange Interactions 106 173-180 Murakami S, see Morita M (2004) 107 115-144 Muller E, see Roewer G (2002) 101 59-136... 

Fig. 11 Temperature dependence of the hole mobility in PMPSi at different electric fields. Full curves are calculated using the theory by Fishchuk et al. [70], The fit parameters are the width a of the density of states distribution, the activation energy (which is p/2), the electronic exchange integral J, and the intersite separation a. From [70] with permission. Copyright (2003) by the American Institute of Physics...

Here W is the ionization potential of an electron in the p-AO of an isolated atom i, (/3M)0 is the one-electron exchange integral between the AO s of atoms i, j, and (ii, jj) and (it, j) are the usual electron repulsion and penetration integrals. In practice the penetration integrals are usually disregarded this should certainly be justifiable in the present connection where we are concerned only with differences in energy between closely related systems. Equation (31) then becomes—... 

S is the overlap integral between the magnetic orbitals, and j is the two-electron exchange integral. 

Triplet energy transfer from chlorophyll to carotenoid is not mechanistically anomalous. The dominant term describing the interaction between the donor triplet and the acceptor is an electron exchange integral, the magnitude of which depends directly on the overlap between the donor and acceptor n-... 

The accuracy of this procedure depends on the thresholds set to form Z. Kashiwaga establishes two the overlap should be below a given threshold, and the two-electron exchange integral must also be below a set threshold. In practice, both these thresholds are set quite small, and the calculations closely resemble their ab initio counterpart. No empirical parameters are introduced. 

Pearson explored Klopman s earlier suggestion of including not only the Coulomb interaction but also the covalent bonding expressed by the two-center, one-electron exchange integral p [58, 59] ... 

Many of the integrals needed to evaluate Wj and W2 have been evaluated in the treatment of H2 in Section 13.5. The only new integrals are those involving l/r,2- The hardest one is the two-center, two-electron exchange integral ... 

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