Exchange integrals limitations

Now, the appropriate integration limits used in the calculation of 11 /ri2 interactions between electrons assigned to the core region / and electrons associated with the valence space t concern both Coulomb and exchange integrals. The latter are of particular interest, namely, the exchange that participates in the evaluation of V . 

The difference between the triplet and singlet energies is approximately 2Kn, where Kn is an exchange integral proportional to (n )-3. As discussed in Section 3.4.2.1.2, the mixing between 3IIi and increases with n, and when n becomes infinite the states are completely mixed and are described by a case (c) basis that corresponds to the limiting solutions,... 

Equation 37 is often modified in order to model experimental results more realistically and/or make theoretical calculations more manageable. One common modification is the alternating chain where the exchange integral between sites in the chain alternate between J and J (58, 181). This model is particularly applicable to a chain composed of dimers with each molecule of the dimer having spin S. In the limit J J - 1, the model reduces to the Heisenberg chain. When J J 0, the model reduces to a set of isolated... 

The integral in Eq. (4.4-9) can be broken into two parts, as follows (we have also exchanged the limits, which changes the sign) ... 

In order to evaluate the upper limit for the exchange integral, the integral intensity of the ESR line in polycrystalline solid was measured at various temperatures. These measurements showed that... 

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