Heisenberg exchange integral

Various predictive methods based on molecular graphs of Jt-systems as described in Section 3 have been critically compared by Klein (Klein et al., 1989) and can be extended to more quantitative treatments. In principle, the effective exchange integrals /ab in the Heisenberg Hamiltonian (4) for the interaction of localized electron spins at sites a and b are calculated as the difference in energies of the high-spin and low-spin states. It was Hoffmann who first tried to calculate the dependence of the M—L—M bond... 

Extensions to more sophisticated 1-D magnetisms have been performed by Takeuchi22 for 1-D helicoidal systems, and by Duffy and Barr23) for alternating Heisenberg chains (two different exchange integrals). 

Before consideration is given to the experimental data, it is of interest to consider the connection between the Weiss field constants used by N6el and the Heisenberg exchange integrals. In the non-collinear models, the Heisenberg formalism is generally used. 

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... 

A system with identical atoms and with one 7r-electron per atom will in this approximation behave as a Heisenberg antiferromagnet with the exchange integrals... 

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