Adjacent exchange integral

The exchange integrals for interaction of adjacent atoms will be... 

In the simple Hiickel molecular orbital theory of w-electronic systems, molecular orbitals are derived by combinations of 2p orbitals, one from each bonded atom. All of the exchange integrals for bonded atoms are taken as equal and interactions between non-adjacent atoms are ignored. The energy of each molecular orbital then has the form,... 

The remaining exchange integrals between non-adjacent atoms as stated above will be assumed to be equal to zero ... 

Below 6 per cent nickel the first observation is that the Weiss constant is zero. The form of the susceptibility isotherm is thus in the case of nickel in no way related to the exchange interaction between adjacent nickel ions. This is not to say that the nickel ions are at infinite magnetic dilution. For nickel in massive nickel oxide the exchange integral, the paramagnetic neighborhood (z), and the number of unpaired electrons are smaller than they are for chromium ions in massive chromia. The quantity. A, is understandably smaller for the case of nickel, and it... 

Here, J is the exchange integral between adjacent metal atoms (1,2 and 2,3) and J that between the two terminal metal atoms (1,3) within the trimer. The total spin of the molecule as well as the order of energy levels depend on the relative values of J and J and the sign of J. It is useful to introduce the new spin quantum numbers S = S] -I-S2-1-S3 and S = Si -l-Ss. For the particular case Sj =S2 = S3 = 1, the resulting energies as well as the values of S and S are listed in Table 2. The magnetic susceptibility per metal atom then follows as... 

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