The Kahn-Briat Model

Based on valence bond reasoning with nonorthogonal atomic-like orbitals, Kahn and Briat derived an elegant model that is capable of explaining and predicting magnetic behavior of transition metal complexes based on the shape of the localized magnetic 

Graaf and R. Broer, Magnetic Interactions in Molecules and Solids, 

Multiplying the spatial part of the wave function (pa Pb = ab with the singlet and triplet Ms = 0) spin functions, the following normalized wave functions are obtained 

As shown in the previous chapter, the energy difference between singlet and triplet is proportional to the magnetic coupling strength. The energy expectation values of Ps and Pt are 

This results in the following expressions for the energy of the singlet and triplet states. 

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The second valence-only model starts from a molecular orbital viewpoint and was derived in the mid 1970s by Hay, Thibeault and Hoffmann (HTH) [2], approximately at the same time as the Kahn-Briat model. The magnetic orbitals are defined as linear combinations of orthogonal atomic-like orbitals... 

Similar to (pa and cpb of the Kahn-Briat model, the atomic-like orbitals of the HTH model have the largest amplitudes on the magnetic centers, but in contrast fa and fb show delocalization tails on the ligands to ensure the orthogonality between them. Therefore, in general fa and fb are slightly more delocalized than the nonorthogonal (pa and (pb. 

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