The Hay-Thibeault-Hoffmann Model

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. 

In the original derivation, three determinants were constmcted with the molecular orbitals (p and / 2 

Si and S2 have the same spin and spatial symmetry and to obtain the energy of the lowest singlet a 2 x 2 matrix has to be diagonalized with Es and Es2 on the diagonal and the interaction between the two determinants as off-diagonal element 

The second-order equation that arises from the condition that the secular determinant is equal to zero can be solved straightforwardly and gives the energy of the singlet 

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