Biquadratic exchange operator

The different 5i and S2 operators are again replaced by the sum of the one-electron operators 5(1)+5(2) and 5(3) 4-5(4) and the effect of the nine operators on the seven different determinants can be evaluated. Using the results summarized in Table3.3, the effect of the biquadratic exchange operator on the spin functions listed in Eq. 3.69 is easily established ... 

To model several other electronic situations (e.g., in mixed-valence compounds), the Heisenberg Hamiltonian can be augmented by specific exchange operators that accommodate, for example, double exchange, antisymmetric exchange, anisotropic exchange, or biquadratic exchange. 

The spin-spin interaction is not necessarily restricted to quadratic terms in the spin operators. Higher-order terms could be considered, among which the (isotropic) biquadratic exchange reads... 

The operator of the biquadratic exchange for a dinuclear system is written as follows... 

The operator of biquadratic exchange involves not only the pair-interaction terms but also the triad-interaction ones... 

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