Antisymmetric exchange interaction

For the simplest system of SA = SB = 1/2 the antisymmetric exchange interaction matrix adopts the form of... 

Lines, M E., Ginsberg, A.P., Martin, R.L., Antisymmetric exchange interaction in tetra-... 

Figure 24. Molecular Sophe Graphical User Interface showing (a) the Isotropic Exchange Interaction, (b) the Axial Anisotropic Exchange Interaction, and (c) the Antisymmetric Exchange Interaction.

The dominating contribution to exchange interaction is isotropic as expressed by the scalar parameter used in (4.80) anisotropic and antisymmetric contributions [87] are mostly ignored. Equation (4.80) can be evaluated in the coupled presenta-... 

For identical hydrons, the symmetry postulate of identical particles has to be fulfilled. For protons and tritons this means that the overall wave function must be antisymmetric under particle exchange and for deuterons it must be symmetric under particle exchange. Due to this correlation of spin and spatial state, the energy difference A between the lowest two spatial eigenstates can be treated as a pure spin Hamiltonian, similar to the Dirac exchange interaction of electronic spins. 

Exchange interaction results from the overlap of the wave-functions of S and A, and is consequently a very short interaction falling off exponentially with the distance between the ions. If the ions S and A have only a single active electron each, the initial and final states S A> and ISA > must be antisymmetrized in the coordinates of the two electrons, and the exchange matrix elements will have the expression... 

The antisymmetric term of the exchange interaction is defined through the operator... 

Several kinds of exchange interactions, which couple the magnetic centres, are distinguished the (bilinear) isotropic, asymmetric, antisymmetric, biquadratic and double exchange. Various fine-structure Hamiltonian terms enter the spin-spin coupling tensor D these were derived from the relativistic Dirac and Breit equation. 

Asymmetric exchange is incapable of removing this kind of degeneracy since there are no interaction elements between l, 1/2) and 0,1/2) kets. Only antisymmetric exchange couples the above states, which lead to the removal of the accidental degeneracy of the two Kramers doublets, yielding... 

The antisymmetric exchange term (Eq. (2), Gat Sa x S ) can be included by selecting the Antisymmetric exchange representation (Fig. 24c), which includes Jiso and the principal components of the G matrix and three Euler angles. Dipole-dipole terms can be also included by selecting the Dipole-Dipole radio button (red is active). This interaction has been found to be important for trinuclear copper(II) systems, where the orbitals containing the unpaired electrons partially overlap. 

---