Magnetic ordered state representation

Figure 4.8 (a) Representation of a magnetic chain in its ordered state, (b) The creation of a domain of reversed spins costs four times the exchange interaction, assuming unitary length for the spins, (c) If the reverse domain... 

The restrictions listed until now are of the type of necessary conditions. In order to obtain sufficient conditions for the observation of the effect of magnetic optical activity of molecules in T states, it is necessary to pass under the sign of the spur in the expression Sp pLK-K Cl J]Clf. J for allowed values of the pairs (JJ ) to appropriate products of irreducible tensor operators for the point group of the molecule. Using the decomposition of the representation DJ of the full spherical group into irreducible representations of the molecular point group, one can present the result in the form of a sum of following terms ... 

In practice, there is quite a difference between atoms and molecules as far as the representation of the one-particle spectrum is concerned. In atomic physics, one often utilizes a radial-angular representation of the one-electron orbitals in order to allow for the analytic integration over all spin-angular coordinates of the system [35,36]. This so-called angular reduction will be briefly discussed below in Subsection 4.4. However, in order to exploit the symmetry of free atoms the reference state must coincide with a closed-shell determinant o> = < >>, i.e. a reference state which should not depend on the magnetic quantum numbers of the one-electron functions. Unfortunately, the complexity of the perturbation expansions increases very rapidly if the number of electrons in the physical states of interest differ from (the number of electrons in) the reference state. 

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