Field tensors irreducible representations

DFT = Density Functional Theory DSD = Diamond-Square-Diamond HOMO = Highest Occupied Molecular Orbital IR = Irreducible Representation LCAO = Linear Combination of Atomic Orbitals Ph = Phenyl PSEPT = Polyhedral Skeletal Electron Pair Theory SCF = Self-Consistent-Field SDDS = Square-Diamond, Diamond-Square TSH = Tensor Surface Harmonic. 

As already noted, the crystal field potential should be invariant under all the transformations of the symmetry point group. This means that it is transformed according to the totally symmetric representation (A ) of the group G. The spherical tensor component Tk m appears within the crystal field potential when the decomposition of the irreducible representations Dof the rotation group R3 in terms of irreducible representations rt of the point group G contains the totally symmetric representation A ... 

Contributions to the magnetoelastic interaction that contain the rotational tensor are important only in an external magnetic field. This will be considered separately in sect. 2.6. For the moment we consider only pure strain contributions. In cubic crystals the components of e can be grouped to form irreducible representations of the cubic point group (Thalmeier and Fulde 1975, du Tremolet de Lacheisserie et al. 1978) ... 

The presence of two nuclear spins means that there is considerable choice in the selection of basis functions the reader who wishes to practice virtuosity in irreducible tensor algebra is invited to calculate the matrix elements in the different coupled representations that are possible In fact the sensible choice, particularly when a strong magnetic field is to be applied, is the nuclear spin-decoupled basis set t], A N, S, J, Mj /N, MN /H, MH). Again note the possible source of confusion here MN is the space-fixed component of the nitrogen nuclear spin /N, not the space-fixed component of N. This nuclear spin-decoupled basis set was the one chosen by Wayne and Radford in their analysis of the NH spectrum. 

The real version of the irreducible tensor method, related to the complex representations as mentioned, is highly useful in the ligand-field theory, as will be shown in the second part of this paper. An additional reason for this is the fact that expansion theorems concerning functions and operators achieve apt forms when the tensor method is applied to real spherical harmonics. 

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