PCEM octahedron

The tetrahedron (Tj) is considered here only theoretically, since CN=4 is too low for lanthanide systems. But it is interesting to compare both octahedron, cube and tetrahedron. The fourfold inversion axis or the threefold rotation axis can be chosen as z-axis. The angular coordinates are given in table 12. The PCEM expressions for the parameters with regard to the fourfold rotation axis are ... 

Because the octahedron and cube have the same symmetry (Oh), the crystal field generated inside a cube is described by the same crystal-field parameters as the octahedron (5g, B, BI and B ). The actual PCEM expressions for the parameters will be different, because of the difference in coordination number ... 

With the aid of these relations and the expressions for the crystal-field parameters of the octahedron, it is easy to build the PCEM expressions for the tetrakishexadron along the threefold rotation axis. 

Other coordination polyhedra with D41, symmetry are the tetragonal bipyramid (CN = 6), which can be seen as a distortion of the octahedron, and the bicapped square prism (CN=10). The tetragonal bipyramid is not discussed here, because an angular distortion cannot lower the symmetry to D4. The distortion scheme of a bicapped square prism (BSP, D4h) to a bicapped square antiprism (BSAP, D4d) is analogue to the one described above. The PCEM expressions for the B and 5 parameters will be exactly the same as for the SP-SAP distortion scheme, since axial ligands do not have an influence on... 

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See also in sourсe #XX -- [ ]

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