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physics_chemistry:point_groups:d3d:orientation_zy [2018/04/05 00:19]
Maurits W. Haverkort created
physics_chemistry:point_groups:d3d:orientation_zy [2018/09/06 13:40] (current)
Maurits W. Haverkort
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 ====== Orientation Zy ====== ====== Orientation Zy ======
  
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-The point group D3d is a subgroup of Oh. Many materials of relavance ​have near cubic symmetry with a small D3d distortion. It thus makes sense to label the sttes in D3d symmetry according to the states they branch from. For d orbitals the eg orbitals in Oh symmetry branch to orbitals that belong to the eg irriducible ​representation in D3d symmetry. The t2g orbitals in Oh symmetry branch to an orbital that belongs to the a1g irriducible ​representation and two that belong to the eg irricucible ​representation. We label the eg orbitals that decend ​from the eg irriducible ​representation in Oh symmetry eg$\sigma$ and the eg orbitals that decend ​from the t2g irriducible ​representation eg$\pi$ orbitals. (The mixing is given by the parameter Meg.)+The point group D3d is a subgroup of Oh. Many materials of relevance ​have near cubic symmetry with a small D3d distortion. It thus makes sense to label the states ​in D3d symmetry according to the states they branch from. For d orbitals the eg orbitals in Oh symmetry branch to orbitals that belong to the eg irreducible ​representation in D3d symmetry. The t2g orbitals in Oh symmetry branch to an orbital that belongs to the a1g irreducible ​representation and two that belong to the eg irreducible ​representation. We label the eg orbitals that descend ​from the eg irreducible ​representation in Oh symmetry eg$\sigma$ and the eg orbitals that descend ​from the t2g irreducible ​representation eg$\pi$ orbitals. (The mixing is given by the parameter Meg.)
  
-As one can see in the list of supergroups of D3d, there are two different orientations of Oh that are a supergroup of this orientation of D3d. The different orientations of Oh with respect to D3d do however change the definitions of the eg$\pi$ and eg$\sigma$ orbitals. We inlcude ​three different representations of the orbitals and potentials for each setting of D3d symmetry. The orientation without ​aditional ​letter takes the tesseral harmonics as a basis. This basis does not relate to the states in Oh symmetry. The orientation with an aditional ​A or B relate to the two differnt supergroup representations of the Oh point group.+As one can see in the list of supergroups of D3d, there are two different orientations of Oh that are a supergroup of this orientation of D3d. The different orientations of Oh with respect to D3d do however change the definitions of the eg$\pi$ and eg$\sigma$ orbitals. We include ​three different representations of the orbitals and potentials for each setting of D3d symmetry. The orientation without ​additional ​letter takes the tesseral harmonics as a basis. This basis does not relate to the states in Oh symmetry. The orientation with an additional ​A or B relate to the two differnt supergroup representations of the Oh point group.
  
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