Electrostatic energy octahedral field

If the metal ion were surrounded by a spherical electrostatic field, the energy of the d orbitals would be raised, but all would be raised by the same amount. As shown in Figure 17.2, an octahedral complex can be considered as a metal ion surrounded by six ligands that are located on the axes. 

Figure 9.9 An energy diagram showing how the energies of the electrons in a dw configuration are affected by spherical and octahedral electrostatic fields.

Figure 2.4 Relative energies of a transition metal 3d orbitals in octahedral coordination. (a) Energy levels of a free cation (b) electrostatic attraction between the cation and anions (c) repulsion between anions and electrons on the cation other than those in 3d orbitals id) repulsion between anions and the 3d electrons (e) splitting of 3d orbital energy levels in an octahedral crystal field (from Bums, 1985a).

Applying Eq. 31 to determine the splitting energies with pa representing the lanthanide cation offers an alternative computational strategy to address this problem. This type of application of Eq. 31 can be seen as the first-principles based realization of such past attempts to refine ligand-field theory which take into account non-electrostatic effects61. In octahedral environment, such as the one occur-... 

If the electrostatic field created by the point charge ligands is octahedral, the energy of the electrons in the 3d orbitals that point directly at the ligands is raised with respect to that in the spherical field, while the energy of the electrons in the orbitals that point between the Ugands is lowered with respect to the spherical field... 

Fig. 20-4. Energy-level diagrams showing the splitting of a set of d orbitals by octahedral and tetrahedral electrostatic crystal fields.

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