Electronic d orbitals

Population of Electronic d Orbitals in Different Idealized Symmetries... 

An inverse relationship also exists between fields of octahedral and tetrahedral symmetries. We saw earlier in this chapter that crystal fields of these two symmetries produce inverse splitting patterns for one-electron d orbitals. This relationship also holds when electron-electron repulsions are added to the picture any free-ion term will be split into the same new terms (except for g and u designations, which are inappropriate for tetrahedral complexes) by tetrahedral and octahedral fields, but the energy ordering will be opposite for the two symmetries. 

Geometric Dependence of Spin-Allowed Ligand Field Transitions Ligand field theory quantitates the splittings of the one-electron d-orbitals due to their repulsion/antibonding interactions with the ligands. 

So how is an electron configuration written First, the number of total electrons must be determined. This is the equal to the mass number for neutral atoms. For ions, the total electron is corrected for the charge (add electrons for anions subtract electrons for cations). The electrons are added according to Hund s rule and the Aufbau principle. Figure 10.3 describes the order in which the electrons are added. Keep in mind the maximum number of electrons in each type of orbital s orbitals hold two electrons, p orbitals hold six electrons, d orbitals hold ten electrons, and f orbitals hold 14 electrons. 

Figure 10. Plots of the one-electron d-orbital energies versus distortion angle values with allowance for 7t-bonding at = 0 (1, 4, and 7), = +0.1 (2, 3, and 8),...

In tetragonal fields the energies and symmetry designations of the one-electron d orbitals are as follows ... 

As for the valence band, the picture is relatively complicated. Considering a single hole near the top of the Fg valence band (for zinc blende crystal structure) and the magnetic ion with five d orbitals occupied by N electrons, the Hamiltonian that is applicable would have ionic, crystal, and hybridization components. The p-d hybridization mediated kinetic exchange depends on the filling of only the orbitals, not all the one-electron d-orbitals of the magnetic ion. The spin-dependent part of the exchange Hamiltonian for interaction between the Fg valence band p-like electrons and all the three d-orbitals occupied by one electron can be described as... 

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