The d Orbitals in an Octahedral Field

The energy difference between the two sets of d orbitals, labeled lODq or is called crystal field splitting in octahedral field. The quantity Dq or I/IOAq is called the crystal field parameter in octahedral field. The magnitude of this parameter depends on a) the nature of central metal ion b) the charge of metal ion and c) the nature of the ligand. 

The crystal field stabilization energy (CFSE) is the energy with which a certain electrostatic configuration is stabilized upon d orbitals splitting. 

The relative energy of the Og and tjg compared to d orbitals before splitting can be calculated based on an ion with configuration. When this ion is introduced in an octahedral field created by 6 ligands, the five d orbitals are split in t2g and eg levels. Because the energetic level eg is higher than the energetic level t2g, the four electrons 

In the case of d d, and configurations, the first three electrons successively occupy the orbitals from the t2g group, according to the Hund rule. The values of CSFE are -4Dq, -8Dq, and -12Dq, respectively. The d , d, d, (T configurations of the associated electrons involve two possible position modes either in the eg orbitals, with uncoupled spin, or in the t2g orbitals with coupled electronic spins. 

From these different arrangements, two types of complexes can be formed high-spin complexes with uncoupled d electrons, and low-spin complexes with coupled d electrons. The crucial factor that occurs in these situations is the spin-pairing energy (P) as follows  

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Electron arrangements in the d orbitals in an octahedral field with maximum number of unpaired electrons for the d1 - d10 systems. 

Similar energy level diagrams may be drawn for dn systems in tetrahedral crystal fields. There is an interesting relationship between these and the ones for certain systems in octahedral fields. We have already seen that the splitting pattern for the d orbitals in a tetrahedral field is just the inverse of that for the d orbitals in an octahedral field. A similar inverse relationship exists between the energy level diagrams of dn systems in tetrahedral and octahedral fields. The components into which each Russell-Saunders state is split are reversed in their energy order in the tetrahedral compared to the octahedral... 

Figure 120 The splitting of the d-orbitals in an octahedral field. In an isolated ion, the d-orbitals have the same energies (l h), but as the ion begins to be surrounded by six anions the energies of aU of the orbitals increase. If the charge of the anions were somehow dispersed over a sphere, the energies of the d-orbitals would still be degenerate (middle). When the anions are positioned at the cornax of an octahedron, the degeneracy of the orbitals is broken and two sets of energy levels are formed.

Using crystal field theory, sketch the energy-level diagram for the d orbitals in an octahedral field then fill in the electrons for the metal ion in each of the following complexes. How many unpaired electrons are there in each case a. V(CN)6 ... 

A low-spin to high-spin transition relates to the crystal field splitting of the d-orbitals in an octahedral or tetrahedral crystal field. However, even in cases where the energy difference between two spin states is much larger, electronic transitions are observed. An atom with total spin quantum number S has (22 + 1) orientations. In a magnetic field the atom will have a number of discrete energy levels with... 

Figure 18 Complete set of d orbitals in an octahedral field. The et orbitals are shaded and the 2g orbitals are unshaded.

FIGURE 16.33 The energy levels of the d-orbitals in an octahedral complex, with the ligand field splitting A0. Each box (that is, orbital) can hold two electrons. 

Figure 1-4. The splitting of the d orbitals in an octahedral crystal field. The total splitting is given by the quantity Aoct.

Figure 3.7 (a) Splitting of the real ti-orbitals in an octahedral field (b) Relationship between real and complex d-orbitals in an octahedral field... 

Figure 22.16 The five d orbitals in an octahedral field of ligands. The direction of ligand approach influences the strength of repulsions of electrons in the five metal d orbitals. A, We assume that ligands approach a metal ion along the three linear axes in an octahedral orientation. B and C, Lobes of the and d orbitals lie directly in line with the approaching ligands, so repulsions are stronger. D to F, Lobes of the d y, dyy, and dy2 orbitals lie between the approaching ligands, so repulsions are weaker.

Figure 22.16 The five (/orbitals in an octahedral field of ligands. A, Ligands approach along the x, y, and zaxes. B and C,The dj(2 y2 and orbitals point directly at some of the ligands. D to F,The d, d, and orbitals point between the ligands.

If you look at the five d orbitals in an octahedral field (electric field of octahe-drally arranged charges), you see that you can divide them into two sets. Orbitals d 2 and d -y are directed toward ligands, and orbitals dy, and d z are directed... 

Ligand field theory allows for coordinate bonding and gives the same description for the splitting of d-orbitals in complexes. For example, it predicts the d-orbitals in an octahedral... 

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