Orgel Diagram, Postulates and Applications

Postulates of Orgel Diagram

Followings are the main postulates of Orgel Diagram-

1. Orgel diagrams cover only the high spin cases.
2. Orgel diagrams are only for the quantative purpose.
3. Orgel diagrams include two sets of graphs which include all the high spin cases of octahedral and tetrahedral complexes.
4. The following relationships are valid for the Orgel diagrams.
a. dⁿ and dⁿ⁺⁵ have the same diagram for octahedral field.
b. dⁿ and dⁿ⁺⁵ have the same diagram for tetrahedral field.
c. dⁿ and dⁿ⁺⁵ in an octahedral field is reverse to that of dⁿ and dⁿ⁺⁵ for a tetrahedral field.
d. dⁿ of octahedral field is same as that of d^10-n of the tetrahedral field.
e. dⁿ of the tetrahedral field is same as that of d^10-n of the octahedral field.

Orgel diagrams are correlation diagrams which show the relative energies of electronic terms in transition metal complexes and is restricted to only show weak field (i.e. HIGH SPIN) cases, and offer no information about strong field (i.e. LOW SPIN) cases. Orgel diagrams are qualitative, so, energy calculations can not be performed from these diagrams, also, Orgel diagrams only show the symmetry states of the highest spin multiplicity instead of all possible terms. Orgel diagrams will, however, show the number of spin allowed transitions, along with their respective symmetry designations.

In an Orgel diagram, the parent term (P, D, or F) in the absence of ligand field is located in the center of the diagram, with the terms due to that electronic configuration in a ligand field at each side. Spectroscopic term 'S' does not split in crystal field because the sum of the energy in three dimensions turns out to be zero. 'D' term splits into two energy levels- T_2g and E_g while 'F' term splits into three energy levels- T_1g, T₂ and A_2g. 'F' term has also the nearest excited state 'P' term. The 'G' term splits into four energy levels- A_1g,E_g,T_2g and T_1g.


Spin multiplicity value should be written in a particular configuration e.g. ³T_1g, ⁴A_2g etc.
If two systems have n₂ + n₁ = 10, then the term splitting is reverse and if n₂ − n₁ = 5, then term splitting is similar to each-other, where n₁ and n₂ are the number of electrons in two systems.
Reverse Splitting Patter occurs in the given d-system(configuration)-
d¹ and d⁹
d² and d⁸
d³ and d⁷
d⁴ and d⁶

Similar Splitting Patter occurs in the given d-system(configuration)-
d⁶ and d¹
d⁷ and d²
d⁸ and d³
d⁹ and d⁴

Splitting in tetrahedral field is reverse to that in octahedral field. Subscripts 'g' is omitted in tetrahedral field as tetrahedral molecule does not have the centre of inversion.


There are two Orgel diagrams, one for d¹, d⁴, d⁶ and d⁹ configurations and the other with d², d³, d⁷ and d⁸ configurations.

'D' Term Orgel diagram

On the left hand side d¹, d⁶ tetrahedral and d⁴, d⁹ octahedral complexes are covered and on the right hand side d⁴, d⁹ tetrahedral and d¹, d⁶ octahedral. For simplicity, the 'g' subscripts required for the octahedral complexes are not shown.

'F' Term Orgel diagram

On the left hand side, d², d⁷ tetrahedral and d³, d⁸ octahedral complexes are covered and on the right hand side d³, d⁸ tetrahedral and d² and high spin d⁷ octahedral. Again for simplicity, the 'g' subscripts required for the octahedral complexes are not shown.

Applications of Orgel Diagram

The Orgel diagram is very useful as it gives us following informations-
1. Ground term in weak crystal field can be obtained e.g. for d¹ system, the octahedral ground term is ²T_2g and the tetrahedral ground term is ²E_g.
2. Since the energy of the ground term in crystal field is the crystal field stabilisation energy (CFSE), hence one can find out the value of CFSE with the help of Orgel diagram e.g. the CFSE value for octahedral field of d¹ system is −4 Dq and of d² system is −6 Dq.

3. One can predict the variation in magnetic moment value with the help of this diagram.
4. It helps us in predicting the distortion in geometry of complexes.
5. With the help of Orgel diagram, it is possible to predict the number of d-d transitions.
Since Orgel diagram does not consider the Racah parameters B & C so it is not fully valid for the system having excited term 'P' e.g. d², d³, d⁷ and d⁸. However it is valid for d¹, d⁹, d⁴ and d⁶ systems where Racah parameters are of no importance.

Limitations of Orgel Diagram

Orgel diagrams are restricted to only show weak field (i.e. high spin) cases, and offer no information about strong field (low spin) cases. Orgel diagrams will, however, show the number of spin allowed transitions, along with their respective symmetry designations.

Orgel diagram does not take into consideration electron repulsion parameters B and C (Racah parameters). Energy of the free ion terms varies with B and C.
Energy difference between terms of same spin multiplicity is function of B, but between different multiplicity is function of both B and C.
For first transition series B =1000cm^-1 and C/B = 4 i.e. C = 4000cm^-1

As energy of the free ion terms vary due to B and C, the energy of the split terms is also affected in the crystal field. For d¹ and d⁹ system there is only one term ²D, for d⁴ and d⁶ system the excited triplet terms are at much high energy relative to ground ⁵D term and so for d¹, d⁹, d⁴ and d⁶ system, inter electronic repulsion parameters are not of importance and Orgel diagram is valid for these.
For d², d³, d⁷ and d⁸ system, there is ^XP excited term near the ^XF ground term and interelectronic repulsion parameter affect the energy of the free ion terms as well as energy of the split free ion terms in crystal field.
Hence, Orgel diagram is not fully valid for these systems.

Racah Parameters

Racah parameters are measures of the energy separations of the various Russell-Saunders states of an atom. The energy differences between states of the same spin multiplicity are, in general, multiple of B only i.e. nB, where 'n' is an integer, whereas the differences between states of different multiplicity are expressed as sum of multiples of both B and C. Both n and B vary for different ions and in case of Ni⁺², the energy difference between ³F and ³p is 15B.
The same term adjusted for the complex is 15B' where B' is the effective value of the Racah inter electronic repulsion parameter in the complex,
β = B^'_complex/B_{free ion}.
β is called naphelauxetic ratio.