Orgel Diagram Postulates and Applications

Orgel Diagram, Postulates and Applications

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 d10-n of the tetrahedral field.
e. dn of the tetrahedral field is same as that of d10-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- T2g and Eg while 'F' term splits into three energy levels- T1g, T2 and A2g. 'F' term has also the nearest excited state 'P' term. The 'G' term splits into four energy levels- A1g,Eg,T2g and T1g.
Splitting of Term D, F and G

Spin multiplicity value should be written in a particular configuration e.g. 3T1g, 4A2g 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

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

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 2T2g and the tetrahedral ground term is 2Eg.
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/Bfree ion.
β is called naphelauxetic ratio.