**12. Tanabe –Sugano diagrams**

12 Advanced Aspects of Spectroscopy

**d1, d9 d2, d8 d3, d7 d4, d6 d5**

*Configuration Free ion* 

**10. Energy level diagram** 

**11.1. Racah parameters** 

metal ion.

*ground state*

2D 3F 4F 5D 6S

*Crystal field substates* 

3T2g, 3A2g

4T2g, 4A2g

**Table 7.** Crystal field components of the ground and some excited states of dn (n=1 to 9) configuration

Energy Level Diagrams are described by two independent schemes - Orgel Diagrams which are applicable to weak field complexes and Tanabe –Sugano (or simply T-S) Diagrams

The inter-electronic repulsions within a configuration are linear combinations of Coulombic and exchange integrals above the ground term. They are expressed by either of the two ways: Condon - Shortley parameters, F0, F2 and F4 and Racah parameters, A, B and C. The

The Racah parameters are A, B and C. The Racah parameter A corresponds to the partial shift of all terms of a given electronic configuration. Hence in the optical transition considerations, it is not taken into account. The parameter, B measures the inter electronic repulsion among the electrons in the d-orbitals. The decrease in the value of the interelectronic repulsion parameter, B leads to formation of partially covalent bonding. The ratio between the crystal B**1** parameter and the free ion B parameter is known as nephelauxetic rato and it is denoted by β. The value of β is a measure of covalency. The smaller the value, the greater is the covalency between the metal ion and the ligands. The B and C values are a measure of spatial arrangement of the orbitals of the ligand and the

Racah redefined the empirical Condon –Shortley parameters so that the separation between states having the maximum multiplicity (for example, difference between is a function of 3F and 3P or 4F and 4P is a function of a single parameter, B. However, separations between

2T2g, 2Eg 3T1g,

5T2g, 5Eg 6A1g

4T1g,

which are applicable to both weak field and strong field complexes.

magnitude of these parameters varies with the nature of metal ion.

**11. Inter-electronic repulsion parameters** 

terms of different multiplicity involve both B and C

*Important excited states* 

3P 4p *Crystal field state* 

3T1g 4T1g

Exact solutions for the excited sate energy levels in terms of Dq, B and C are obtained from Tanabe-Sugano matrices. However, these are very large (10 x 10) matrices and hand calculations are not feasible. For this reason Tanabe-Sugano have drawn energy level diagrams known as T-S diagrams or energy level diagrams. The T-S diagrams are valid only if the value of B, C and Dq ae lower for a complex than for the free ion value.

Quantitative interpretation of electronic absorption spectra is possible by using Tanabe – Sugano diagrams or simply T-S diagrams. These diagrams are widely employed to correlate and interpret spectra for ions of all types, from d2 to d8. Orgel diagrams are useful only qualitatively for high spin complexes whereas T-S diagrams are useful both for high spin and low spin complexes. The x-axis in T-S diagrams represent the ground state term. Further, in T-S diagrams, the axes are divided by B, the interelectronic repulsion parameter or Racah Parameter. The x-axis represents the crystal field strength in terms of Dq/ B or Δ / B and the Y-axis represents the energy in terms of E/B.

The energies of the various electronic states are given in the T-S diagrams on the vertical axis and the ligand field strength increases from left to right on the horizontal axis. The symbols in the diagram omit the subscript, g, with the understanding that all states are *gerade* states. Also, in T.S. diagrams, the zero of energy for any particular dn ion is taken to be the energy of the ground state. Regardless of the ligand field strength, then, the horizontal axis represents the energy of the ground state because the vertical axis is in units of E/B and x-axis is also in units of Δ /B. Thus, the unit of energy in T-S diagram is B, Racah Parameter.

The values of B are different for different ions of the same dn (or different dn configuration) which is shown on the top of each diagram. One T-S diagram is used for all members of an isoelectronic group. Also some assumption is made about the relative value of C/B.
