**9. Splitting of energy states**

10 Advanced Aspects of Spectroscopy

For high spin complexes,

**Table 5.** λ and ζ values for 3d series

removed. There are two processes by which i is removed.

*8.3.2. La Porte selection rule* 

upon the energy difference in the orbital states and magnitude of spin –orbit coupling constant. Therefore electronic transitions occur between different states of spin multiplicity and also between states in which Δ L is not equal to ± 1. For example, if the ground state were 99% singlet and 1% triplet (due to spin– orbit coupling) and the excited state were 1% singlet and 99 % triplet, then the intensity would derive from the triplet –triplet and singlet-singlet interactions. Spin-orbit coupling provides small energy differences between degenerate state.

This coupling is of two types. The single electron spin orbit coupling parameter ζ, gives the strength of the interaction between the spin and orbital angular momenta of a single electron for a particular configuration. The other parameter, λ, is the property of the term.

> 2*S*

Here positive sign holds for shells less than half field and negative sign holds for more than half filled shells. S is the same as the one given for the free ion. The λ values in crystals are close to their free ion values. Λ decreases in crystal with decreasing Racah parameters B and C. For high spin d5 configuration, there is no spin orbit coupling because 6S state is

unaffected by the ligand fields. The λ and ζ values for 3d series are given in Table-5.

Ion Ti(II) V(II) Cr(II) Mn(II) Fe(II) Co(II) Ni(II) Ξ (cm-1) 121 167 230 347 410 533 649 λ(cm-1) 60 56 57 0 -102 -177 -325

Physically 3d (even) and 4p (odd) wave functions may be mixed, if centre of inversion (i) is

a. The central metal ion is placed in a distorted field (tetrahedral field, Tetragonal distortions, etc.,) The most important case of distorted or asymmetric field is the case of a tetrahedral complex. Tetrahedron has no inversion centre and so d-p mixing takes place. So electronic transitions in tetrahedral complexes are much more intense, often by a factor 100, than in a analogous octahedral complexes. *Trans* isomer of [Co(en)2Cl2] + in aqueous solution is three to four times less intense than the *cis* isomer because the former is centro-symmetric. Other types of distortion include Jahn –Teller distortions. b. Odd vibrations of the surrounding ligands create the distorted field for a time that is long enough compared to the time necessary for the electronic transition to occur (Franck Condon Principle).Certain vibrations will remove the centre of symmetry. Mathematically this implies coupling of vibrational and electronic wave functions. Breaking down of La Porte rule by vibrionic coupling has been termed as "Intensity Stealing". If the forbidden excited term lies energetically nearby a fully allowed transition, it would produce a very intense band. Intensity Stealing by this mechanism decreases in magnitude with

increasing energy separation between the excited term and the allowed level.

The symbols **A**(or **a**) and **B** (or **b**) with any suffixes indicate wave functions which are singly degenerate. Similarly **E** (or **e**) indicates double degeneracy and **T** (or **t**) indicates triple degeneracy. Lower case symbols, **a1g**, **a2g**, **eg**, etc., are used to indicate electron wave functions(orbitals) and upper case symbols are used to describe electronic energy levels. Thus **2T2g** means an energy level which is triply degenerate with respect to orbital state and also doubly degenerate with respect to its spin state. Upper case symbols are also used without any spin multiplicity term and they then refer to symmetry (ex., **A1g** symmetry). The subscripts **g** and **u** indicate *gerade* (even) and *ungerade* (odd).

**d** orbitals split into two sets - **t2g** orbitals and **eg** orbitals under the influence crystal field. These have **T2g** and **Eg** symmetry respectively. Similarly **f** orbitals split into three sets - **a2u** (**fxyz**) , **t2u** (**fx (y2- z2)** , **fy (z2-x2), fz (x2-y2**) and **t1u** ( **fx3** , **fy3** , **fz3**). These have symmetries **A2u**, **T2u** and **T1u** respectively.

Splitting of **D** state parallels the splitting of **d** orbitals and splitting of **F** state splits parallels splitting of **f** orbitals. For example, **F** state splits into either **T1u**, **T2u** and **A2u** or **T1g**, **T2g** and **A2g** sub-sets. Which of these is correct is determined by **g** or **u** nature of the configuration from which **F** state is derived. Since **f** orbitals are **u** in character **2F** state corresponding to **f1** configuration splits into **2T1u**, **2T2u**, and **2A2u** components; similarly **3F** state derived from **d2** configuration splits into **3T2g**, **3T1g** and **3A2g** components because **d** orbitals are **g** in character.
