Factors Affecting the Magnitude Of Δo: - Coordination Chemistry | Inorganic Chemistry PDF Download

Factors Affecting Magnitude of ∆_o:

There are several factors which affect the magnitude of crystal field splitting (∆_o) of d orbitals. 

• Oxidation State of Metal Ion: The higher the oxidation state of metal ion, the greater will be the magnitude of crystal field splitting. For example, the values of crystal field splitt ing for Co²⁺ and Co³⁺ are given below.

∆_o for [Co(H₂O)₆] ²⁺ = 9200 cm^–1 
And ∆_o for [Co(H₂O)₆]³⁺ = 20760 cm^–1

This is because; the higher the o.s. of metal causes the ligands to approach more closely to it and, therefore, the more repulsion which causes more splitting.

• Nature of Ligands: The ligands are of two types, strong field ligands and weak field ligands. Generally, carbon and nitrogen donor ligands are considered as strong field ligands whereas oxygen and halogen donor ligands are termed as weak field ligands. The weak field ligands causes the small splitting because of low attraction (and therefore less repulsion) whereas strong field ligands causes more splitting due to strong attraction (therefore strong repulsion). The common ligands have been arranged in order of their increasing crystal field splitting power and this order is known as Spectrochemical Series.

CO > CN^– > R₃P > C₆H₅^–, CH₃^– > NO₂^– > Phen, bpy > NH₂OH > SO₃^2–, en > Py, NH₃ > gly > NCS^– > H₂O > O^2– > C₂O₄^2–, > C₂H₅OH > OH^– > urea > F > N₃^– > Cl^– > SCN^– >^– S^2– > Br^– > I^–

The order of field strength of the common ligand is independent of the nature of the metal cation and geometry of the complex. Usually,

Carbon donor > N-donor > O-donor > X-donor

•  No. of d-electrons: For a given series of transition elements (e.g. 3d series), in complexes having metal cation with the same o.s., the magnitude of ∆_o decrease with increase in no. of d electrons. For example, the crystal field splitting values for the following metal complexes are given below:
  ∆_o for [Co (H₂O)₆]²⁺ = 9200 cm^–1 (3d⁷)
  ∆_o for [Ni (H₂O)₆]²⁺ = 8500 cm^–1 (3d⁸)
  
  This is due to the fact that the higher no. of d electrons prevents the ligands to come closer to the metal cation. 

• Nature of the Series (n) of d Orbitals: In case of complexes having metal cations with same o.s. and same no. of d electrons, the magnitude of for analogous complexes within a given group increases from 3d to 4d to 5d.
  For example,
  For [Co (NH₃)₆]³⁺, ∆_o = 23000 cm^–1 (3d)
  For [Rh (NH₃)₆]³⁺, ∆_o = 34100 cm^–1 (4d)
  For [Ir (NH₃)₆]³⁺, ∆_o = 41200 cm^–1 (5d)
  
  This is because, on moving to 3d to 4d to 5d, the size of d orbitals increases and electron density decreases in them. Therefore the attraction increases between the d orbital and ligands. Consequently, the ligands approach more closely to the metal cation causes increase in crystal field splitting.
   
•  No. of Ligands: The magnitude of crystal field splitting increases with increase of the no. of ligands. For example,

∆_o > ∆_t

High Spin and Low Spin Complexes

We saw how to calculate the CFSE of complexes having metal ion of d¹, d² and d³ configurations. Let’s discuss how to calculate CFSE of higher d electron metal complexes. For a d4 ion, two arrangements are available: the four electrons ma y occupy the t 2g set wit h the configuration t²_g⁴e_g⁰, or may singly occupy four d orbitals i.e. t²_g³e_g¹. 

                      High spin configuration                                     Low spin configuration

First configuration is called high spin and the second is called the low spin.
High spin complexes or spin free complexes are formed in the presence of weak field ligands (oxygen and halogen donor ligands) while low spin or spin paired complexes are formed in the presence of strong field ligands (carbon and nitrogen donor ligands). In low spin complexes we forcibly pair up electrons. Hence pairing energy is introduced while calculating CFSE of low spin complexes according to the ground state configuration.

Pairing Energy: The energy required to pair up two unpaired electrons in a orbital is called pairing energy. It is denoted by P.
If ∆_o > P, low spin complexes are formed.
If ∆_o < P, high spin complexes are formed.
If ∆_o = P, high spin and low spin complexes exist in equilibrium.

CFSE in High and Low Spin Complexes: 

 d⁴ Configuration:

   d⁵ Configuration:

d⁶ Configuration:

Pairing energy is only taken for those electrons which are not paired in the ground state and we are forcibly pairing up them in the complex.

d⁷ Configuration:

d⁸ Configuration:

CFSE = 6 × (–0.4∆_o) + 2 × (0.6∆_o)
CFSE = –1.2∆_o
 

d9 Configuration:

CFSE = 6 × (–0.4∆_o) + 3 × (0.6∆_o)
CFSE = –0.6∆_o

d¹⁰ Configuration:

CFSE = 6 × (–0.4∆_o) + 4 × (0.6∆_o) = 0

The following table summarises the CFSE values of all the electronic configurations in an octahedral complex.