Factors Affecting the magnitude of ∆

There are several factors that affect the magnitude of splitting (0)of d-orbitals by the surrounding ligands.

1. Oxidation State of the Metal Cation:

The higher the oxidation state of the metal cation, the greater will be the magnitude of ∆. The higher the oxidation state of the metal causes the ligand to approach more closely to it and, therefore the ligand causes more splitting of metal d-orbitals.
     For example               ∆0 for [Co(H2O)6]2+ = 9200 cm-1
             and                     ∆0 for [Co(H2O)6]3+ = 20760 cm-1

2. Same Oxidation State of Metal Cation but the number of d-electrons is                   Different:

In general, for a given series of transition elements(say 3d-series), in complexes having the metal cation with the same oxidation state but the different number of electrons in the d-orbitals, the magnitude of  decreases with increase in the number of d-electrons. It is due to the fact that the higher number of d-electrons prevents the ligands to come closer to the metal cation.
                                 For example        0 for [Co(H2O)6]2+ = 9200 cm-1(3d7)
                                        and                ∆0 for [Ni(H2O)6]2+ = 8500 cm-1(3d8)

3. Principal Quantum Number(n) of the d-orbital of the Metal Cation:

In case of complexes having the metal cation with the same oxidation states and the same number of d-electrons, the magnitude of for analogous complexes within a given group increases about 30% to 50% from 3d to 4d and by about the same amount from 4d to 5d. It is because:
  (1) On moving from 3d to 4d and 4d to 5d, the size of the d-orbital increases and electron density              decreases in them. Therefore the ligands can approach the metal cation with larger d-orbital                more closely.
  (2) There is less steric hindrance around a larger metal cation.
        For example      ∆0 for [Co(NH3)6]2+ = 2300 cm-1 
                                  ∆0 for [Rh( NH3)6]2+= 34100 cm-1 
                                  ∆0 for [Ir( NH3)6]2+= 41200 cm-1 

 4. Nature of Ligands:

The ligands are classified as a weak and strong ligand. The ligand which causes a small degree of splitting of d-orbitals are called weak ligands and the ligands which cause a large splitting are called strong ligands. The common ligands have been arranged in order of their increasing crystal field splitting power to cause splitting of d-orbitals from a study of their effects on the spectra of transition metal ions.
(weak end)O22−< I < Br < S2− < SCN (S–bonded) < Cl− < N3 < F< NCO < OH < C2O42− < H2O < NCS (N–bonded) < CH3CN < gly (glycine) < py (pyridine) < NH3 < en (ethylenediamine) < bipy (2,2′-bipyridine) < phen (1,10-phenanthroline) < NO2 < PPh3 < CN < CO < CH2(strong end)
 This order s usually called as Spectrochemical series
The order of the field strength of common ligands is independent of the nature of the metal cation and the geometry of the complex.

5. Number of Ligands:

The magnitude of crystal field splitting(∆)increases with the increase of the number of ligands.For example  > ∆t
 Though the number of ligands in a square planar complex is smaller than that of octahedral complexes, the magnitude of  ∆sp is greater than ∆0. It is because of the fact that square planar complexes are formed by much strong ligands with dmetal cation of 3d-series transition metal cation and 4d and 5d series d8metal cation with either weak or strong ligand. The very strong ligands and 4d or 5d series transition metal cations are responsible for higher crystal field splitting. Also in square planar complexes of dmetal cation, the dZ2 orbital with two electrons is stabilized and the vacant dX2-y2 orbital is destabilized.

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