2. CRYSTAL FIELD SPLITTING

CRYSTAL FIELD SPLITTING 

Before the study of this topic we have first know about the spatial orientation of d- orbitals. The five d orbitals can be designated as follow

The first three orbital are oriented in between the XY, YZ, ZX axes respectively and these three orbital are called t2g or dE and the rest two orbitals are oriented along the XY and Z axes respectively and are known as eg  or dr.

Now we will discuss about our topic which is CRYSTAL FIELD SPLITTING,  in the absence of any ligands or in the case of free metal ion, all the five d-orbitals have the same energy and the orbitals having the  same energy are called degenerate orbitals. However in the approach of the ligands, the orbital electrons will be repelled by the lone pair (or negative charge) of the ligands. The repulsion will raise the energy of d-orbitals, the energy of each orbital will increase by the same amount, due to spherical field or symmetrical field of ligands. Therefore these orbitals will still remain degenerated, but they will have higher energy than that of the free ion. But we know that d-orbitals have different orientations and therefore, these orbitals will experience different interactions from the ligands due to which the d-orbitals can be divided into two or more group such division of d-orbitals into these groups are known as crystal field splitting.

There are different kinds of splitting on the basis of the shape of complex, which are as follow.

Crystal field splitting in Octahedral Complexes 

In the octahedral the ligands occupy the six corner of the octahedron, as shown in fig.

Since the ligands are attached at the axes of the central metal atom or ion so those orbitals will affected much which lie along the axes of central metal atom or ion i.e. eg  as a results the energy of these orbital will be raised to the same extant. The other three orbitals t2g which are present between the axes will undergo repulsive interaction to lesser extant and their energy will be lowered to the same extant .

Note - the energy difference between the split up orbit sets is called 'Crystal Field Stabilizing Energy'
that we will discus below.

Crystal field splitting in tetragonal Complexes

The distorted octahedral is called the tetrahedron
In actual tetragonal is slightly differ from the octaheadral fashion in the tetragonal the distance of one pair of ligands attached to the ends of one axis (say z-axis) of octahedral is greater or lesser than the rest two axis. So in this fashion energy of d orbitals attached to the z axis will be vary to the rest orbitals in each type of t2g and eg . This distortion may take place in two ways
i) elongation
ii) compressed

i) elongation

In this tetragonal the distance of one pair of ligands attached to the ends of one axis (say z-axis) of octahedral is greater than the rest two axis. So in this fashion energy of d orbitals attached to the z axis will be decrease to the rest orbitals in each type of t2g and eg . 

Hence the energy order of d orbital will become dx2-y2>dz2>dxy>dyz=dzx.

ii) compressed

In this tetragonal the distance of one pair of ligands attached to the ends of one axis (say z-axis) of octahedral is lesser than the rest two axis. So in this fashion energy of d orbitals attached to the z axis will be increase to the rest orbitals in each type of t2g and eg . 

Hence the energy order of d orbital will become dz2>dx2-y2>dyz=dzx>dxy.

FOR MORE DETAIL RELATED TO ELONGATED OCTAHEDRAL CLICK HERE 

Crystal field splitting in square planner

In the square planner geometry of the coordination compounds the ligands are not present in the z-axis, it exist only at the ends of x and y axes respectively. So the energy of the orbitals containing the z-axis gets lower repulsion and hence the decreasing order of energy will be,

dx2-dy2>dxy>dz2>dyz=dzx

Crystal Field Splitting in Tetrahedral Geometry-

In the tetrahedral geometry the ligands exist at the middle of the axis so the t2g orbitals will experience more repulsion as the eg. Thus the energy of of t2g orbitals is greater than that of the eg orbitals so their decreasing order of energy is 

dxy = dyz= dzx > dx2-y2 = dz2

        

           Tetrahedron inside a cube                                                          Crystal Field Splitting in tetrahedral 

Crystal Field Splitting in Square Pyramid-

In square pyramid the five ligands exist at the ends of the coordinate axes except the one end of the z-axis as shown in figure

According to the above fig. the repulsion at the ends of axes will be grater than between the axis. Hence their energy order is

dx2-y2  > dz2 > dxy > dyz= dzx 

Crystal Field Splitting in Trigonal Bi-pyramidal Geometry-

In trigonal bi-pyramidal geometry there are 5 ligands present, two of them exist at one end of the Z-axis e.g. dz2, one of them exists at the end of X or Y- axis e.g. dX2-Y2 by making an angle of 900 with dz2 and the remaining two exist in the XY- plane e.g dxy by making an angle of 1200 with the orbital dX2-Y2 as shown in figure. So the decreasing order of energies of these orbital will be.

dz2 > dX2-Y2 = dxy > dzx = dyz

Crystal Field Splitting in Trigonal Planar Geometry

In this type of geometry there are three ligands are attached to the central metal atom or ions. Out of which one lignad is attached to the end of either X or Y axis e.g. dx2-dy2. and the rest two will be lie on XY plane e.g. dxy. So the decreasing order of energies of these orbital will be.

dX2-Y2 = dxy > dz2 > dzx = dyz

Here we are in confusion why is the energy of dz2 is greater than that of the dzx = dyz?

The reason is that -

dz2has a central ‘hoop’ that is still pointing towards the ligands in the xy plane while the other two have a nodal plane in the xy plane. Thus, the later two should have a lower energy. The reason is applicable for the square planner structure.

Crystal Field Splitting in Linear Geometry

In linear geometry the lignads will attached to the ends of z-axis only, so the energy of z2 orbital will be greater to the other orbitals and the decreasing order of their energy is given by

dz2 > dzx = dyz > dX2-Y2 = dxy