We know that, Valence bond theory consider the bonding between metal ion and the ligand as “purely covalent”. On the other hand crystal field theory considers the bond between metal ion and ligand as “purely Electrostatic”.

i.e. this theory assumes that metal ion and ligands act as Point charges and hence intraction between them is purely electrostatic.

•Central idea of this theory is that the electrons of the metal ion in the environment(electrical field) of other ions or ligands.

Basis of CFT

•Transition metal ion is surrounded by the ligands with lone pairs of electrons.

•All types of ligands are considered as point charges irrespective of their nature (Ionic or molecule).

•the bond between the metal and ligands is considered 100% ionic.

•The ligands surrounding the metal ion produce Electrical field and this electrical field influences the energies of orbitals of central metal ion(particularly d-orbitals).

•In case of Free metal ions all the five d-orbitals have the same energies ,called degenerate orbitals. On approach of ligands,the orbital electrons will be repelled by the lone pairs of the ligands. Since d-orbitals have different orientations ,these orbitals experience different intractions from the ligands.The orbitals lying in the direction of the ligands, will experience greater repulsion and their energies will be raised to greater extent.On the other hand, the orbitals lying away from the approach of the ligands will have lesser intractions and their energies will be raised to lesser extent.

Therefore,due to electrical field of ligands, the energies of five d-orbitals will split up,this splitting is called Crystal field Splitting.

•Crystal field splitting will be different in different structures with different number of ligands(coordination number ).

Now before discussing CFT ,we must have clear picture of d-orbitals to understand the splitting of orbitals.

Shape of d-orbitals

• dxy , dyz , dzx orbitals are similar and each consist of four lobes (lying in between the x and y axes) of high electron density lying in xy , yz, zx planes respectively.

•dx2-y2 orbital has also four lobes of high density along the principal axes x and y like dxy orbital but it is rotated through 45° around the z-axis.

•dz2 orbital consist of two lobes along the z-axis with a ring of high electron density in xy plane.

shapes of d orbitals

Note:- dz2 and dx2-y2 orbitals looks quite different but they are equivalent so far as interactions with the metal ions are concerned.

Crystal field splitting in Octahedral Complexes

In octahedral complex ,metal ion is at the centre of the octahedron and ligands are at the six corners along the three axes x,y,z. Let metal ion be Mn+ having d1 configuration ,when it is in free state ,electron can occupy and one of the d-orbitals because all are of same energy and are called degenerate orbitals.

However, in octahedral complex MX6 , all five d-orbitals will not remain of equal energy.this can be shown by comparison of arrangement of d-orbitals .

•two lobes of dz2 orbitals and four lobes of dx2-y2 orbitals point directly towards the corners of the octahedron, where -ve charges of ligands are concentrated.the remaining three orbitals are oriented in between the axes.this means that the electrons in dxy ,dyz ,dzx orbitals will be repelled less by -ve point charges of the ligands than those of dz2 and dx2-y2.

Thus 5 d-orbitals split up into two sets ,one set consisting 2 orbitals dx2-y2 and dz2 of higher energy, designated as “eg” and another set consisting of three orbitals (dxy,dyz,dzx) of lower energy & designated as “t2g”.

crystal field splitting in octahedral complexes

The energy difference between two set of d-orbitals; t2g and eg is called Crystal Field Splitting Energy .

For octahedral complexes it is repersented as ∆°.

Note:- Crystal field splitting occurs in such a way that the average energy of the d-orbitals does not change .this is known as “BarryCentre Rule” ,according to which decrease in energy of the set of orbitals that lie at the lower energy level must be balanced by corresponding increase in other set.

Crystal field stabilization energy(CFSE)

We know that electron always prefer to occupy of lower thus in octahedral field for each electron entering into the t2g orbital ,the crystal field stabilization is -4Dq and for each electron entering into the eg orbital the crystal field destabilization energy is +6Dq.

The amount of stabilization provided by splitting of the d-orbitals into two levels is called Crystal field stabilization energy.

•CFSE for d1 system having one electron is -4Dq,similarly for d2 and d3 systems CFSE is -8Dq & -12Dq.

For d4 system, there are two possibilities.
high spin low spin octahedral complexes

Configuration is decided on the basis of Splitting energy ∆° and pairing energy(P):the energy required to pair the electrons with one another.

•configuration t2g4 is possible if ∆° > P ,called strong field complex because ∆° is large. Here complex has less no. Of unpaired electrons (due to pairing) and called low spin complexes.

•Configuration t2g3eg1 is possible if ∆° P ,called weak field complex .here maximum number of electrons remain unpaired and complex is called high spin complex.

¶ Similarly strong field and weak field complexes are formed for d5,d6,d7 electronic configurations.

Note : d8, d9, d10 has only one possible electronic configuration.

Crystal Field Splitting in tetrahedral Complexes

Tetrahedral complex can be visualized by placing 4 ligands on four of the eight corners of the cube.the direction of X,Y,Z axis point to the centre of faces of cube.

crystal field splitting in tetrahedral complexes

Note :

•dxy ,dyz,dzx orbitals points in between X,Y,Z axis whereas the orbitals dx2-y2 and dz2 point along X,Y,Z axis.

•In tetrahedral field , none of the d-orbitals point exactly towards the ligands and therefore,the splitting of energy will be less than that of octahedral field.

•The three orbitals( dxy ,dyz, dzx) ,designated as ‘t2 are pointing close to the direction in which the ligands are approaching and become unstable and their energy raised. while two orbitals dx2-y2 and dz2 ,designated as ‘e’ are lying inbetween the ligands thus, their energies are lowered
And become stable.

crystal field splitting in tetrahedral complexes

*subsript ‘g’ is dropped in case of tetrahedral geometry as it has no centre of symmetry.

•the magnitude of Crystal field splitting is a difference between ‘e’ and ‘t2‘ orbitals and is designated as ∆t.

Crystal field splitting in tetrahedral is smaller than octahedral complexes.

t = 4/9 ∆°

Because ,(i)there are only 4 ligands in comparison to six in case of octahedral.Thus lesser ligands produce less crystal field splitting. Also (ii)None of the orbital is pointing directly towards the ligands,therefore splitting is less.

Since the magnitude of crystal field splitting in tetrahedral field is quite small and is always less than the pairing energy ,therefore ,the pairing of electrons will never be energetically favourable. thus,all the tetrahedral complexes are High spin complexes.

•No tetrahedral complex with low spin has been found to exist.

Crystal field spliting in tetrahedral and square Planar Complexes

The spliting of d orbitals in tetragonal and square planar complexes can be understood by withdrawing two trans ligands from an Octahedral complex.this process is called elongation.

Generally we consider the removal of trans ligands along the z-axis.As the ligands lying on z-axis are moved away ,the ligands in the XY plane tends to approach the central ion more closely.

As a Result of increase in M-L bond length along z-axis,the repulsion from the ligands to electrons in dz2 orbital decreases therefore its energy is decreased relative to that in octahedral field.At the sametime, M4-L bond along X and Y are shortened ,so that d-orbital in XY plane ,dx2-y2 experiences greater repulsion from the ligands and therefore its energy is raised.

Similarly, the dxz and dyz orbitals are lowered in energy because of decrease in repulsion effect along the z-axis while the energy of dxy orbital is raised. The Resulting splitting pattern Repersents Tetragonal Structure.

crystal field splitting in tetragonal and square pyramidal complexes

As the trans ligands lying along Z-axis are completely removed, a Square planar complex is formed. There is further rise in the energies of dx2-y2 and dxy orbitals and a further fall in the energies of dz2 ,dxz, dyz orbital.

•it has been observed that in squre planar Complex, the energy of dz2 orbital fall even below the dxy orbital.

crystal field splitting in tetragonal and square pyramidal complexes

CFT and magnetic properties of complexes

Magnetic properties depends on number of unpaired electrons and no. Of unpaired electrons in a given complex of known geometry can be easily predicted provided we know whether the complex is low spin or high spin.

•If P>∆°, the electrons will not pair up and the complex will be high spin complex.

•if ∆°>P ,the electrons will prefer to pair up and complex will be low spin complex.

Thus the complexes with weak ligand field are high spin complexes(Paramagnetic) and those with strong ligand field are low spin complexes (diamagnetic or low magnetic character).

Examples: Consider Complexes of Fe(iii) such as [Fe(CN)6]3- and [Fe(H2O)6]3+ , here Fe has 3d5 configuration in both case ,but as CN is strong field ligand it results into large splitting and hence pairing of electrons while H2O is weak field ligand which has small splitting of d-orbitals .thus electrons are not paired and complexes is paramagnetic with 5 unpaired electrons.

crystal field splitting in [Fe(H2O)6]3+ and [Fe(CN)6]3-

Example of [CoF6]3- and [Co(NH3)6]3+ complexes.

crystal field splitting in [Co(NH3)6]3+ and [Co(F)6]3-

Here cobalt is in +3 oxidation state with d6 electronic configuration. It has been observed that F ion is weak field ligand therefore complex will be high spin ie paramagnetic. Whereas NH3 is strong field ligand and electrons pair up and this results in a low spin complex.

Factors Determining the magnitude of Crystal field splitting

a)Nature of ligands :the greater the ease with which the ligands can approach the metal ion and intract with it ,greater will be the crystal field splitting energy.

Ligands which cause only small degree of crystal field splitting are called weak field ligands while those which cause a large value of ∆ are called strong field ligands.

•Small ligands can cause greater crystal field splitting bcoz they can approach the metal more closely. Example ,F ion produces more ∆ value large Cl and Br ions.

•ligands containing easily polarizable electron pair will be drawn more closely to the metal ion.

•ligands having tendency to form multiple bond cause more splitting. this is attributed to thr π bonding in metal.

Spectrochemical Series

:ligands can be arranged in increasing order of crystal field splitting ∆ .this order remain almost same for different metal ions.

I< Br< Cl < NO3 < F< OH< H2O< EDTA< Py~NH3< en< dipy< o-phen< NO2 < CN < CO

Spectrochemical arrangement of ligands

b) Oxidation state of metal ion: metal ion with higher oxidation state causes larger crystal field splitting than ion in lower oxidation state.

c)Type of d-orbitals : the extent of CFS for similar complexes of metal in the same oxidation state increased by about 30 to 50% on going from 3d-series to 4d-series or on going from 4d series to 5d series.

This is bcoz size of 4d-orbitals is bigger than 3d-orbitals. As a result ,4d orbitals can intract more strongly with the ligands and hence crystal field splitting is more.

Complex ion electronic configuration °(cm-1)
[Co(NH3)6]3+ 3d6 23000
[Rh(NH3)6]3+ 4d6 34000
[Ir(NH3)6]3+ 5d6 41000

d)Geometry of complex
Splitting energy of tetrahedral complexes is almost half the value for octahedral complex.

Limitations of CFT

a) it does not take into account the partial covalent character of M-L bonds.

b)it does not consider the multiple bonding (π bonds) between metal ion and the ligands.therefore it does not explain the formation of π bonding in complexes.

c) it does not explain the relative strengths of ligands. For example ,it does not explain why neutral water appears as stronger ligand in Spectrochemical series than negatively charged OH ion.

d) it consider only d-orbitals of metal ions and does not consider at all the other metal orbitals such as s, p orbitals .

e) it does not explain the charge transfer bands.