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Crystal Field Theory- Crystal Field Theory, Crystal Field Splitting, Crystal Field Splitting Energy, Practice Problems and FAQs

Crystal Field Theory- Crystal Field Theory, Crystal Field Splitting, Crystal Field Splitting Energy, Practice Problems and FAQs

Pauling and Slater are overjoyed with their accomplishments for VBT and went out to a beautiful place for vacations. Hans Bethe met with Pauling and Slater there and congratulated them on their endeavours. 'I am truly honoured to meet both of you,' he said. "May I ask you a quick question?" He went on to say, is it possible to predict the nature of a compound without using laboratory techniques, such as whether it is paramagnetic or diamagnetic, and why coordination compounds exhibit colours? What exactly are ligands? After listening to these questions, Pauling and Slater patted bethe on the back and smiled, saying, "We are waiting for you to find out the answers to these questions." So, Hans Bethe discovered the answer to all his questions.

Table of Contents

Crystal field theory

The interaction of metal ions with ligands is treated as a purely electrostatic event in crystal field theory, which treats the ligands as point charges in the region of the central atom's atomic orbitals. There are some basic assumptions which are listed below as

Assumption-1: The crystal field theory (CFT) is an electrostatic model.

The metal-ligand bond must be ionic, and the interactions must be entirely electrostatic, according to the electrostatic model.

Assumption-2: The transition metal is said to be a positive point charge that serves as the complex's core atom.

Assumption-3: The ligands are arranged around the core metal ion in such a way that there are fewer repulsions between these sites.

Assumption-4: It addresses the impact of ligands on the relative energies of the core metal atom/d-orbitals.Five d-orbitals (energy-identical orbitals) are degenerate in an isolated gaseous metal ion.

Assumption-5: If a spherically symmetrical field of ligands surrounds the metal atom/ion. This degeneracy is still maintained.

Degenerate d-orbitals of metal in free state and in complex

Crystal Field Splitting

Because d-orbitals have different orientations, they will interact with ligands in multiple ways. The orbitals heading in the direction of ligands will be more repelled, and their energies will be higher than if they were in a symmetrical field.

The orbitals lying away from the approach of the ligands will have fewer interactions with the negative charge of donor atoms, and their energies will be lower than they would be in a spherical field. As a result, the energies of the five d-orbitals will split up due to the electrical field of the ligands.

Crystal field splitting is the conversion of five degenerate d-orbitals of a metal ion into multiple sets of orbitals with varying energies in the presence of an electrical field of ligands.

Crystal field splitting in octahedral complex

As ligands are approaching from the axes, The repulsion between the electrons in metal 
d- orbitals and the ligands are greater when the metal d- orbital is directed towards the ligand than when it is directed away from the ligand in an octahedral entity. 
As a result, the dz2, dx2-y2 orbitals that point toward the axes along the ligand's direction will suffer more repulsion and gain energy than the dxy, dyz and dxz orbitals that point between the axes. 

Due to ligand electron-metal electron repulsions in the octahedral complex, the degeneracy of the d orbitals has been lifted, yielding three lower-energy t2g orbitals and two higher-energy eg orbitals.

Crystal field splitting in octahedral complex

Crystal Field splitting energy for octahedral complex

The energy difference between the two sets of energy levels is known as crystal field splitting energy and is written as o (the octahedral subscript 'o'). It evaluates the ligands' crystal field strength.

The average energy of the d-orbitals does not change as a result of the crystal field splitting. This is referred to as the barycentre rule.

This suggests that the three orbitals are -2/5 or -4 Dq below the average d-orbital energy, while the two d-orbitals are 3/5 o or 6Dq above it.

Crystal field splitting in tetrahedral complex

As ligands are approaching away from the axes, the dz2, dx2-y2 orbitals that point towards the axes will suffer lesser repulsion from ligands than the dxy, dyz and dxz orbitals that point between the axes in case of the tetrahedral complex. 

Due to ligand electron-metal electron repulsions in the tetrahedral complex, the degeneracy of the d orbitals has been reduced, yielding three higher-energy t2 orbitals and two lower-energy eorbitals.

The octahedral and square planar complexes with the centre of symmetry contain the 'g' subscript. The 'g' subscript is not utilized with energy levels because tetrahedral compounds lack symmetry.


Crystal Field splitting for tetrahedral complex

Crystal Field splitting energy for tetrahedral complex

The average energy of the d-orbitals does not change as a result of crystal field splitting as per the barycentre rule. This suggests that the three orbitals are 2/5 t or 4 Dq above the average d-orbital energy, while the two d-orbitals are -3/5 or -6 Dq below it.

The d orbital splitting is smaller in tetrahedral coordination entity generation than in octahedral field splitting due to less number of ligands. 

t = (4/9) o

Crystal Field Stabilization Energy(CFSE)

The energy levels in a chemical environment generally split as directed by the symmetry of the local field surrounding the metal ion. The difference in energy between the eg and t2g levels is denoted by or 10Dq. It is stated that each electron that enters the lower t2g level stabilizes the system by -4Dq and each electron that enters the eg level destabilises the system by +6Dq. That is, the t2g is reduced by 4Dq while the eg level is increased by +6Dq.

Spectrochemical Series

The nature of the ligands influences crystal field splitting (). The crystal field splitting generated by the ligand will be stronger the easier the ligand can approach the metal ion. Weak field ligands cause a little amount of crystal field splitting, whereas strong field ligands cause a large amount of splitting.

In general, ligands can be arranged in the following order of increasing field strength:

I< Br< SCN< Cl< S2- < F< OH< H2O < NCS< edta4- < NH< en < CN< CO

This type of series is known as a spectrochemical series.

High spin and Low spin complexes

Configuration

CFSE of Octahedral Complexes

CFSE of Tetrahedral Complexes

d1




(-4Dq)= -4 Dq



1(-6Dq)= -6 Dq

d2



2(-4Dq)= -8Dq



2(-6Dq)= -12 Dq

d3



3(-4Dq)= -12Dq



2(-6Dq)+4Dq= -8 Dq

In tetrahedral complexes, the orbital splitting energies are insufficiently large to force pairing, and low spin configurations are uncommon.

There are two possible electron distribution patterns for d4 ions. Which of these scenarios occurs is determined by the magnitude of the crystal field splitting, and the pairing energy, P. (P represents the energy required for electron pairing in a single orbital). 

There are two options:

(i) If o< P, the fourth electron enters one of the eg orbitals, resulting in high spin complexes formed by weak field ligands.

(ii) As o> P, it becomes more energetically advantageous for the fourth electron to occupy a t2g orbital resulting in low spin complexes formed by strong field ligands.

Configuration

CFSE of Octahedral Complexes

CFSE of Tetrahedral Complexes

d4



3(-4Dq)+6 Dq= -6Dq 4(-4Dq)= -16Dq

 



2(-6Dq)+2(4Dq)= -4 Dq

d5



3(-4Dq)+2(6 Dq)= 0 Dq 5(-4Dq)= -20Dq



2(-6Dq)+3(4Dq)= 0 Dq

d6



4(-4Dq)+2(6 Dq)= -4 Dq 6(-4Dq)= -24Dq



3(-6Dq)+3(4Dq)= -6 Dq

d7



5(-4Dq)+2(6 Dq)= -8 Dq 6(-4Dq)+6Dq= -18Dq



4(-6Dq)+3(4Dq)= -12 Dq

d8



6(-4Dq)+2(6Dq)= -12Dq



4(-6Dq)+4(4Dq)= -8 Dq

d9



 6(-4Dq)+3(6Dq)= -6Dq



4(-6Dq)+5(4Dq)= -4 Dq

d10



6(-4Dq)+4(6Dq)= 0 Dq


4(-6Dq)+6(4Dq)= 0 Dq

Limitation of Crystal Field theory

The following are some of CFT's limitations:

  • This theory only considers a central atom's d-orbitals. The s and p orbits are not considered in this study.
  • The theory fails to explain the behaviour of certain metals, which show significant splitting while others show minor splitting the g. The theory, for example, does not explain why H2O is a stronger ligand than OH-.
  • The possibility of p bonding is ruled out by the theory. Because it is found in many complexes, this is a significant disadvantage.
  • The orbits of the ligands are irrelevant in the theory. As a result, it cannot explain any ligand orbital properties or interactions with metal orbitals.

Related Video

Practice Problems

Q1. How many unpaired electrons are present in [CoF6]3- the complex?
A) 2

B) 3
C) 4
D) 5

Solution: The configuration of Co3+ in [CoF6]3- is 3d6. The ligand F- is a weak field ligand, Hence pairing will not occur in this case. So, this complex is a high spin octahedral complex. There are 4 unpaired electrons present in this complex. 

So, the correct answer is (C).

Q2. Calculate the number of unpaired electrons and CFSE in [Fe(CN)6]4- the complex?
A) 4, -4Dq
B) 5, -8Dq
C) 4, -4 Dq
D) 0, -24 Dq 

Solution: The configuration of Fe2+ in [Fe(CN)6]4- is 3d6. The ligand CN- is a strong field ligand, Hence pairing will occur in this case. So, this complex is a low spin octahedral complex. There are no unpair electrons present in this complex.

CFSE= 6(-4Dq) = -24 Dq
So, the correct answer is (D).

Q3. Calculate CFSE in [Ti(H2O)6]3+ the complex?
A) -4 Dq
B) -12 Dq
C) -8 Dq
D) 0 Dq 

Solution: The configuration of Ti3+ in [Ti(H2O)6]3+ is 3d1. The ligand H2O is a weak field ligand, Hence pairing will not occur in this case. So, this complex is a high spin octahedral complex. There is 1 unpaired electron present in this complex. 

CFSE= 1(-4Dq)= -4 Dq
So the correct answer is (A).

Q4. Calculate the CFSE in [CrCl6]3- complex?
A) -4 Dq
B) -12 Dq
C) -8 Dq
D) 0 Dq 

Solution: The configuration of Cr3+ in [CrCl6]3- is 3d3. In this case, the condition of nither low spin nor high spin complex occurs. There are 3 unpaired electron present in this complex. 

CFSE= 3(-4Dq)= -12 Dq
So the correct answer is (B).

Frequently Asked Questions

Question 1. What is the purpose of crystal field theory?
Answer. The breaking of degeneracies of electron orbital states, often d or f orbitals, triggered by a static electric field generated by a surrounding charge distribution is described by crystal field theory (CFT) (anion neighbours).

Question 2. Why is CFT better than VBT?
Answer. Valence Bond Theory detailed how orbitals combine during bond formation (VBT). The explanation was mostly based on principles of hybridization. While Crystal Field Theory describes how orbitals divide when ligands approach to metal, VBT failed to explain magnetic behaviour sufficiently. It couldn't explain how outer and inner orbital complexes formed. CFT, on the other hand, was quite clear.

Question 3. Are the CFT and LFT the same?
Answer. The main advantage of CFT is its simplicity. The more advanced Ligand Field Theory (LFT) is based on molecular orbital theory. It's more difficult, but it's also more accurate. LFT will not only get you to the right solution more frequently but it will also be built on true concepts.

Question 4. Why is crystal field theory important in chemistry?
Answer. The stability of complexes can be described using this approach. The larger the splitting energy of the crystal field, the more stable it is. This theory helps explain the colour and spectra of complexes. This hypothesis explains the magnetic characteristics of complexes.

Related Topics

Oxidation number of elements in coordination compounds

Organometallic Compounds

EAN Rule

Ligands

Bonding in coordination compounds

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