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Crystal Field Theory or (CFT)

What is Crystal Field Theory or CFT?

The valence bond approach does not explain to us the Electronic spectra, Magnetic moments, and Reaction mechanisms of the complexes. Hence Crystal Field Theory was designed to overcome the limitation of valance Bond Theory (VBT). Crystal Field Theory (CFT) is commonly used for explaining the bonding in coordination complexes. It explains many important properties of transition-metal complexes, including their colors, magnetism, structures, stability, and reactivity which were not explained by VBT. The central assumption of CFT is that metal-ligand interactions are purely electrostatic in nature. Interaction between metal ions and legends is the backbone of this theory.

Crystal Field Splitting (CFS)

Define Crystal field Splitting or CFS.

Splitting of the five degenerated orbitals of the free metal ion by the ligand field into two groups, having different energies is called Crystal field splitting or CFS.

Crystal Field Splitting in Octahedral complexes

Explain in brief crystal field splitting in the octahedral complexes.

  1. In an octahedral complex, the metal ion is at the center of the regular octahedron and ligands are at the six corners of the octahedron along the X, Y, and Z axes.
  2. In free metal ion, all the five d-orbitals have the same energy i.e. they are degenerate (State-I). As the ligands approach the central metal ion, repulsion will take place between metal electrons and the negative electric field of ligands. This repulsion will raise the energy levels of d-orbitals. If all the ligands approaching metal ion are at an equal distance from each of the d-orbitals, then the energy of each d-orbital will increase by the same amount i.e. they will remain still degenerate (State-II). However, this is only a hypothetical situation.
  3. Because of different directional properties, the five d-orbitals will be repelled to different extents. Therefore their energies no longer remain the same but split up into two sets of orbitals called t2g and eg. The t2g orbitals include dxy, dyz and dxz orbitals while “eg” orbitals include dx2-y2 and dz2orbitals.
  4.  ‘t2g’ orbitals, which lie in between the axes do not face the ligands directly and hence will experience less repulsion. Therefore ‘t2g’ orbitals will be lowered in energy by 4Dq relative to barycenter. ‘eg’ orbitals which lie along the axes, face the ligands directly and hence will experience more repulsions. Therefore ‘eg’ orbitals will be raised to a higher energy level by 6Dq relative to the barycenter.
  5. The difference in energy between the t2g and eg sets of d-orbitals is denoted by 10 Dq or ∆o and is called crystal field splitting energy in Octahedral complexes (State-III).
Crystal field splitting in octahedral complex
Crystal field splitting in an octahedral complex

Weak and strong field ligands

What are Weak and strong field ligands?

Ligands that produce weak fields and cause a smaller degree of splitting of d-orbitals are called weak field ligands. Examples, are F-, OH-, and H2O. Ligands that produce a strong field and cause a larger degree of splitting of d-orbitals are called strong field ligands. Examples, are CN and CO.

Crystal Field Stabilization Energy (CFSE)

What is Crystal Field Stabilization Energy? or What is CFSE?

The decrease in energy achieved by preferential filling of the lower energy d-levels is known as Crystal Field Stabilization Energy

Crystal Field Stabilization Energy C.F.S.E. for the Octahedral complexes with d1 to d10 Configuration.

Crystal Field Stabilization Energy for the various configurations in the Octahedral field can be calculated by, CFSE formula:-

C.F.S.E.  = x (-4Dq) + y (+6Dq) + P

Where,

x= number of electrons in t2g orbitals.

y = number of electrons in eg orbitals

P = Pairing energy

Crystal field splitting in octahedral complex d1
Crystal field splitting in octahedral complex d2
Crystal field splitting in octahedral complex d3
Crystal field splitting in octahedral complex d4
crystal field splitting in octahedral complex d5
crystal field splitting in octahedral complex d6
Crystal field splitting in octahedral complex
Crystal field splitting in d8

Crystal field splitting in tetrahedral complexes.

Describe Crystal field splitting in tetrahedral complexes.

  1. In a tetrahedral complex, the metal ion is at the center of the regular tetrahedron and ligands are at the four alternate corners of the tetrahedron.
  2. In free metal ion, all the five d-orbitals have the same energy i.e. they are degenerate (State-I). As the ligands approach the central metal ion, repulsion will take place between metal electrons and the negative electric field of ligands. This repulsion will raise the energy levels of d-orbitals. If all the ligands approaching metal ion are at an equal distance from each of the d-orbitals, then the energy of each d-orbital will increase by the same amount i.e. they will remain degenerate (State-II). However, this is only a hypothetical situation.
  3. Because of different directional properties, the five d-orbitals will be repelled to different extents. Therefore their energies no longer remain the same but split up into two sets of orbitals called e and t2. The e orbitals include dx2-y2 and dz2orbitals while “t” orbitals include dxy, dyz, and dxz orbitals.
  4.  ‘e’ orbitals, which lie along the axes do not face the ligands directly and hence will experience less repulsion. Therefore it will be lowered in energy by – 6Dq relative to barycenter. On the other hand, ‘t2’ orbitals which lie in between the axes, also do not face the ligands directly but are closer to ligands than ‘e’ orbitals and hence will experience more repulsions. Therefore it will be raised to a higher energy level by +4Dq relative to the barycenter.
  5. The angle between the ‘e’ orbital, the central metal, and the ligand is 540, 44’ which is half the tetrahedral angle. The angle between the ‘t2‘ orbital, the central metal, and the ligand is 350, 16’.
  6. The difference in energy between the two sets of d-orbitals is denoted by 10 Dq or ∆t and is called crystal field splitting energy in tetrahedral complexes (State-III).
  7. It is found that ∆the t value is always less than that of ∆o

Comparison of ∆t with ∆o

Reasons for a smaller ∆t value compared to ∆o are as follows,

  1. In octahedral complexes, 6 ligands are involved while in tetrahedral complexes only 4. This resulted in 33% decrease in the field strength on metal d-orbitals.
  2. In octahedral complexes, the ligands are situated exactly in direction of the dz2 and dx2-y2 orbital (‘eg’ orbitals). In tetrahedral complexes, the ligands are not situated at any of the d-orbitals but exert more influence on the “t2 orbitals than on the “e” orbitals.
Crystal field splitting in tetrahedral complex
Crystal field splitting in tetrahedral complex

Crystal field stabilization energy C.F.S.E. for the tetrahedral complexes

What is Crystal Field Stabilization Energy? Calculate C.F.S.E. for the tetrahedral complexes with d1 to d10 Configuration.

The decrease in energy achieved by preferential filling of the lower energy d-levels is known as Crystal Field Stabilization Energy.

Crystal Field Stabilization Energy for the various configurations in the tetrahedral field can be calculated by the general formula,

C.F.S.E.  = x (-6Dq) + y (+4Dq)

Where,

x = number of electrons in e orbitals.

y = number of electrons in t2 orbitals.

P = Pairing energy

Crystal field splitting in tetrahedral complex CFSE
Crystal field splitting in tetrahedral complexes CFSE
Crystal field splitting in tetrahedral complexes CFSE
Crystal field stabilization energy C.F.S.E. for the tetrahedral complexes

Tetrahedral complexes – high spin complexes

Most of the tetrahedral complexes are high spin complexes

In tetrahedral complexes, the five degenerate metal ‘d’-orbitals split into two energy levels, the upper ‘t2’ and the lower ‘e’ level. The energy gap between ‘e’ and ‘t2‘ is denoted by t.

Since t is much smaller compared to o and t < pairing energy(P), the electron prefers ‘t2’ orbitals rather than pairing up in ‘e’ orbitals in tetrahedral complexes. Hence most of the tetrahedral complexes are high spin complexes.

Crystal field splitting in Square Planar complexes.

Define crystal field splitting. Explain in brief Crystal field splitting in Square Planar complexes.

Splitting of the five degenerated orbitals of the free metal ion by the ligand field into two groups, having different energies is called Crystal field splitting.

Crystal field splitting in square planar complexes

  1. In an octahedral complex, all ligands are at an equal distance from the central metal. If two trans ligands lying along Z-axis are slightly moved away from the central metal, then the distance between the central metal and trans ligands becomes more than that between metal and the other ligands on XY plane. This will result in a tetragonally distorted octahedral structure.
  2. In the tetragonal structure, the metal d-orbitals, dz2, dxz, dyz with Z component will experience less repulsions, and the other two d-orbitals dx2-y2, dxy will experience more repulsions from the ligands than they do in an octahedral environment. Therefore, under the influence of ligands in a tetragonal complex, the energies of dz2, dxz, dyz are lowered and dx2-y2, dxy is raised. Therefore, the order of increasing energy of d-orbitals is as follows, dxz= dyz<dxy<dz2<dx2- y2
  3. A square planar complex can be derived from the tetragonal structure by removing completely the two trans ligands along Z-axis. In a square planar complex, there are only 4 ligands on the XY plane. The loss of two ligands on the Z-axis allows the remaining 4 ligands to move closer to the central metal ion destabilizing the dx2-y2 and dxy orbitals. Hence the d-orbitals of central metal involving Z component i.e. dz2, dxz, dyz are further lowered while the other two i.e. dx2-y2,dxy are further raised in energy.

Therefore the order of increasing energy of d-orbitals in a square planar complex is as follows,

dxz = dyz<dz2< dxy<dx2 y2.

In square planar complexes, the d-orbitals split into 4 levels. The energy difference between the lowest degenerate dxz, dyz pair, and the highest dx2-y2 is called Crystal field splitting energy and is denoted by sp. The value of sp is larger than o. It has been found that sp is about1.3 times o.

Crystal field splitting in square planar complexes
Crystal field splitting in square planar complexes
Crystal field splitting in square planar complexes
Crystal field splitting in square planar complexes

Factors affecting the Magnitude of 10Dq

What are the factors which affect the Magnitude of 10Dq or o

The factors affecting the magnitude of 10 Dq or o are as follows,

  • The geometry of the complex:

The splitting of the d-orbitals in the octahedral complex is twice as strong as in the tetrahedral complex. This difference in the 10 Dq value is due to two factors.

  1. In octahedral complexes, 6 ligands are involved while in tetrahedral complexes only 4. This resulted is a 33% decrease in the field strength on metal d-orbitals.
  2. In octahedral complexes, the ligands are situated exactly in direction of dz2 and   dx2-y2 orbital (‘eg’ orbitals). In tetrahedral complexes, the ligands are not situated at any of the d-orbitals but exert more influence on the “t2 orbitals than on the “e” orbitals.

In square planar complexes, the value of sp is about1.3 times o

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  • Nature of the ligands

The value of 10 Dq for any given metal ion depends upon the ligand attached to it. The values of 10 Dq for Cr3+ complex with different ligands are as follows,

Complex10 Dq or 0 [KJ mol-1]
[CrCl6]3-160.5
[Cr(H2O)6]3+213.1
[Cr(NH3)6]3+259.1
[Cr(CN)6]3-314.1

It is clear that CN1- ligand produces more splitting and hence it is a strong ligand while Cl1- ligand produces less splitting and hence is a weak ligand.

  • Charges on the Metal

The magnitude of D0 increases as the charge on the metal ions increases. A metal ion with a higher charge draws the ligands closer, and hence produces more splitting than an ion with a lower charge. e.g.

Complex10 Dq or 0 [KJ mol-1]
[Cr(H2O)6]2+166.1
[Cr(H2O)6]3+213.1
  • Position of metal in the transition series.

The magnitude of D0depends upon the position of the metal in the transition series, i.e., whether the metal is from the first, second, or third transition series involving 3d, 4d & 5d orbitals respectively. The value of 10Dq increases on descending down a group from the first to the third transition series.

Complex10 Dq or 0 [KJ mol-1]
[Co(NH3)6]3+ 274.9
[Rh(NH3)6]3+ 406.4
[Ir(NH3)6]3+   489.9

This is explained on the basis that 4d orbitals in comparison to 3d orbitals are bigger in size and extend further into space. As a result, the 4d orbital can interact more strongly with the ligands and, therefore, the crystal field splitting is more. Similarly, 5d orbitals are still bigger than 4d orbitals and hence crystal field splitting is still greater.

Nephelauxetic Effect

Write a note on the Nephelauxetic Effect

a) It is found that the inter electron repulsions in the complexed metal ion,{[Fe(CN)63-]} are less than those in the free metal ion (Fe3+).

b) The decrease in the inter electron repulsions in the complexed metal ion may be possibly due to the increase in the distance between the d-electrons. This increase in the distance can be attributed to increasing in the size of the d-orbitals. This expansion of the d-electron cloud could be partly due to the overlap of metal ion d-orbitals with the ligand orbitals. This effect of ligands causing the expansion of the d-electron cloud is known as the Nephelauxetic (cloud expanding) effect.

c) Depending upon the ability of the ligands to expand the d-electron cloud of metal ion, they are arranged in the form of a series called the Nephelauxetic series,

F< H2O < NH3< C2O42-< en < NCS1-< Cl1-< CN1-< Br1-< I1- d) This series is independent of the central metal ion, like spectrochemical series. From the series, it is clear that F1- and I1- are at the two ends of the series. Therefore iodo complexes are more covalent than fluoro complexes. Thus, the Nephelauxetic effect provides evidence in support of covalent bonding.

Spectrochemical series

Write a note on the spectrochemical series

Magnitudes of crystal field splitting depend upon the nature of the ligands. Different ligands cause crystal field splitting to a different extent.

          b) From the absorption spectra of the complexes of the same metal ion with different ligands, the value of 10Dq can be predicted. From the values of 10Dq, the ligands can be listed in the order of increasing capacity to cause splitting. The order is as follows,

I< Br< S2-< SCN< Cl< NO3< F<OH< C2O42-< H2O < NCS<NH3< en < dipy < Phen < NO2< CN< CO This arrangement of ligands in the order of increasing field strength is called Fajans-Tschida spectrochemical series because it is derived from spectral studies of the complexes. The ligands at the upper end of the series are called the weak field ligands and usually give high spin complexes, while the ligands at the lower end of the series are called the strong field ligands and usually give low spin complexes

FAQs

Q. What are High and Low spin complexes?

Complexes in which electrons remain unpaired to the maximum possible extent leaving a maximum number of unpaired electrons are called high spin complexes.In a weak field, 10Dq is usually lesser than pairing energy, i.e. 10Dq < P. hence electrons remain unpaired and form high spin complexes.
Complexes in which electrons pair up to the maximum possible extent leaving a minimum number of unpaired electrons are called low spin complexes. In a strong field, 10Dq is usually greater than pairing energy, i.e. 10Dq > P. Hence electrons pair up in the lower energy orbitals and form low spin complexes.

Q. What is the CFSE formula?

C.F.S.E.  = x (-4Dq) + y (+6Dq) + P
Where,
x= number of electrons in t2g orbitals.
y = number of electrons in eg orbitals
P = Pairing energy

Q. What is 10Dq or o

The energy difference between two groups of orbitals (t2g and eg) is called10Dq or o.

Q. What is CFSE full form?

Crystal Field Stabilization Energy.

Q. What is CFT full form?

Crystal Field Theory.


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32 thoughts on “Crystal Field Theory | CFT | Crystal Field Splitting in Octahedral complexes | Crystal Field Splitting in Tetrahedral complexes.

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