Crystal Field Theory | CFT | Crystal Field Splitting in Octahedral complexes | Crystal Field Splitting in Tetrahedral complexes.

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. The 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 ions, 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 dz2 orbitals.
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).

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 t_2g orbitals.

y = number of electrons in e_g orbitals

P = Pairing energy

Crystal field splitting in tetrahedral complexes or splitting of d orbitals in tetrahedral complexes.

Describe Crystal field splitting of d orbital 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 ions, 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

The 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 a 33% decrease in the field strength of metal d-orbitals.
2. In octahedral complexes, the ligands are situated exactly in direction of the dz² and dx²-y² orbital (‘e_g’ 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 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 = the number of electrons in e orbitals.

y = number of electrons in t₂ orbitals.

P = Pairing energy

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 the 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 about 1.3 times ∆_o.

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 in a 33% decrease in the field strength of 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,

Complex	10 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 CN^1- ligand produces more splitting and hence it is a strong ligand while Cl^1- 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.

Complex	10 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 D₀ depends 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.

Complex	10 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)₆^3-]} 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 an increase 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 ions, they are arranged in the form of a series called the Nephelauxetic series,

F^–< H₂O < NH₃< C₂O₄^2-< en < NCS^1-< Cl^1-< CN^1-< Br^1-< I^1- d) This series is independent of the central metal ion, like spectrochemical series. From the series, it is clear that F^1- and I^1- 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 extents.

          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^–< S^2-< SCN^–< Cl^–< NO₃^–< F^–<OH^–< C₂O₄^2-< 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

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