Crystal Field Theory (CFT)

The bonding of transition metal complexes can be explained by two approaches: crystal field theory and molecular orbital theory.

Molecular orbital theory takes a covalent approach, and considers the overlap of d-orbitals with orbitals on the ligands to form molecular orbitals; this is not covered on this site.

Crystal field theory takes the ionic approach and considers the ligands as point charges around a central metal positive ion, ignoring any covalent interactions. The negative charge on the ligands is repelled by electrons in the d-orbitals of the metal. The orientation of the d orbitals with respect to the ligands around the central metal ion is important, and can be used to explain why the five d-orbitals are not degenerate (= at the same energy). Whether the d orbitals point along or in between the cartesian axes determines how the orbitals are split into groups of different energies.

Why is it required?

The valence bond approach could not explain the Electronic spectra, Magnetic moments, Reaction mechanisms of the complexes.

Assumptions of CFT:

1. The central Metal cation is surrounded by ligand which contain one or more lone pair of electrons.

2. The ionic ligand (F-, Cl- etc.) are regarded as point charges and neutral molecules (H2O, NH3 etc.) as point dipoles. 3. The electrons of ligand does not enter metal orbital. Thus there is no orbital overlap takes place. 4. The bonding between metal and ligand is purely electrostatic i.e. only ionic interaction.

The approach taken uses classical potential energy equations that take into account the attractive and repulsive interactions between charged particles (that is, Coulomb's Law interactions).

Description of d-Orbitals: To understand CFT, one must understand the description of the lobes:

dxy : lobes lie in-between the x and the y axes. dyz : lobes lie in-between the y and the z axes.

dxz : lobes lie in-between the x and the z axes. dx2-y2 : lobes lie on the x and y axes.

dz2 : there are two lobes on the z axes and there is a doughnut shape ring that lies on the xy plane around the other two lobes.

The Octahedral Crystal Field:

Consider a molecule with octahedral geometry. The lone pair of electrons on each of the six ligands is treated as a negative point charge. The ligands are cantered on the cartesian axes. There are two forces: electrostatic attraction between each of the ligands and the positive metal ion and electrostatic repulsion between the ligands and electrons in the d-orbitals.

Figure : Octahedral complex ML6

In octahedral geometry, ligands approach the metal ion along the x, y , and z axes. Therefore, the electrons in the dz2 and dx2-y2 orbitals (which lie along these axes) experience greater repulsion. This causes a splitting in the energy levels of the d-orbitals. This is known as crystal field splitting. For octahedral complexes, crystal field splitting is denoted by Δo(or Δoct ). The energies of the and orbitals increase due to greater interactions with the ligands. The dxy , dxz , and dyz orbitals decrease with respect to this normal energy level and become more stable.

The two sets of orbitals are labelled eg and t2g and the separation between these two sets is called the

ligand field splitting parameter, Δo (10 Dq) .The subscript o is used to signify an octahedral crystal field. Degenerate orbitals means orbitals having same energy. "e" refers to doubly degenerate orbitals. It consists of two d-orbitals. "t" refers to triply degenerate levels orbitals. It consists of three d-orbitals. They derive from group theory. The "g" tells you that the orbitals are gerade (german for even) - they have the same symmetry with respect to the inversion centre. The overall stabilization of one set of orbitals equals the overall destabilization of the other set. In the octahedral crystal field the overall stabilization of the t2g set equals the overall destabilization of the eg set. If the eg set is raised by two units, the t2g set is lowered by three units to achieve this energy balance.

Therefore, the eg set is raised by 0.6Δo and the t2g set is lowered by 0.4Δo Some texts will use 10Dq instead of Δo, these are equivalent.

Factors affecting the magnitude of splitting

Many experiments have shown that the magnitude of splitting is depending upon both metal and ligands.

Jorgenson’s Relation :

Δ o = f . g where f = metal parameter and g = ligand parameter

Metal factors: For complexes having same geometry and same ligands the crystal field splitting :

1. Charge on the metal ion. It increases with the increase in charge on the ion (Same number of d - electrons)

2. Number of d- electrons. It decreases with increasing number of d -electrons (Same charge on the ion)

3. Principle quantum number of the metal d electron (With increasing n value the splitting increases)

Ligand factor: The strength of the ligands determine splitting; the stronger the ligand, the larger the splitting. Ligands are classified as strong or weak based on the spectrochemical series:

─ ─ ─ 4─ ─ CN = CO = C2H4 > PR3 > NO2 = phen > bipy > SO32 > en = py = NH3 > edta > NCS > H2O > C2O42─ > ONO2- > OSO32─ > OH─ = ONO─ > F─ > Cl─ = SCN─ > Br─ > I─

─ ─ Note that SCN and NO2 ligands are represented twice in the above spectrochemical series since there are two different Lewis base sites (e.g., free electron pairs to share) on each ligand (e.g., for the SCN ligand, the electron pair on the sulfur or the nitrogen can form the coordinate covalent bond to a metal). The specific atom that binds in such ligands is underlined. Electronic distribution in splitted d orbitals : According to the Aufbau principle, electrons are filled from lower to higher energy orbitals. For the octahedral case above, this corresponds to the dxy , dxz , and dyz orbitals. Following Hund's rule, electrons are filled in order to have the highest number of unpaired electrons. For example, if one had a d3 complex, there would be three unpaired electrons. If one were to add an electron, however, it has the ability to fill a higher energy orbital (dz² or dx²-y² ) or pair with an electron residing in the dxy , dxz or dyz orbitals. This pairing of the electrons requires energy (spin pairing energy). If the pairing energy is less than the crystal field splitting energy, ∆0, then the next electron will go into the dxy , dxz or dyz orbitals due to stability. This situation allows for the least amount of unpaired electrons, and is known as low spin.

If the pairing energy is greater than ∆0, then the next electron will go into the dz² or dx²-y² orbitals as an unpaired electron. This situation allows for the most number of unpaired electrons, and is known as high spin.

Ligands that cause a transition metal to have a small crystal field splitting, which leads to high spin, are called weak-field ligands. Ligands that produce a large crystal field splitting, which leads to low spin, are called strong field ligands. Hence: The strong field ligand form a low spin complex, while the weak field ligand form a high spin complex. 3d metals are generally high spin complexes except with strong ligands or higher oxidation state. 4d & 5d metals generally have a larger value of Δo than for 3d metals. As a result, complexes are typically low spin.

Tetrahedral complex:

Consider a tetrahedral arrangement of ligands around the central metal ion. The best way to picture this arrangement is to have the ligands at opposite corners of a cube. As with octahedral complexes there is an electrostatic attraction between each of the ligands and the positive metal ion, and there is electrostatic repulsion between the ligands and electrons in the d orbitals. None of the d-orbitals point directly at the ligands as they did with the octahedral geometry. However some orbitals come closer to the ligands than others.

We can now construct the d orbital splitting diagram for a tetrahedral complex. The d-orbital splitting diagram is the inverse of that for an octahedral complex.

Note, here not t2g or eg it is only t2 or e as there is not centre of symmetry in tetrahedral complex. (g stands for gerade)

The difference in the splitting energy is tetrahedral splitting constant (∆t), which less than (∆0) for the same ligands as number of ligands are less and the ligands not directly facing the orbitals.

The relationship between them is : ∆t = 4/9Δ0

Consequentially, is typically smaller than the spin pairing energy, so tetrahedral complexes are usually high spin.

Crystal Field Stabilization Energy (CFSE):

The Crystal Field Stabilization Energy is defined as the energy of the electronic configuration in the ligand field minus the energy of the electronic configuration in the isotropic field (without ligand).

CFSE =ΔE = Eligand field−Eisotropic field

The CSFE will depend on multiple factors including: 1. Geometry (which 2. Number of d-electrons 5. Ligand character (via changes the d-orbital 3. Spin Pairing Energy Spectrochemical Series) splitting patterns) 4. Charge on metal ion/atom

For an octahedral complex, an electron in the more stable subset t2g is treated as contributing -0.4 Δ0 whereas an electron in the higher energy subset eg contributes to a destabilization of +0.6 Δ0 . The final answer is then expressed as a multiple of the crystal field splitting parameter Δ0 . If any electrons are paired within a single orbital, then the term P is used to represent the spin pairing energy. Paring energy represents the energy required to pair up electrons within the same orbital. For a given metal ion P (pairing energy) is constant, but it does not vary with ligand and oxidation state of the metal ion).

Jahn-Teller Distortions

In 1937 H.A. Jahn and E. Teller put forward a theorem which explained some of the distortions observed in transition metal complexes. This became known as the Jahn-Teller theorem. It states: For any non-linear molecule in an electronically degenerate state, distortion must occur to lower the symmetry, remove the degeneracy and lower the energy."

Thus the Jahn-Teller effect is a geometric distortion of a non-linear molecular system that reduces its symmetry and energy. This distortion is typically observed among octahedral complexes where the two axial bonds can be shorter or longer than those of the equatorial bonds. This effect can also be observed in tetrahedral compounds. This effect is dependent on the electronic state of the system. When an octahedral complex exhibits elongation, the axial bonds are longer than the equatorial bonds. For a compression, it is the reverse; the equatorial bonds are longer than the axial bonds. Elongation and compression effects are dictated by the amount of overlap between the metal and ligand orbitals. Thus, this distortion varies greatly depending on the type of metal and ligands. In general, the stronger the metal-ligand orbital interactions are, the greater the chance for a Jahn-Teller effect to be observed. Elongation and compression in octahedron is known as tetragonal distortion.

If distortion occurs due to unsymmetric electronic

configuration t2g set then the extent of distortion will be weak,but if distortion occurs due to unsymmetric

electronic configuration eg set then the extent of distortion will be strong.

Square planar coordination:

In the presence of strong field ligands, the strong extent of z-out distortion leads to the removal of all the two axial metal-ligand bond and the octahedral geomerty gets converted to square planar.

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