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Summary by www.lecturesummary.com: 28. Transition Metals: Crystal Field Theory Part I by MIT OpenCourseWare
Introduction to Crystal Field Theory and Transition Metal Properties (0:00)
The goal of chemistry is to comprehend a
Ligand Field Theory vs. Crystal Field Theory (0:48)
Both theories attempt to explain the observed characteristics of transition metals:
- The fundamental concept is that a metal ion in a coordination complex has different energy levels than a free metal ion.
- Crystal field theory considers only the ionic description of the metal-ligand bond.
- Ligand field theory includes both covalent and ionic bonding.
- Crystal field theory is popular for its simplicity in explaining general properties.
The Basic Concept of Crystal Field Theory (1:41)
The fundamental concept is that ligands are negative point charges that repel the d-orbitals containing electrons.
The core idea of crystal field theory is this negative point charge repulsion.
Octahedral Crystal Field Splitting (2:24)
The octahedral case is the first topic covered in the lecture:
- Six ligands encircle the metal ion in the centre of an octahedral complex.
- Ligands are found along the x, y, and z axes in octahedral geometry.
- The degree of repulsion is determined by how ligands point at the d-orbitals.
D-orbital Repulsion and Destabilisation in Octahedral Geometry (3:19)
Ligands point directly at the d₂² and dₓ²₋ᵧ² orbitals, causing:
- Destabilisation and large repulsion in these orbitals.
- Both d₂² and dₓ²₋ᵧ² are destabilised by the same amount, indicating they are degenerate.
- Less repulsion occurs in the dxy, dyz, and dxz orbitals due to their 45-degree orientation.
- The dxy, dyz, and dxz orbitals are stabilised and degenerate in relation to one another.
Octahedral Crystal Field Splitting Diagram (5:17)
The energy splitting of d-orbitals in an octahedral field is shown graphically:
- In a hypothetical spherical crystal field, all five d-orbitals would have the same energy.
- Real octahedral geometry divides the energy levels.
- The energy of the three orbitals (dxy, dyz, dxz) decreases, stabilising them as T₂G orbitals.
- More repulsion causes two orbitals (d₂², dₓ²₋ᵧ²) to become destabilised, referred to as EG orbitals.
- The octahedral crystal field splitting energy, represented by Δ₀, is the energy difference between T₂G and EG orbitals.
- Overall energy is conserved: stabilisation and destabilisation balance each other.
Splitting Energy Controlling Factors: The Spectrochemical Series (7:09)
The nature of the ligands controls the magnitude of the splitting energy (Δ₀):
- The amount of splitting varies depending on the ligand.
- The spectrochemical series ranks ligands by their ability to split crystal field energies.
- Strong field ligands result in a large splitting (large Δ₀).
- Weak field ligands cause very little splitting (small Δ₀).
- Examples include: Weak field ligands are halides; hydroxide and water are intermediate; cyanide (CN) is a strong field ligand.
- The ligand's strength influences colour and magnetic properties.
Influence of Ligands on Properties
Colour and magnetic properties (paramagnetic or diamagnetic) are influenced by the ligand's strength.
Diagrams of Electron Configuration and Crystal Field Splitting
As an illustration, compare:
- [Fe(H₂O)₆]³⁺
- [Fe(CN)₆]³⁻
Both belong to the d⁵ system Fe³⁺.
A small splitting diagram results from the presence of water (intermediate/weak field) in [Fe(H₂O)₆]³⁺.
A large splitting diagram results from the presence of cyanide (strong field) in [Fe(CN)₆]³⁻.
Electron filling adheres to the Aufbau principle and Hund's rule, but the order is impacted by the splitting.
The energy needed to pair two electrons in the same orbital is known as the Pairing energy (P).
Electrons fill all d-orbitals singly first, including the higher energy EG orbitals, before pairing in the lower energy T₂G orbitals in a weak field (small Δ₀ < P). A high spin complex (maximum number of unpaired electrons) is the result of this.
Electrons fully fill and pair in the lower energy T₂G orbitals before occupying the higher energy EG orbitals in a strong field (large Δ₀ > P). A low spin complex (minimum number of unpaired electrons) is the result of this.
T₂Gⁿ EGᵐ (n electrons in T₂G, m electrons in EG) is the notation used for electron configuration. T₂G³ EG² for d⁵ in a weak field. T₂G⁵ EG⁰ for d⁵ in a strong field.
Crystal Field Stabilisation Energy (CFSE)
The energy difference between the split d-orbitals and the hypothetical spherical field, where all d-orbitals have the same energy, is known as the CFSE.
- It takes into account the degree to which electrons are destabilised by higher energy orbitals or stabilised by lower energy orbitals.
- For d⁵ weak field (T₂G³ EG²), CFSE = (3 * -²⁄₅Δ₀) + (2 * ³⁄₅Δ₀) = ⁻⁶⁄₅Δ₀ + ⁶⁄₅Δ₀ = 0. Splitting prevents stabilisation.
- CFSE = (5 * -²⁄₅Δ₀) + (0 * ³⁄₅Δ₀) = ⁻¹⁰⁄₅Δ₀ = -2Δ₀ for d⁵ strong field (T₂G⁵ EG⁰). Notable stabilisation.
- The stabilisation of the two iron compounds differs significantly.
Magnetism: Diamagnetic vs. Paramagnetic
A magnetic field attracts paramagnetic materials. Unpaired electrons are present in them.
A magnetic field repels diamagnetic materials. No unpaired electrons are present in them.
- Complexes with weak fields (high spin) are typically more likely to be paramagnetic (have unpaired electrons).
- Diamagnetic (minimum number of unpaired electrons) complexes are typically more likely to be strong field (low spin).
- Both complexes in the d⁵ iron examples are paramagnetic because they contain unpaired electrons (the d⁵ strong field has one unpaired electron, while the d⁵ weak field has five).
Colour and Absorption of Light
The absorption of photons that excite electrons to higher energy levels is correlated with a substance's colour.
A photon will be absorbed by a transition metal complex if its energy is equal to the crystal field splitting energy (Δ₀).
A photon's energy (E) is equal to its frequency (v) * Planck's constant (h).
- Consequently, Δ₀ = hν.
- The speed of light (c) = λν is the formula that represents the relationship between frequency and wavelength (λ). Thus, Δ₀ = hc/λ.
- Long wavelengths (the red end of the spectrum) are associated with low frequency absorbed light.
- Short wavelengths (the violet end of the spectrum) are associated with high frequency absorbed light.
- The colour seen is the complementary colour of the absorbed light. Complementary colours can be found using a colour wheel.
Instances of Colour: Iron Complexes
Low frequency/longer wavelength light is absorbed by the high spin iron-water complex ([Fe(H₂O)₆]³⁺, intermediate field). Depending on the circumstances, it can appear in a range of colours, most frequently yellowish-brown in solution or pale violet (transmitting shorter wavelengths).
High frequency/short wavelength light is absorbed by the low spin iron-cyanide complex ([Fe(CN)₆]³⁻, strong field) because it produces a large splitting (high Δ₀). It appears bright orange-red and transmits longer wavelengths.
Both Fe³⁺ and Fe²⁺ with cyanide are present in the complex known as Prussian blue (blueprint blue).
Colourless Complexes
If there is no splitting (all d-orbitals are degenerate, which is merely hypothetical), coordination complexes are colourless.
No electron can be excited to a higher energy d-orbital if all d-orbitals are filled (d¹⁰ configuration).
If the energy transitions are outside the visible range, the complex will also be colourless.
Colourless Transition Metal Complex Examples
- Cadmium²⁺
- Zinc²⁺
Both belong to Group 12 and have a d¹⁰ configuration (12 - 2 = 10) due to their +2 oxidation state.
There are no d-d transitions in the visible spectrum because the d-orbitals are filled with all 10 d-electrons.
Because it is colourless, zinc²⁺ can be "sneaky" in proteins. It is frequently found in biology and vitamin supplements.
Cadmium²⁺ is toxic; it was occasionally used to coat old barbeque grills.
Coloured Transition Metal Complex
Cobalt³⁺ is an example of a coloured transition metal complex.
Since Cobalt³⁺ (Group 9 - 3 = d⁶) is not a d³⁰ system, it is usually coloured.
Cobalt is a component of vitamin B12, which can form stunning red crystals.
Calculating Absorbed Wavelength
The octahedral crystal field splitting energy (Δ₀) is used to calculate the absorbed wavelength and predict colour.
λ = hc/Δ₀ is the formula.
Use the proper units (kJ to J and Avogadro's number to convert kJ/mol to J/molecule).
An example of a calculation: Determine the absorbed wavelength for a cobalt complex with Δ₀ = 239 kJ/mol.
- λ = (6.626 x 10⁻³⁴ J·s * 2.998 x 10⁸ m/s) / (239 x 10³ J/mol / 6.022 x 10²³ mol⁻¹).
The wavelength that results is approximately 500 nm.
The green portion of the spectrum is located at 500 nm.
The complementary colour to the absorbed colour is the one that is observed (transmitted).
Red is the colour that goes well with green. The cobalt complex with Δ₀ = 239 kJ/mol is expected to be red in colour.
Cobalt Chloride Hydration Colour Change Demo
Cobalt chloride and water demonstration.
Pinkish-red is the result of the formation of a hydrated octahedral complex by cobalt chloride with lots of water. This is consistent with the computation that indicates red for a cobalt complex with a particular Δ₀.
Chlorides are incorporated into the complex to form a new complex when the water is removed (dehydrated). With water ligands, this complex is less hydrated and not strictly octahedral.
This dehydration results in a blue colour shift.
The colour shift illustrates how the ligands (water versus chloride) and degree of hydration impact the structure and characteristics of the complex, including colour. This reversible colour change is illustrated visually by the flower.
This section discusses orbital shapes and how they explain transition metal properties in relation to crystal field theory.
- Colour and magnetism are two essential characteristics of transition metals.
- Transition metals are referred to as "superheroes of the periodic table" due to their amazing and practical qualities.
- Applications for transition metals include new imaging agents for MRIs and blueprints using a transition metal complex for the blue colour.
nd classify the properties observed, such as colour and magnetism.