Calculate crystal field stabilization energy (CFSE in terms of Dq) for the following complexes
(i)
(ii)
(iii)
The correct answer and explanation is :
To calculate the Crystal Field Stabilization Energy (CFSE) for a coordination complex, we need to consider the arrangement of electrons in the metal’s d-orbitals in the presence of the ligand field. CFSE is the energy difference between the stabilized state (due to the interaction between the metal ions and the ligands) and the energy of the unperturbed system. It is expressed in terms of the crystal field splitting energy ( \Delta ) (also known as ( D_q ) or ( 10D_q ) for octahedral complexes).
General Steps for CFSE Calculation:
- Determine the geometry of the complex: Whether it is octahedral, tetrahedral, square planar, etc.
- Electron configuration: Determine the number of d-electrons of the central metal ion.
- Crystal field splitting: In an octahedral field, the five degenerate d-orbitals split into two sets:
- ( e_g ) orbitals (higher energy: ( d_{z^2} ) and ( d_{x^2 – y^2} )).
- ( t_{2g} ) orbitals (lower energy: ( d_{xy} ), ( d_{xz} ), and ( d_{yz} )). In a tetrahedral field, the splitting is smaller, and the ( e )-type orbitals are lower in energy than the ( t_2 )-type orbitals.
- Determine the electron configuration in the split d-orbitals: Depending on the number of electrons and whether the metal is in a high or low-spin state, distribute the electrons among the orbitals.
- CFSE Formula:
- Octahedral Complex (high-spin): ( \text{CFSE} = -0.4 \Delta (\text{number of electrons in } t_{2g}) + 0.6 \Delta (\text{number of electrons in } e_g) ).
- Octahedral Complex (low-spin): The calculation is similar, but more electrons are likely to occupy the lower energy ( t_{2g} ) orbitals.
- Tetrahedral Complex: ( \text{CFSE} = -0.4 \Delta_t (\text{number of electrons in } t_2) + 0.6 \Delta_t (\text{number of electrons in } e) ), where ( \Delta_t ) is the crystal field splitting energy for a tetrahedral geometry.