The crystal field splitting energy CFSE in transition metal complexes is influenced by the coordination number and the nature of the ligands. The coordination number refers to the number of ligand atoms that are directly bonded to the central metal ion, while the nature of the ligands refers to their chemical and electronic properties. Both factors play a crucial role in determining the energy difference between the d-orbitals of the central metal ion, which in turn affects the stability, color, and reactivity of the complex.1. Coordination number: The coordination number affects the geometry of the complex, which in turn influences the crystal field splitting. For example, in an octahedral complex coordination number 6 , the d-orbitals split into two groups: the lower energy t2g set dxy, dyz, and dxz and the higher energy eg set dx^2-y^2 and dz^2 . In a tetrahedral complex coordination number 4 , the splitting is reversed, with the t2 set being higher in energy and the e set being lower in energy. The energy difference between these sets of orbitals is generally larger in octahedral complexes than in tetrahedral complexes due to the higher coordination number and stronger ligand field.2. Nature of the ligands: The nature of the ligands affects the crystal field splitting energy through their ability to donate electron density to the central metal ion. This ability is often described by the spectrochemical series, which ranks ligands based on their ability to cause splitting of the d-orbitals. Ligands that are strong-field e.g., CO, CN-, NO2- cause a larger splitting, while weak-field ligands e.g., I-, Br-, Cl- cause a smaller splitting. This is because strong-field ligands have a greater electron-donating ability, which results in a stronger interaction with the metal ion and a larger energy difference between the d-orbitals.Example: Let's consider two octahedral complexes of Fe III : [Fe H2O 6]^3+ and [Fe CN 6]^3-. In both cases, the coordination number is 6, but the nature of the ligands is different.In [Fe H2O 6]^3+, water is a weak-field ligand, so the crystal field splitting energy will be relatively small. This results in a high-spin complex, where the five d-electrons occupy all five d-orbitals before pairing up. The complex will be relatively less stable and will have a certain color due to the electronic transitions between the d-orbitals.In [Fe CN 6]^3-, the cyanide ion CN- is a strong-field ligand, causing a larger crystal field splitting energy. This results in a low-spin complex, where the five d-electrons are all paired up in the lower energy t2g orbitals. The complex will be more stable and will have a different color compared to the [Fe H2O 6]^3+ complex due to the different electronic transitions between the d-orbitals.In summary, both the coordination number and the nature of the ligands play a significant role in determining the crystal field splitting energies in transition metal complexes, which in turn affects their stability, color, and reactivity.