The geometry of the ligand coordination sphere can significantly affect the magnetic properties of transition metal complexes. This is primarily due to the influence of the ligand field on the energy levels of the d-orbitals of the central metal ion. The splitting of d-orbitals in different geometries can lead to variations in the number of unpaired electrons, which in turn affects the magnetic properties of the complex.There are two main types of magnetic behavior in transition metal complexes: diamagnetic and paramagnetic. Diamagnetic complexes have no unpaired electrons, while paramagnetic complexes have one or more unpaired electrons.Here are some examples to illustrate the effect of geometry on the magnetic properties of transition metal complexes:1. Octahedral complexes: In an octahedral geometry, the d-orbitals split into two sets: the lower energy t2g set dxy, dyz, and dxz and the higher energy eg set dx2-y2 and dz2 . For example, in [Fe H2O 6]2+ complex, Fe II has six unpaired electrons 3d6 configuration . The ligand field causes the d-orbitals to split, and four of the six electrons fill the t2g orbitals, while the remaining two occupy the eg orbitals. This results in a high-spin complex with four unpaired electrons, making it paramagnetic.2. Tetrahedral complexes: In a tetrahedral geometry, the d-orbitals split into two sets: the lower energy eg set and the higher energy t2 set. The splitting is usually smaller than in octahedral complexes. For example, in [CoCl4]2- complex, Co II has a 3d7 configuration. Due to the smaller splitting, all seven electrons can occupy the lower energy orbitals, resulting in a high-spin complex with three unpaired electrons, making it paramagnetic.3. Square planar complexes: In a square planar geometry, the d-orbitals split into three different energy levels: the lower energy dz2 orbital, the intermediate energy dx2-y2 orbital, and the higher energy dxy, dyz, and dxz orbitals. For example, in [Ni CN 4]2- complex, Ni II has a 3d8 configuration. The ligand field splitting is large, and all eight electrons fill the lower and intermediate energy orbitals, resulting in a low-spin complex with no unpaired electrons, making it diamagnetic.In summary, the geometry of the ligand coordination sphere can significantly affect the magnetic properties of transition metal complexes by influencing the splitting of d-orbitals and the distribution of unpaired electrons. Different geometries, such as octahedral, tetrahedral, and square planar, can lead to variations in the magnetic behavior of the complexes, ranging from diamagnetic to paramagnetic.