The phenomenon you're referring to is related to the Crystal Field Theory (CFT) and the splitting of d-orbitals in transition metal complexes. In CFT, the ligands surrounding a transition metal ion create a crystal field, which affects the energy levels of the metal's d-orbitals.
As you move down a group or increase the atomic number in a series of transition metals, the crystal field splitting generally increases. This can be explained by the increasing effective nuclear charge experienced by the d-electrons.
When moving down a group, the atomic radius increases due to the addition of new electron shells. As a result, the d-electrons are further from the nucleus, leading to a weaker shielding effect from the inner electrons. The increased effective nuclear charge attracts the d-electrons more strongly, causing the d-orbitals to become lower in energy and resulting in a larger crystal field splitting.
Additionally, as you move down a group, the principal quantum number (n) increases. Higher n values correspond to larger atomic orbitals, and when these orbitals interact with the ligands, they experience a greater extent of overlap. This increased overlap leads to a stronger crystal field interaction and a larger splitting of the d-orbitals.
It's important to note that there can be exceptions to this trend due to various factors, such as electronic configurations, ligand effects, and the presence of additional d-orbital electrons. However, as a general trend, the crystal field splitting tends to increase as the atomic number increases or when moving down a group in the periodic table.