d-orbital splitting
/ dee-OR-bih-tal SPLIT-ing /
Imagine five identical chairs around a table, all equally comfortable. Now someone shines heat lamps from certain directions: the chairs facing the lamps get hot and uncomfortable, while those tucked away stay cool. The chairs are no longer equal. d-orbital splitting is the same idea for the five d orbitals of a metal ion: once ligands surround it, the orbitals stop being equal in energy and separate into sets.
In a free ion the five d orbitals — dz2, dx2-y2, dxy, dxz, dyz — all share one energy. The first three points to remember are that two of them (dz2 and dx2-y2) have their lobes pointing along the x, y, z axes, straight at where ligands sit, while the other three (dxy, dxz, dyz) point into the gaps between the axes. When ligand point charges arrive, the orbitals aimed at the ligands feel more repulsion and rise in energy, and the ones aimed between the ligands feel less and drop. The exact pattern of who rises and who falls depends on the shape of the arrangement — octahedral, tetrahedral, or square planar each split differently. The energy gap between the resulting sets is the splitting parameter, written delta.
This single idea underlies almost everything distinctive about transition-metal chemistry: their colors come from electrons hopping across the splitting gap, their magnetism from how electrons distribute among the split levels, and many of their structural and stability trends from the energy saved by filling the lower set first. Without splitting, all transition-metal ions would be colorless and behave alike; splitting is what makes them a rainbow.
Picture the dx2-y2 orbital, whose lobes lie along the x and y axes. In an octahedral complex, four ligands sit exactly on those axes. The electrons in dx2-y2 are pointed right at the incoming negative charges, so this orbital is shoved up in energy, while dxy — whose lobes lie between the axes — is shoved up much less.
An orbital's energy shift depends on whether its lobes aim at the ligands or between them.
The set that rises and the set that falls are not symmetric about the original energy: the overall center of gravity is preserved (the barycenter rule), so in an octahedral field the three lower orbitals drop by 2/5 delta while the two upper ones rise by 3/5 delta.