Degenerate
Definition and meaning of Degenerate in chemistry.
Degenerate describes two or more orbitals, energy levels, or quantum states that share exactly the same energy. The term applies whenever multiple distinct wavefunctions of a system happen to coincide in energy, even though they differ in shape, spatial orientation, or quantum numbers.
In more detail
Degeneracy arises from symmetry: orbitals within the same subshell of an isolated atom (all three 2p orbitals, for instance) are equivalent by spherical symmetry and therefore have identical energy. This matters because Hund's rule tells electrons to occupy degenerate orbitals singly, with parallel spins, before any pairing occurs, minimizing electron-electron repulsion. Degeneracy can be lifted (partially or fully removed) when the symmetry is broken, such as by an external magnetic field (Zeeman effect), an electric field (Stark effect), or the surrounding ligands in a transition-metal complex (crystal field/ligand field splitting).
Key facts
| Field | Physical Chemistry |
|---|---|
| Governing principle | Hund's rule (fill degenerate orbitals singly first) |
| Common example | The three 2p orbitals (px, py, pz) of a free atom |
| Degeneracy is removed by | Ligand/crystal field splitting, applied magnetic or electric fields |
The five 3d orbitals of an isolated Mn2+ ion are degenerate (all equal in energy). When Mn2+ sits at the center of an octahedral complex, the ligand field splits this degenerate set into a lower-energy t2g group (three orbitals) and a higher-energy eg group (two orbitals).
Frequently asked questions
What does it mean when orbitals are 'degenerate'?
It means the orbitals have identical energy even though they differ in spatial shape or orientation, so electrons distribute among them singly (per Hund's rule) before pairing up.
How does crystal field theory relate to degeneracy?
In a free transition-metal ion, all five d orbitals are degenerate. Placing the ion in a ligand field (e.g., octahedral) breaks that symmetry, splitting the orbitals into subsets of different energy such as t2g and eg.