Ligand K edge

Pre-edges

Transitions at energies lower than the edge can occur, provided they lead to orbitals with some ligand p character; these features are called pre-edges. Pre-edge intensities (D₀) are related to the amount of ligand (L) character in the unfilled orbital:

D 0 ( L   1 s → ψ ∗ ) = c o n s t   | ⟨ L   1 s | r | ψ ∗ ⟩ | 2 = α 2   c o n s t   | ⟨ L   1 s | r | L   n p ⟩ | 2

where ψ ∗ is the wavefunction of the unfilled orbital, r is the transition dipole operator, and α 2 is the "covalency" or ligand character in the orbital. Since ψ ∗ = 1 − α 2 | M d ⟩ − α | L n p ⟩ , the above expression relating intensity and quantum transition operators can be simplified to use experimental values:

D 0 = α 2 h 3 n I s

where n is the number of absorbing ligand atoms, h is the number of holes, and I_s is the transition dipole integral which can be determined experimentally. Therefore, by measuring the intensity of pre-edges, it is possible to experimentally determine the amount of ligand character in a molecular orbital.