Ligand K-edge

Ligand K-edge spectroscopy is a spectroscopic technique used to study the electronic structures of metal-ligand complexes. This method measures X-ray absorption caused by the excitation of ligand 1s electrons to unfilled p orbitals (principal quantum number n <= 4) and continuum states, which creates a characteristic absorption feature called the 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:

$D_0(L \ 1s \rightarrow \psi^*) = const \ \vert \langle L \ 1s \vert \mathbf{r} \vert \psi^* \rangle \vert^2 = \alpha^2 \ const \ \vert \langle L \ 1s \vert \mathbf{r} \vert L \ np \rangle \vert^2$

where $\psi^*$ is the wavefunction of the unfilled orbital, r is the transition dipole operator, and $\alpha^2$ is the "covalency" or ligand character in the orbital. Since $\psi^* = \sqrt{1-\alpha^2} \vert M_d \rangle - \alpha \vert L_{np} \rangle$, the above expression relating intensity and quantum transition operators can be simplified to use experimental values:

$D_0 = \frac{\alpha^2 h}{3n}I_s$

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.

See also

• Metal K-edge
• Metal L-edge
• Extended X-ray absorption fine structure