Ligand K-edge

Ligand K-edge XAS is a spectroscopic technique that allows the direct study of metal-ligand bonding.^[1] In a XAS experiment, electrons in ligand 1s orbitals are excited to unfilled p (principal quantum number n <= 4) and continuum states. This results in a large spectral feature known as a rising edge. Transitions at energies lower than the edge can occur, provided they are to orbitals with some ligand p character, and are called pre-edges. Such transitions are often observed in the data of complexs with metal-ligand bonding.

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 the determine the amount of ligand character in a molecular orbital.

References

^ Solomon, E.; Hedman, B.; Hodgson, K.; Dey, A.; Szilagyi, R. (2005). "Ligand K-edge X-ray absorption spectroscopy: covalency of ligand–metal bonds". Coordination Chemistry Reviews 249: 97–76. doi:10.1016/j.ccr.2004.03.020. edit