Ligand K-edge

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Ligand K-edge spectroscopy is a spectroscopic technique used to study the electronic structures of metal-ligand complexes.[1] 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.


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 Is 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.

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  1. ^ 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