Physics:Ligand K-edge
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.
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:
[math]\displaystyle{ 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 }[/math]
where [math]\displaystyle{ \psi^* }[/math] is the wavefunction of the unfilled orbital, r is the transition dipole operator, and [math]\displaystyle{ \alpha^2 }[/math] is the "covalency" or ligand character in the orbital. Since [math]\displaystyle{ \psi^* = \sqrt{1-\alpha^2} \vert M_d \rangle - \alpha \vert L_{np} \rangle }[/math], the above expression relating intensity and quantum transition operators can be simplified to use experimental values:
[math]\displaystyle{ D_0 = \frac{\alpha^2 h}{3n}I_s }[/math]
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.
See also
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: 97–129. doi:10.1016/j.ccr.2004.03.020.
 |
