The jj-coupling scheme by tensor operators and a thorough interpretation of the spectra of some nickel(II) complexes

The ligand field theory of complexes has been completely developed and the energy matrix elements for complexes in various geometries in different coupling schemes have been worked in considerable detail. However for many coupling schemes the computing of energy matrix elements is a tedious and laborious process. In the first part of my thesis we present a solution to the Weak-Field II problem using ladder operators and tensor operators. We used the Weak-Field II as an example to stress the complexity of computing energy matrix elements using ladder operators versus the simplicity of calculating matrix elements with tensor operators. Also the Weak-Field II was used as a model example hoping to be able to accomplish the same with the jj-II coupling scheme. In the last part of my thesis we present a derivation of simplifying expressions for the energy matrix elements for the d 2 complex in the jj-II coupling scheme. It is worth mentioning that the expressions derived can be applied to complexes other than octahedral and further they can be generalized for complexes with n-electrons in the valence shell. Finally, we present a thorough analysis of the electronic spectra of some Nickel(II) complexes.