Lanthanides, arrays, solid state

As we will see from the examples on the following pages, a wide range of approaches have been developed to access lanthanide arrays. We will deal with them by using examples of a number of different classes of systems in the solid state and in solution to illustrate key aspects of the strategies used to prepare these complexes. 

The solid phase lends itself to the preparation of lanthanide arrays. Indeed, lanthanide doped yttrium aluminium garnets are weU known as laser materials, while doped materials containing more than one kind of lanthanide have proved very effective at upconversion of energy - the sequential absorption of two photons giving rise to anti-Stokes emission [9]. In such systems, excited state absorption by the intermediate state gives rise to formation of a high energy... 

The SIC-LSD still considers the electronic structure of the solid to be built from individual one-electron states, but offers an alternative description to the Bloch picture, namely in terms of periodic arrays of localized atom-centred states (i.e., the Heitler-London picture in terms of the exponentially decaying Warmier orbitals). Nevertheless, there still exist states that will never benefit from the SIC. These states retain their itinerant character of the Bloch form and move in the effective LSD potential. This is the case for the non-f conduction electron states in the lanthanides. In the SIC-LSD method, the eigenvalue problem, Eq. (23), is solved in the space of Bloch states, but a transformation to the Wannier representation is made at every step of the self-consistency process to calculate the localized orbitals and the corresponding charges that give rise to the SIC potentials of the states that are truly localized. TTiese repeated transformations between Bloch and Wannier representations constitute the major difference between the LSD and SIC-LSD methods. 

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