How to Model a Defect

we mainly focus on the modeling of point defects in a perfect crystal. Because of their local nature, we can assume that the perturbation in the crystal is small. Therefore, both structural and electronic effects can be considered as confined in the finite region close to the defect (defect zone). The rest of the system can then be treated as a perfect host with a well-defined periodic structure. On the basis of these assumptions, two strategies can be envisaged in the modeling of point defects  

Both perfect and defective systems are simulated as a finite cluster, i.e., a relatively small cluster is cut out of the bulk structure containing the defect. This kind of strategy is also called the cluster approach The main advantage of this approach is its flexibility first, because it does not assume any translational symmetry and allows us to investigate complex structures as defects in amorphous or disordered solids. Second, high quality standard molecular ab initio codes can be used, which thus allow a high-level quantum-mechanical treatment of the defect zone. 

Finally, size and shape of the cluster are critically important and results should converge with the cluster size. Unfortunately, when enlarging the cluster, the number of atoms grows fast, which makes the calculation rapidly unaffordable. For solids with complex frameworks and containing a large unit cell, such as zeolites, it is also difficult to preserve the memory of the original crystalline structure in the cluster. 

The host system is treated as a perfect crystalline structure, and the exploitation of periodicity or quasi-periodicity is an essential ingredient when treating the defect as an impurity. From a quantum-mechanical point of view, the defect is treated as a perturbation to the electronic structure of the perfect crystal environment. 

The embedded cluster approach is based on schemes that smoothly link the quantum-mechanical solution of the cluster to the perfect crystal. Different methods have been developed based on either Green function or group-function (localized crystalHne orbitals) techniques. 

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