Infinite solids cluster size calculation

Another standing topic during the last two decades has been to evaluate the electronic structure of solids, surfaces and adsorbates on surfaces. This can be done using standard band structure methods [107] or in more recent years slab codes for studies of surfaces. An alternative and very popular approach has been to model the infinite solid or surface with a finite cluster, where the choice of the form and size of the cluster has been determined by the local geometry. These clusters have in more advanced calculations been embedded in some type of external potential as discussed above. It should be noted that these types of cluster have in general quite different geometries compared with... 

Cluster size for the calculation of infinite solids CmO The cluster size, when we calculate an infinite solid, is an important parameter using the cluster approximation. The size of the cluster or the termination method of the cluster (the charge of a cluster) has the largest effect on the accuracy of the DV-Xa calculation. 

In order to overcome these problems, simplified systems are studied theoreti-eally. One such corresponds to approximating the semi-infinite solid through a finite cluster and then studying the interactions between this and the reactants. In this approximation a number of bonds that are present in the infinite solid have been cut and the resulting dangling bonds have therefore to be saturated through, e.g. hydrogen atoms. Nevertheless, finite-size effects as well as effects due to the saturated bonds may obscure the results of such calculations. 

In molecular DFT calculations, it is natural to include all electrons in the calculations and hence no further subtleties than the ones described arise in the calculation of the isomer shift. However, there are situations where other approaches are advantageous. The most prominent situation is met in the case of solids. Here, it is difficult to capture the effects of an infinite system with a finite size cluster model and one should resort to dedicated solid state techniques. It appears that very efficient solid state DFT implementations are possible on the basis of plane wave basis sets. However, it is difficult to describe the core region with plane wave basis sets. Hence, the core electrons need to be replaced by pseudopotentials, which precludes a direct calculation of the electron density at the Mossbauer absorber atom. However, there are workarounds and the subtleties involved in this subject are discussed in a complementary chapter by Blaha (see CD-ROM, Part HI). 

Solids and surfaces can be modeled as large clusters, as embedded clusters, and as infinite periodic systems. Each of these strategies has been used in conjunction with semiempirical MO methods. The most straightforward semiempirical approach employs clusters of increasing size, taking advantage of the fact that semiempirical calculations can be extended easily to systems with more than 1000 atoms which facilitates convergence studies to the bulk limit. Semiempirical work in this field has been reviewed recently [45]. 

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