Point cyclic-cluster model

SCM is used as a rule for the neutral-point-defects calculations (for the charged point defects the field of periodically repeated charge has to be suppressed in one or another way). The molecular- and cyclic-cluster models are more universal as they can be apphed both for the neutral and charged point defects. 

The point symmetry of the cyclic-cluster model coincides with point groups F and Fd for the host and defective crystal. 

Supercell and Cyclic-cluster Models of Neutral and Charged Point Defects... 

The idea to use relatively small cyclic clusters for comparative perfect-crystal and point-defect calculations appeared as an alternative to the molecular-cluster model in an attempt to handle explicitly the immediate environment of the chemisorbed atom on a crystalline surface [285] and the point defects in layered solids [286,287] or in a bulk crystal [288,289,292,293]. The cluster is formed by a manageable group of atoms around the defect and the difference between the molecular-cluster model (MCM) and the cychc cluster model (COM) is due to the choice of boundary conditions for the one-electron wavefunctions (MOs). Different notations of COM appeared in the literature molecular vmit ceU approach [288], small periodic cluster [286], large rmit cell [289,290]. We use here the cychc cluster notation. 

The CCM model allows real-space calculations (formaUy corresponding to the BZ center for the infinite crystal composed of the supercells). From this point of view the cyclic cluster was termed a quasimolecular large unit ceb [289] or a molecular unit ceb [288]. 

What happens when the cychc cluster is increased Depending on its shape and size different sets of fe-points are reproduced, but in the EHT matrix elements the number of interactions included (interaction radius) increases as the periodically reproduced atomic sites distance is defined by the translation vector of a cyclic cluster as a whole. It is important to reproduce in the cyclic-cluster calculations the states defining the bandgap. As the overlap matrix elements decay exponentially with the interatomic distance one obtains the convergence of results with increasing cyclic cluster. Of course, this convergence is slower the more diffuse are the AOs in the basis. Prom band-structure calculations it is known that for BNhex in the one-layer model the top of the valence band and the bottom of the conduction band are at the point P of the BZ reproduced in the cyclic cluster considered. 

The actual natural charge in the cyclic pentamer is qnat = 0.570, which makes the Coulombic point-charge estimate entirely unrealistic.) Thus, no matter how q is chosen, a simple Coulombic point-charge model will give >10% errors for one or the other of these clusters. 

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