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On the accuracy of «Divide-and-Conquer» algorithm in application to problems of electronic structure calculation of graphen and its analogs by quantum-chemical methods


V.G. Maslov, A.I. Svitenkov

The problem is considered of the applicability of «Divide-and-Conquer» (DC) algorithm for the semi-empirical quantum chemical calculations of planar systems of graphen and its derivatives containing 104–105 atoms. Three modifications of DC algorithm are proposed differing from its «standard» version by the smaller volume of calculations and more stable convergence of the self-consistency process: (1) the version with a single calculation of the Fermi level, (2) the variant of calculating the Fermi level position in the few first iterations and (3) the version with periodic calculation of the Fermi level during the self-consistency process. It is found that the modified algorithm of determining the number of neighboring atoms on the example of grapheme sheet, depending on the value of overlap integral «cut-off» and the position of the atom gives the number of neighbors from 20 to 100, that leads us to expect a high efficiency of DC algorithm in application to systems containing 104–105 atoms. An accuracy of calculation of the density matrix achieved by using three proposed modifications in comparison with the standard DC procedure were investigated on the example of semi-empirical ZINDO/S scheme in application to graphene sheet C508H62. The results clearly showed that the simplest version of DC algorithm – a variant with a single calculation of the Fermi level – can be recommended for use in the application to the planar grapheme-like systems as it gives results quite comparable in accuracy to the more stringent versions of the DC algorithm. And this method has advantages over other more complex implementations both in terms of convergence of the self-consistency process and in ease of implementation.

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