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By Pechenberg P., Mössenböck H.

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A type of basis set which has the characteristic to be unbiased is based on plane waves. Such basis sets have a quite simple form and naturally benefit from the periodicity of the crystalline solids. In fact, one can re-define the Kohn–Sham equations in the reciprocal space, taking advantage of the peculiar form of plane waves. If we consider a crystal with dimensions L 1 = N1 |a1 |, L 2 = N2 |a2 |, and L 3 = N3 |a3 |, with ai being the primitive vectors of the lattice (shown in Fig. 4 a), one can define the wave vector k in the reciprocal space as: k= n2 n3 n1 b1 + b2 + b3 .

Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. Seitsonen, A. Smogunov, P. Umari, R. Wentzcovitch, J. Phys. Condens. Matter 21(39), 395502 (2009) 26. X. M. Beuken, R. Caracas, F. Detraux, M. M. Rignanese, L. Sindic, M. Verstraete, G. ZÃt’erah, F. Jollet, M. Torrent, A. Roy, M.

Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. Seitsonen, A. Smogunov, P. Umari, R. Wentzcovitch, J. Phys. Condens. Matter 21(39), 395502 (2009) 26. X. M. Beuken, R. Caracas, F. Detraux, M. M. Rignanese, L. Sindic, M. Verstraete, G. ZÃt’erah, F. Jollet, M. Torrent, A. Roy, M. Mikami, P. Y. C. Allan, Comput. Mater. Sci. 25, 478 (2002) 27. C. Slater, Phys. Rev.

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A Compiller Generator for Microcomputers by Pechenberg P., Mössenböck H.


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