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Extrapolation of real‐space quantum chemical calculations from finite‐size supercells to the ideal infinite system. III. Application to two‐dimensional systems
Author(s) -
Nolting V.,
Verwoerd W. S.
Publication year - 1997
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1997)63:4<895::aid-qua9>3.0.co;2-r
Subject(s) - supercell , extrapolation , brillouin zone , density matrix , physics , quantum mechanics , matrix (chemical analysis) , ideal (ethics) , quantum , mathematics , mathematical analysis , chemistry , meteorology , philosophy , epistemology , thunderstorm , chromatography
A previously presented extrapolation method of the density matrix of a standard finite supercell calculation to an infinite supercell is extended to two‐dimensional systems. The density matrix of the finite supercell is transformed into q space where it is interpolated and extrapolated in such a way that all its fundamental properties are guaranteed by construction. The resulting modified density matrix contains information from a continuum of q points in the first Brillouin zone which allows for a more realistic calculation of properties like the total energy E tot per atom and the band structure ϵ 1 (q). It is shown that this more realistic calculation takes better care of the crystal symmetries and is essential in reproducing both important degeneracies in the band structure and rotationally symmetric results. In the special case of π electrons only, an exact analytical solution for the density matrix of the infinite supercell is presented. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 895–911, 1997