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On the use of symmetry in the ab initio quantum mechanical simulation of nanotubes and related materials
Author(s) -
Noel Yves,
D'arco Philippe,
Demichelis Raffaella,
ZicovichWilson Claudio M.,
Dovesi Roberto
Publication year - 2010
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.21370
Subject(s) - irreducible representation , carbon nanotube , symmetry (geometry) , ab initio , wave function , quantum mechanics , symmetry operation , atom (system on chip) , fock matrix , nanotube , atomic orbital , physics , unit (ring theory) , molecular symmetry , fock space , basis set , symmetry group , materials science , mathematics , nanotechnology , electron , computer science , geometry , molecule , mathematics education , embedded system
Nanotubes can be characterized by a very high point symmetry, comparable or even larger than the one of the most symmetric crystalline systems (cubic, 48 point symmetry operators). For example, N = 2 n rototranslation symmetry operators connect the atoms of the ( n ,0) nanotubes. This symmetry is fully exploited in the CRYSTAL code. As a result, ab initio quantum mechanical large basis set calculations of carbon nanotubes containing more than 150 atoms in the unit cell become very cheap, because the irreducible part of the unit cell reduces to two atoms only. The nanotube symmetry is exploited at three levels in the present implementation. First, for the automatic generation of the nanotube structure (and then of the input file for the SCF calculation) starting from a two‐dimensional structure (in the specific case, graphene). Second, the nanotube symmetry is used for the calculation of the mono‐ and bi‐electronic integrals that enter into the Fock (Kohn‐Sham) matrix definition. Only the irreducible wedge of the Fock matrix is computed, with a saving factor close to N . Finally, the symmetry is exploited for the diagonalization, where each irreducible representation is separately treated. When M atomic orbitals per carbon atom are used, the diagonalization computing time is close to Nt , where t is the time required for the diagonalization of each 2 M × 2 M matrix. The efficiency and accuracy of the computational scheme is documented. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010