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Molecular symmetry and ab initio calculations. I. Symmetry‐matrix and symmetry‐supermatrix
Author(s) -
Cao Xiaoping
Publication year - 1989
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.540100714
Subject(s) - supermatrix , symmetry (geometry) , molecular symmetry , matrix (chemical analysis) , symmetry operation , physics , symmetry group , fock matrix , mathematical physics , quantum mechanics , molecule , computational chemistry , chemistry , hartree–fock method , mathematics , pure mathematics , algebra over a field , geometry , current algebra , chromatography , affine lie algebra
In this article the matrix elements can be grouped into classes by means of the molecular symmetry. By introducing the concepts of symmetry‐matrix and symmetry‐supermatrix and determining their operation rules, the storage of the supermatrix can be asymptotically reduced by a factor of ca. g 2 ( g is the order of the molecular symmetry group) and the calculation of Fock matrix during each SCF cycle can be reduced proportionally. Besides, by using the DIIS method combined with the symmetry‐matrices, the convergence behavior for highly symmetric molecules can be improved.