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A novel approach for constructing symmetry‐adapted basis sets for quantum‐chemical calculations. I. Real symmetry‐adapted orbitals
Author(s) -
Kantorovich L.,
Livshits A.
Publication year - 1992
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221740108
Subject(s) - symmetry operation , atomic orbital , symmetry (geometry) , rotation formalisms in three dimensions , basis (linear algebra) , irreducible representation , simple (philosophy) , unitary group , group (periodic table) , character table , matrix (chemical analysis) , symmetry group , computer science , theoretical physics , algebra over a field , unitary state , projection (relational algebra) , group theory , operator (biology) , representation (politics) , quantum mechanics , pure mathematics , algorithm , mathematics , physics , chemistry , geometry , character (mathematics) , electron , philosophy , law , epistemology , chromatography , political science , repressor , biochemistry , transcription factor , politics , gene
A novel method for generating symmetry‐adapted basis orbitals (widely applied in quantum chemistry) is proposed. It extensively combines the ideas of both the local‐group and projection‐operator methods. Some important improvements of the previous formalisms are made, namely: (i) the simple procedure for the construction of the transformation matrix (TM) while the matrix making this TM unitary is extracted individually for further usage, (ii) the partial reduction of the initial reducible representation results in the possibility of conserving all matrices real even in the cases when the group in question has complex irreducible representations. The procedure proposed in this paper is applied to the general finite group which could be both the usual point or large unit cell group. Our method is well suited for computer utilization.