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Point group symmetry and cartesian force constant redundancy
Author(s) -
Stanton John F.
Publication year - 1991
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/qua.560390105
Subject(s) - cartesian coordinate system , symmetry operation , invariant (physics) , rotational symmetry , mathematics , redundancy (engineering) , point group , group (periodic table) , symmetry (geometry) , pure mathematics , geometry , physics , quantum mechanics , mathematical physics , computer science , operating system
A procedure for identifying redundancy in the Cartesian force constant matrix is described, and a prescription is given for generating the entire matrix of second derivatives from the minimal set of information. A proof is supplied which demonstrates that the number of nonredundant rows corresponding to a symmetry unique atom is necessarily less than three if the atom is invariant with respect to a symmetry operation of the point group other than the identity or inversion. Furthermore, only one row is required if the atom lies on a threefold or higher‐order rotation axis. An application of the procedure to the evaluation of harmonic force constants by numerical differentiation of gradient vectors is briefly described.