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Characters for symmetric and antisymmetric higher powers of representations: Application to the number of anharmonic force constants in symmetrical molecules
Author(s) -
Zhou XueFeng,
Pulay Peter
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.540100711
Subject(s) - antisymmetric relation , quartic function , anharmonicity , symmetry (geometry) , molecule , representation (politics) , force constant , distortion (music) , quantum mechanics , physics , chemistry , computational chemistry , mathematical physics , classical mechanics , mathematics , pure mathematics , geometry , law , amplifier , optoelectronics , cmos , politics , political science
Explicit formulas are given for the characters of symmetric and antisymmetric powers of an arbitrary representation up to the sixth, and a general method for obtaining the higher ones is described. The results allow, among others, the determination of nonvanishing higher force constants in symmetrical molecules. The benzene molecule, for instance, has 237 nonvanishing cubic and 1890 quartic force constants. Other potential applications are a general method for the symmetry species of vibrational overtones, the determination of the number of independent centrifugal distortion constants, and the symmetry classification of vibrational multiplets.