Reduction formula for point group O



Characters for molecular motions
Motion E 8C3 6C'2 6C4 3C2 =(C4)2
Cartesian 3N 21 0 -1 3 -3
Translation 3 0 -1 1 -1
Rotation 3 0 -1 1 -1
Vibration 15 0 1 1 -1



Decomposition into Irreducible representations
Motion A1 A2 E T1 T2 Total
Cartesian 3N 1 0 1 4 2 8
Translation 0 0 0 1 0 1
Rotation 0 0 0 1 0 1
Vibration 1 0 1 2 2 6



Molecule Parameter
Number of Atoms (N) 7
Number of internal coordinates 15
Number of independant internal coordinates 1
Number of vibrational modes 6





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E T1 T2 Total
Linear (IR) 1 0 1 2 2 2 / 4
Quadratic (Raman) 1 0 1 2 2 4 / 2
IR + Raman - 0 - - - 0 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 8C3 6C'2 6C4 3C2 =(C4)2
linear 1 15 0 1 1 -1
quadratic 2 120 0 8 0 8
cubic 3 680 5 8 0 -8
quartic 4 3.060 0 36 4 36
quintic 5 11.628 0 36 4 -36
sextic 6 38.760 15 120 0 120


Decomposition into Irreducible representations
Force field Tensor
Order
A1 A2 E T1 T2
linear 1 1 0 1 2 2
quadratic 2 8 4 12 12 16
cubic 3 31 27 53 84 88
quartic 4 142 122 264 370 386
quintic 5 490 470 960 1.450 1.466
sextic 6 1.665 1.605 3.255 4.800 4.860


Literature




Character tables for chemically important point groups Character table for point group O Jacobs University Bremen

Last update Mai, 23rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement