Reduction formula for point group O



Characters for molecular motions
Motion E 8C3 6C'2 6C4 3C2 =(C4)2
Cartesian 3N 48 0 0 0 0
Translation 3 0 -1 1 -1
Rotation 3 0 -1 1 -1
Vibration 42 0 2 -2 2



Decomposition into Irreducible representations
Motion A1 A2 E T1 T2 Total
Cartesian 3N 2 2 4 6 6 20
Translation 0 0 0 1 0 1
Rotation 0 0 0 1 0 1
Vibration 2 2 4 4 6 18



Molecule Parameter
Number of Atoms (N) 16
Number of internal coordinates 42
Number of independant internal coordinates 2
Number of vibrational modes 18





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E T1 T2 Total
Linear (IR) 2 2 4 4 6 4 / 14
Quadratic (Raman) 2 2 4 4 6 12 / 6
IR + Raman - 2 - - - 0 / 2



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 8C3 6C'2 6C4 3C2 =(C4)2
linear 1 42 0 2 -2 2
quadratic 2 903 0 23 3 23
cubic 3 13.244 14 44 -4 44
quartic 4 148.995 0 275 15 275
quintic 5 1.370.754 0 506 -26 506
sextic 6 10.737.573 105 2.277 37 2.277


Decomposition into Irreducible representations
Force field Tensor
Order
A1 A2 E T1 T2
linear 1 2 2 4 4 6
quadratic 2 47 34 81 105 115
cubic 3 572 552 1.110 1.638 1.662
quartic 4 6.315 6.170 12.485 18.525 18.655
quintic 5 57.298 57.058 114.356 171.148 171.414
sextic 6 448.297 447.140 895.332 1.341.352 1.342.472


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