Reduction formula for point group Oh



Characters for molecular motions
Motion E 8C3 6C2 6C4 3C2 =(C4)2 i 6S4 8S6 3h 6d
Cartesian 3N 156 0 -2 0 0 0 0 0 4 14
Translation (x,y,z) 3 0 -1 1 -1 -3 -1 0 1 1
Rotation (Rx,Ry,Rz) 3 0 -1 1 -1 3 1 0 -1 -1
Vibration 150 0 0 -2 2 0 0 0 4 14



Decomposition into Irreducible representations
Motion A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u Total
Cartesian 3N 5 2 7 8 11 1 5 6 12 8 65
Translation (x,y,z) 0 0 0 0 0 0 0 0 1 0 1
Rotation (Rx,Ry,Rz) 0 0 0 1 0 0 0 0 0 0 1
Vibration 5 2 7 7 11 1 5 6 11 8 63



Molecule Parameter
Number of Atoms (N) 52
Number of internal coordinates 150
Number of independant internal coordinates 5
Number of vibrational modes 63





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u Total
Linear (IR) 5 2 7 7 11 1 5 6 11 8 11 / 52
Quadratic (Raman) 5 2 7 7 11 1 5 6 11 8 23 / 40
IR + Raman - 2 - 7 - 1 5 6 - 8 0* / 29
* Center of inversion: Mutual Exclusion Principle



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 8C3 6C2 6C4 3C2 =(C4)2 i 6S4 8S6 3h 6d
linear 1 150 0 0 -2 2 0 0 0 4 14
quadratic 2 11.325 0 75 3 77 75 1 0 83 173
cubic 3 573.800 50 0 -4 152 0 0 0 312 1.512
quartic 4 21.947.850 0 2.850 42 3.002 2.850 38 0 3.466 11.866
quintic 5 675.993.780 0 0 -80 5.852 0 0 0 12.320 79.492
sextic 6 17.463.172.650 1.275 73.150 118 79.002 73.150 38 25 97.174 490.042


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u
linear 1 5 2 7 7 11 1 5 6 11 8
quadratic 2 279 216 495 672 733 222 246 468 716 691
cubic 3 12.180 11.803 23.958 35.644 36.023 11.763 12.142 23.880 36.061 35.684
quartic 4 459.560 455.861 915.421 1.369.685 1.373.344 456.032 458.285 914.317 1.372.719 1.370.464
quintic 5 14.094.266 14.074.413 28.168.679 42.238.529 42.258.422 14.072.853 14.092.746 28.165.599 42.259.942 42.240.089
sextic 6 363.899.267 363.758.430 727.657.047 1.091.371.472 1.091.512.231 363.761.544 363.865.747 727.626.666 1.091.496.976 1.091.392.733


Literature




Character tables for chemically important point groups Character table for point group Oh Constructor University Bremen

Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement