Reduction formula for point group D6h



Characters for molecular motions
Motion E 2C6 (z) 2C3 C2 3C'2 3C''2 i 2S3 2S6 h (xy) 3d 3v
Cartesian 3N 36 0 0 0 -4 0 0 0 0 12 0 4
Translation 3 2 0 -1 -1 -1 -3 -2 0 1 1 1
Rotation 3 2 0 -1 -1 -1 3 2 0 -1 -1 -1
Vibration 30 -4 0 2 -2 2 0 0 0 12 0 4



Decomposition into Irreducible representations
Motion A1g A2g B1g B2g E1g E2g A1u A2u B1u B2u E1u E2u Total
Cartesian 3N 2 2 0 2 2 4 0 2 2 2 4 2 24
Translation 0 0 0 0 0 0 0 1 0 0 1 0 2
Rotation 0 1 0 0 1 0 0 0 0 0 0 0 2
Vibration 2 1 0 2 1 4 0 1 2 2 3 2 20



Molecule Parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 2
Number of vibrational modes 20





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1g A2g B1g B2g E1g E2g A1u A2u B1u B2u E1u E2u Total
Linear (IR) 2 1 0 2 1 4 0 1 2 2 3 2 4 / 16
Quadratic (Raman) 2 1 0 2 1 4 0 1 2 2 3 2 7 / 13
IR + Raman - 1 0 2 - - 0 - 2 2 - 2 0* / 9
* Center of inversion: Mutual Exclusion Principle



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C6 (z) 2C3 C2 3C'2 3C''2 i 2S3 2S6 h (xy) 3d 3v
linear 1 30 -4 0 2 -2 2 0 0 0 12 0 4
quadratic 2 465 8 0 17 17 17 15 0 0 87 15 23
cubic 3 4.960 -10 10 32 -32 32 0 4 0 472 0 72
quartic 4 40.920 8 0 152 152 152 120 0 0 2.112 120 256
quintic 5 278.256 -4 0 272 -272 272 0 0 0 8.184 0 680
sextic 6 1.623.160 7 55 952 952 952 680 13 5 28.336 680 1.904


Decomposition into Irreducible representations
Force field Tensor
Order
A1g A2g B1g B2g E1g E2g A1u A2u B1u B2u E1u E2u
linear 1 2 1 0 2 1 4 0 1 2 2 3 2
quadratic 2 34 16 14 16 32 48 16 17 22 20 44 31
cubic 3 237 219 170 204 370 455 179 197 228 226 448 377
quartic 4 1.890 1.720 1.598 1.632 3.232 3.608 1.610 1.628 1.798 1.764 3.564 3.236
quintic 5 12.031 11.861 11.089 11.395 22.483 23.893 11.179 11.349 11.941 11.907 23.847 22.529
sextic 6 69.448 68.326 66.290 66.596 132.876 137.754 66.381 66.551 68.902 68.596 137.484 132.921


Literature




Character tables for chemically important point groups Character table for point group D6h Jacobs University Bremen

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