Reduction formula for point group D2h



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
Cartesian 3N 18 0 0 -2 0 6 2 0
Translation 3 -1 -1 -1 -3 1 1 1
Rotation 3 -1 -1 -1 3 -1 -1 -1
Vibration 12 2 2 0 0 6 2 0



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 3 3 2 1 1 2 3 3 18
Translation 0 0 0 0 0 1 1 1 3
Rotation 0 1 1 1 0 0 0 0 3
Vibration 3 2 1 0 1 1 2 2 12



Molecule Parameter
Number of Atoms (N) 6
Number of internal coordinates 12
Number of independant internal coordinates 3
Number of vibrational modes 12





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag B1g B2g B3g Au B1u B2u B3u Total
Linear (IR) 3 2 1 0 1 1 2 2 5 / 7
Quadratic (Raman) 3 2 1 0 1 1 2 2 6 / 6
IR + Raman - - - - 1 - - - 0* / 1
* Center of inversion: Mutual Exclusion Principle



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
linear 1 12 2 2 0 0 6 2 0
quadratic 2 78 8 8 6 6 24 8 6
cubic 3 364 14 14 0 0 74 14 0
quartic 4 1.365 35 35 21 21 195 35 21
quintic 5 4.368 56 56 0 0 456 56 0
sextic 6 12.376 112 112 56 56 976 112 56


Decomposition into Irreducible representations
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 3 2 1 0 1 1 2 2
quadratic 2 18 11 7 6 7 7 11 11
cubic 3 60 53 38 31 38 38 53 53
quartic 4 216 188 148 141 148 148 188 188
quintic 5 624 596 496 468 496 496 596 596
sextic 6 1.732 1.648 1.432 1.404 1.432 1.432 1.648 1.648


Literature




Character tables for chemically important point groups Character table for point group D2h Jacobs University Bremen

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