Reduction formula for point group D2h



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
Cartesian 3N 48 0 0 0 0 0 0 0
Translation 3 -1 -1 -1 -3 1 1 1
Rotation 3 -1 -1 -1 3 -1 -1 -1
Vibration 42 2 2 2 0 0 0 0



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 6 6 6 6 6 6 6 6 48
Translation 0 0 0 0 0 1 1 1 3
Rotation 0 1 1 1 0 0 0 0 3
Vibration 6 5 5 5 6 5 5 5 42



Molecule Parameter
Number of Atoms (N) 16
Number of internal coordinates 42
Number of independant internal coordinates 6
Number of vibrational modes 42





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag B1g B2g B3g Au B1u B2u B3u Total
Linear (IR) 6 5 5 5 6 5 5 5 15 / 27
Quadratic (Raman) 6 5 5 5 6 5 5 5 21 / 21
IR + Raman - - - - 6 - - - 0* / 6
* 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 42 2 2 2 0 0 0 0
quadratic 2 903 23 23 23 21 21 21 21
cubic 3 13.244 44 44 44 0 0 0 0
quartic 4 148.995 275 275 275 231 231 231 231
quintic 5 1.370.754 506 506 506 0 0 0 0
sextic 6 10.737.573 2.277 2.277 2.277 1.771 1.771 1.771 1.771


Decomposition into Irreducible representations
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 6 5 5 5 6 5 5 5
quadratic 2 132 110 110 110 111 110 110 110
cubic 3 1.672 1.650 1.650 1.650 1.672 1.650 1.650 1.650
quartic 4 18.843 18.590 18.590 18.590 18.612 18.590 18.590 18.590
quintic 5 171.534 171.281 171.281 171.281 171.534 171.281 171.281 171.281
sextic 6 1.343.936 1.341.912 1.341.912 1.341.912 1.342.165 1.341.912 1.341.912 1.341.912


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