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 8 8
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 8 8



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 8 4 6 6 4 8 6 6 48
Translation 0 0 0 0 0 1 1 1 3
Rotation 0 1 1 1 0 0 0 0 3
Vibration 8 3 5 5 4 7 5 5 42



Molecule Parameter
Number of Atoms (N) 16
Number of internal coordinates 42
Number of independant internal coordinates 8
Number of vibrational modes 42





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag B1g B2g B3g Au B1u B2u B3u Total
Linear (IR) 8 3 5 5 4 7 5 5 17 / 25
Quadratic (Raman) 8 3 5 5 4 7 5 5 21 / 21
IR + Raman - - - - 4 - - - 0* / 4
* 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 8 8
quadratic 2 903 23 23 23 21 21 53 53
cubic 3 13.244 44 44 44 0 0 256 256
quartic 4 148.995 275 275 275 231 231 1.095 1.095
quintic 5 1.370.754 506 506 506 0 0 4.056 4.056
sextic 6 10.737.573 2.277 2.277 2.277 1.771 1.771 13.803 13.803


Decomposition into Irreducible representations
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 8 3 5 5 4 7 5 5
quadratic 2 140 102 110 110 103 118 110 110
cubic 3 1.736 1.586 1.650 1.650 1.608 1.714 1.650 1.650
quartic 4 19.059 18.374 18.590 18.590 18.396 18.806 18.590 18.590
quintic 5 172.548 170.267 171.281 171.281 170.520 172.295 171.281 171.281
sextic 6 1.346.944 1.338.904 1.341.912 1.341.912 1.339.157 1.344.920 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