Reduction formula for point group D2h



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
Cartesian 3N 36 0 0 0 0 4 4 4
Translation 3 -1 -1 -1 -3 1 1 1
Rotation 3 -1 -1 -1 3 -1 -1 -1
Vibration 30 2 2 2 0 4 4 4



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 6 4 4 4 3 5 5 5 36
Translation 0 0 0 0 0 1 1 1 3
Rotation 0 1 1 1 0 0 0 0 3
Vibration 6 3 3 3 3 4 4 4 30



Molecule Parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 6
Number of vibrational modes 30





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag B1g B2g B3g Au B1u B2u B3u Total
Linear (IR) 6 3 3 3 3 4 4 4 12 / 18
Quadratic (Raman) 6 3 3 3 3 4 4 4 15 / 15
IR + Raman - - - - 3 - - - 0* / 3
* 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 30 2 2 2 0 4 4 4
quadratic 2 465 17 17 17 15 23 23 23
cubic 3 4.960 32 32 32 0 72 72 72
quartic 4 40.920 152 152 152 120 256 256 256
quintic 5 278.256 272 272 272 0 680 680 680
sextic 6 1.623.160 952 952 952 680 1.904 1.904 1.904


Decomposition into Irreducible representations
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 6 3 3 3 3 4 4 4
quadratic 2 75 55 55 55 54 57 57 57
cubic 3 659 607 607 607 605 625 625 625
quartic 4 5.283 5.079 5.079 5.079 5.061 5.113 5.113 5.113
quintic 5 35.139 34.663 34.663 34.663 34.629 34.833 34.833 34.833
sextic 6 204.051 202.623 202.623 202.623 202.453 202.929 202.929 202.929


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