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 -4 0 0 12 0 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 12 0 4



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 6 6 2 4 2 4 6 6 36
Translation 0 0 0 0 0 1 1 1 3
Rotation 0 1 1 1 0 0 0 0 3
Vibration 6 5 1 3 2 3 5 5 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 5 1 3 2 3 5 5 13 / 17
Quadratic (Raman) 6 5 1 3 2 3 5 5 15 / 15
IR + Raman - - - - 2 - - - 0* / 2
* 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 12 0 4
quadratic 2 465 17 17 17 15 87 15 23
cubic 3 4.960 32 -32 32 0 472 0 72
quartic 4 40.920 152 152 152 120 2.112 120 256
quintic 5 278.256 272 -272 272 0 8.184 0 680
sextic 6 1.623.160 952 952 952 680 28.336 680 1.904


Decomposition into Irreducible representations
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 6 5 1 3 2 3 5 5
quadratic 2 82 64 46 48 47 48 66 64
cubic 3 692 674 540 574 556 574 676 674
quartic 4 5.498 5.328 4.830 4.864 4.846 4.864 5.362 5.328
quintic 5 35.924 35.754 33.572 33.878 33.708 33.878 35.788 35.754
sextic 6 207.202 206.080 199.166 199.472 199.302 199.472 206.386 206.080


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