Reduction formula for point group D2h



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
Cartesian 3N 72 0 -2 -2 0 24 2 2
Translation (x,y,z) 3 -1 -1 -1 -3 1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1 3 -1 -1 -1
Vibration 66 2 0 0 0 24 2 2



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 12 12 6 6 5 7 12 12 72
Translation (x,y,z) 0 0 0 0 0 1 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 0 0 0 0 3
Vibration 12 11 5 5 5 6 11 11 66



Molecule Parameter
Number of Atoms (N) 24
Number of internal coordinates 66
Number of independant internal coordinates 12
Number of vibrational modes 66





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag B1g B2g B3g Au B1u B2u B3u Total
Linear (IR) 12 11 5 5 5 6 11 11 28 / 38
Quadratic (Raman) 12 11 5 5 5 6 11 11 33 / 33
IR + Raman - - - - 5 - - - 0* / 5
* 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 66 2 0 0 0 24 2 2
quadratic 2 2.211 35 33 33 33 321 35 35
cubic 3 50.116 68 0 0 0 3.104 68 68
quartic 4 864.501 629 561 561 561 24.081 629 629
quintic 5 12.103.014 1.190 0 0 0 158.424 1.190 1.190
sextic 6 143.218.999 7.735 6.545 6.545 6.545 914.641 7.735 7.735


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 12 11 5 5 5 6 11 11
quadratic 2 342 308 236 236 236 237 308 308
cubic 3 6.678 6.644 5.868 5.868 5.868 5.902 6.644 6.644
quartic 4 111.519 110.924 105.044 105.044 105.044 105.078 110.924 110.924
quintic 5 1.533.126 1.532.531 1.492.925 1.492.925 1.492.925 1.493.520 1.532.531 1.532.531
sextic 6 18.022.060 18.014.920 17.787.896 17.787.896 17.787.896 17.788.491 18.014.920 18.014.920


Literature




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

Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement