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 0 -4 0 24 4 0
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 2 -2 0 24 4 0



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 12 12 7 5 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 6 4 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 6 4 5 6 11 11 28 / 38
Quadratic (Raman) 12 11 6 4 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 2 -2 0 24 4 0
quadratic 2 2.211 35 35 35 33 321 41 33
cubic 3 50.116 68 68 -68 0 3.104 144 0
quartic 4 864.501 629 629 629 561 24.081 841 561
quintic 5 12.103.014 1.190 1.190 -1.190 0 158.424 2.660 0
sextic 6 143.218.999 7.735 7.735 7.735 6.545 914.641 11.585 6.545


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 6 4 5 6 11 11
quadratic 2 343 307 237 235 236 237 307 309
cubic 3 6.679 6.643 5.903 5.833 5.867 5.903 6.643 6.645
quartic 4 111.554 110.889 105.079 105.009 105.043 105.079 110.889 110.959
quintic 5 1.533.161 1.532.496 1.493.555 1.492.295 1.492.890 1.493.555 1.532.496 1.532.566
sextic 6 18.022.690 18.014.290 17.788.526 17.787.266 17.787.861 17.788.526 18.014.290 18.015.550


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