Reduction formula for point group D2h



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
Cartesian 3N 180 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 174 2 2 2 0 4 4 4



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 24 22 22 22 21 23 23 23 180
Translation 0 0 0 0 0 1 1 1 3
Rotation 0 1 1 1 0 0 0 0 3
Vibration 24 21 21 21 21 22 22 22 174



Molecule Parameter
Number of Atoms (N) 60
Number of internal coordinates 174
Number of independant internal coordinates 24
Number of vibrational modes 174





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag B1g B2g B3g Au B1u B2u B3u Total
Linear (IR) 24 21 21 21 21 22 22 22 66 / 108
Quadratic (Raman) 24 21 21 21 21 22 22 22 87 / 87
IR + Raman - - - - 21 - - - 0* / 21
* 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 1 174 2 2 2 0 4 4 4
quadratic 2 15.225 89 89 89 87 95 95 95
cubic 3 893.200 176 176 176 0 360 360 360
quartic 4 39.524.100 4.004 4.004 4.004 3.828 4.540 4.540 4.540
quintic 5 1.407.057.960 7.832 7.832 7.832 0 16.376 16.376 16.376
sextic 6 41.977.229.140 121.396 121.396 121.396 113.564 145.604 145.604 145.604


Decomposition into Irreducible representations
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 24 21 21 21 21 22 22 22
quadratic 2 1.983 1.891 1.891 1.891 1.890 1.893 1.893 1.893
cubic 3 111.851 111.583 111.583 111.583 111.581 111.673 111.673 111.673
quartic 4 4.944.195 4.939.923 4.939.923 4.939.923 4.939.833 4.940.101 4.940.101 4.940.101
quintic 5 175.891.323 175.879.219 175.879.219 175.879.219 175.879.041 175.883.313 175.883.313 175.883.313
sextic 6 5.247.267.963 5.247.134.463 5.247.134.463 5.247.134.463 5.247.130.369 5.247.142.473 5.247.142.473 5.247.142.473


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