Reduction formula for point group D2h



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
Cartesian 3N 324 0 0 0 0 24 12 8
Translation 3 -1 -1 -1 -3 1 1 1
Rotation 3 -1 -1 -1 3 -1 -1 -1
Vibration 318 2 2 2 0 24 12 8



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 46 41 38 37 35 40 43 44 324
Translation 0 0 0 0 0 1 1 1 3
Rotation 0 1 1 1 0 0 0 0 3
Vibration 46 40 37 36 35 39 42 43 318



Molecule Parameter
Number of Atoms (N) 108
Number of internal coordinates 318
Number of independant internal coordinates 46
Number of vibrational modes 318





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag B1g B2g B3g Au B1u B2u B3u Total
Linear (IR) 46 40 37 36 35 39 42 43 124 / 194
Quadratic (Raman) 46 40 37 36 35 39 42 43 159 / 159
IR + Raman - - - - 35 - - - 0* / 35
* 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 1 318 2 2 2 0 24 12 8
quadratic 2 50.721 161 161 161 159 447 231 191
cubic 3 5.410.240 320 320 320 0 6.128 2.200 1.360
quartic 4 434.171.760 13.040 13.040 13.040 12.720 72.528 25.080 18.000
quintic 5 27.960.661.344 25.760 25.760 25.760 0 741.552 201.432 116.112
sextic 6 1.505.215.602.352 708.400 708.400 708.400 682.640 6.858.544 1.748.824 1.120.816


Decomposition into Irreducible representations
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 46 40 37 36 35 39 42 43
quadratic 2 6.529 6.343 6.289 6.279 6.272 6.297 6.351 6.361
cubic 3 677.611 676.561 675.579 675.369 675.189 675.919 676.901 677.111
quartic 4 54.292.401 54.275.111 54.263.249 54.261.479 54.260.319 54.264.569 54.276.431 54.278.201
quintic 5 3.495.224.715 3.495.132.449 3.494.997.419 3.494.976.089 3.494.959.941 3.495.026.447 3.495.161.477 3.495.182.807
sextic 6 188.153.517.297 188.152.445.687 188.151.168.257 188.151.011.255 188.150.914.591 188.151.277.801 188.152.555.231 188.152.712.233


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