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 0 0 8 8 8
Translation 3 -1 -1 -1 -3 1 1 1
Rotation 3 -1 -1 -1 3 -1 -1 -1
Vibration 66 2 2 2 0 8 8 8



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 12 8 8 8 6 10 10 10 72
Translation 0 0 0 0 0 1 1 1 3
Rotation 0 1 1 1 0 0 0 0 3
Vibration 12 7 7 7 6 9 9 9 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 7 7 7 6 9 9 9 27 / 39
Quadratic (Raman) 12 7 7 7 6 9 9 9 33 / 33
IR + Raman - - - - 6 - - - 0* / 6
* 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 8 8 8
quadratic 2 2.211 35 35 35 33 65 65 65
cubic 3 50.116 68 68 68 0 352 352 352
quartic 4 864.501 629 629 629 561 1.809 1.809 1.809
quintic 5 12.103.014 1.190 1.190 1.190 0 7.752 7.752 7.752
sextic 6 143.218.999 7.735 7.735 7.735 6.545 31.441 31.441 31.441


Decomposition into Irreducible representations
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 12 7 7 7 6 9 9 9
quadratic 2 318 268 268 268 261 276 276 276
cubic 3 6.422 6.212 6.212 6.212 6.158 6.300 6.300 6.300
quartic 4 109.047 107.828 107.828 107.828 107.550 108.140 108.140 108.140
quintic 5 1.516.230 1.511.759 1.511.759 1.511.759 1.510.416 1.513.697 1.513.697 1.513.697
sextic 6 17.917.884 17.898.296 17.898.296 17.898.296 17.892.667 17.904.520 17.904.520 17.904.520


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