Reduction formula for point group D2h



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
Cartesian 3N 252 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 246 2 2 2 0 4 4 4



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 33 31 31 31 30 32 32 32 252
Translation 0 0 0 0 0 1 1 1 3
Rotation 0 1 1 1 0 0 0 0 3
Vibration 33 30 30 30 30 31 31 31 246



Molecule Parameter
Number of Atoms (N) 84
Number of internal coordinates 246
Number of independant internal coordinates 33
Number of vibrational modes 246





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag B1g B2g B3g Au B1u B2u B3u Total
Linear (IR) 33 30 30 30 30 31 31 31 93 / 153
Quadratic (Raman) 33 30 30 30 30 31 31 31 123 / 123
IR + Raman - - - - 30 - - - 0* / 30
* 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 1 246 2 2 2 0 4 4 4
quadratic 2 30.381 125 125 125 123 131 131 131
cubic 3 2.511.496 248 248 248 0 504 504 504
quartic 4 156.340.626 7.874 7.874 7.874 7.626 8.626 8.626 8.626
quintic 5 7.817.031.300 15.500 15.500 15.500 0 32.000 32.000 32.000
sextic 6 327.012.476.050 333.250 333.250 333.250 317.750 380.750 380.750 380.750


Decomposition into Irreducible representations
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 33 30 30 30 30 31 31 31
quadratic 2 3.909 3.781 3.781 3.781 3.780 3.783 3.783 3.783
cubic 3 314.219 313.843 313.843 313.843 313.841 313.969 313.969 313.969
quartic 4 19.549.719 19.541.469 19.541.469 19.541.469 19.541.343 19.541.719 19.541.719 19.541.719
quintic 5 977.146.725 977.122.975 977.122.975 977.122.975 977.122.725 977.130.975 977.130.975 977.130.975
sextic 6 40.876.866.975 40.876.509.975 40.876.509.975 40.876.509.975 40.876.501.975 40.876.525.725 40.876.525.725 40.876.525.725


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