Reduction formula for point group D2h



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
Cartesian 3N 60 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 54 2 2 2 0 4 4 4



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 9 7 7 7 6 8 8 8 60
Translation 0 0 0 0 0 1 1 1 3
Rotation 0 1 1 1 0 0 0 0 3
Vibration 9 6 6 6 6 7 7 7 54



Molecule Parameter
Number of Atoms (N) 20
Number of internal coordinates 54
Number of independant internal coordinates 9
Number of vibrational modes 54





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag B1g B2g B3g Au B1u B2u B3u Total
Linear (IR) 9 6 6 6 6 7 7 7 21 / 33
Quadratic (Raman) 9 6 6 6 6 7 7 7 27 / 27
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 54 2 2 2 0 4 4 4
quadratic 2 1.485 29 29 29 27 35 35 35
cubic 3 27.720 56 56 56 0 120 120 120
quartic 4 395.010 434 434 434 378 610 610 610
quintic 5 4.582.116 812 812 812 0 1.856 1.856 1.856
sextic 6 45.057.474 4.466 4.466 4.466 3.654 7.134 7.134 7.134


Decomposition into Irreducible representations
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 9 6 6 6 6 7 7 7
quadratic 2 213 181 181 181 180 183 183 183
cubic 3 3.531 3.443 3.443 3.443 3.441 3.473 3.473 3.473
quartic 4 49.815 49.293 49.293 49.293 49.263 49.351 49.351 49.351
quintic 5 573.765 572.431 572.431 572.431 572.373 572.895 572.895 572.895
sextic 6 5.636.991 5.631.191 5.631.191 5.631.191 5.630.727 5.632.061 5.632.061 5.632.061


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