Reduction formula for point group D2h



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
Cartesian 3N 57 -3 -3 -3 -3 9 9 9
Translation 3 -1 -1 -1 -3 1 1 1
Rotation 3 -1 -1 -1 3 -1 -1 -1
Vibration 51 -1 -1 -1 -3 9 9 9



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 9 6 6 6 3 9 9 9 57
Translation 0 0 0 0 0 1 1 1 3
Rotation 0 1 1 1 0 0 0 0 3
Vibration 9 5 5 5 3 8 8 8 51



Molecule Parameter
Number of Atoms (N) 19
Number of internal coordinates 51
Number of independant internal coordinates 9
Number of vibrational modes 51





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag B1g B2g B3g Au B1u B2u B3u Total
Linear (IR) 9 5 5 5 3 8 8 8 24 / 27
Quadratic (Raman) 9 5 5 5 3 8 8 8 24 / 27
IR + Raman - - - - 3 - - - 0* / 3
* 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 51 -1 -1 -1 -3 9 9 9
quadratic 2 1.326 26 26 26 30 66 66 66
cubic 3 23.426 -26 -26 -26 -82 354 354 354
quartic 4 316.251 351 351 351 459 1.671 1.671 1.671
quintic 5 3.478.761 -351 -351 -351 -1.161 6.831 6.831 6.831
sextic 6 32.468.436 3.276 3.276 3.276 4.788 25.564 25.564 25.564


Decomposition into Irreducible representations
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 9 5 5 5 3 8 8 8
quadratic 2 204 158 158 158 147 167 167 167
cubic 3 3.041 2.877 2.877 2.877 2.796 2.986 2.986 2.986
quartic 4 40.347 39.336 39.336 39.336 38.979 39.639 39.639 39.639
quintic 5 437.130 433.890 433.890 433.890 432.297 435.888 435.888 435.888
sextic 6 4.069.968 4.055.548 4.055.548 4.055.548 4.049.598 4.060.742 4.060.742 4.060.742


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