Reduction formula for point group D2h



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
Cartesian 3N 24 0 -2 -2 0 4 6 2
Translation 3 -1 -1 -1 -3 1 1 1
Rotation 3 -1 -1 -1 3 -1 -1 -1
Vibration 18 2 0 0 0 4 6 2



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 4 3 3 2 1 4 3 4 24
Translation 0 0 0 0 0 1 1 1 3
Rotation 0 1 1 1 0 0 0 0 3
Vibration 4 2 2 1 1 3 2 3 18



Molecule Parameter
Number of Atoms (N) 8
Number of internal coordinates 18
Number of independant internal coordinates 4
Number of vibrational modes 18





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag B1g B2g B3g Au B1u B2u B3u Total
Linear (IR) 4 2 2 1 1 3 2 3 8 / 10
Quadratic (Raman) 4 2 2 1 1 3 2 3 9 / 9
IR + Raman - - - - 1 - - - 0* / 1
* 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 18 2 0 0 0 4 6 2
quadratic 2 171 11 9 9 9 17 27 11
cubic 3 1.140 20 0 0 0 48 92 20
quartic 4 5.985 65 45 45 45 133 273 65
quintic 5 26.334 110 0 0 0 308 714 110
sextic 6 100.947 275 165 165 165 693 1.715 275


Decomposition into Irreducible representations
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 4 2 2 1 1 3 2 3
quadratic 2 33 19 21 17 17 22 19 23
cubic 3 165 137 143 125 125 153 137 155
quartic 4 832 725 755 703 703 765 725 777
quintic 5 3.447 3.241 3.315 3.164 3.164 3.370 3.241 3.392
sextic 6 13.050 12.470 12.698 12.338 12.338 12.753 12.470 12.830


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