Reduction formula for point group D2h



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
Cartesian 3N 78 0 0 -6 0 26 6 0
Translation (x,y,z) 3 -1 -1 -1 -3 1 1 1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1 3 -1 -1 -1
Vibration 72 2 2 -4 0 26 6 0



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 13 13 8 5 5 8 13 13 78
Translation (x,y,z) 0 0 0 0 0 1 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 0 0 0 0 3
Vibration 13 12 7 4 5 7 12 12 72



Molecule Parameter
Number of Atoms (N) 26
Number of internal coordinates 72
Number of independant internal coordinates 13
Number of vibrational modes 72





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag B1g B2g B3g Au B1u B2u B3u Total
Linear (IR) 13 12 7 4 5 7 12 12 31 / 41
Quadratic (Raman) 13 12 7 4 5 7 12 12 36 / 36
IR + Raman - - - - 5 - - - 0* / 5
* 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 72 2 2 -4 0 26 6 0
quadratic 2 2.628 38 38 44 36 374 54 36
cubic 3 64.824 74 74 -156 0 3.874 254 0
quartic 4 1.215.450 740 740 970 666 32.100 1.380 666
quintic 5 18.474.840 1.406 1.406 -3.116 0 225.030 5.466 0
sextic 6 237.093.780 9.842 9.842 14.364 8.436 1.381.730 22.946 8.436


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 13 12 7 4 5 7 12 12
quadratic 2 406 363 283 280 281 283 363 369
cubic 3 8.618 8.575 7.670 7.549 7.586 7.670 8.575 8.581
quartic 4 156.589 155.650 147.970 147.849 147.886 147.970 155.650 155.886
quintic 5 2.338.129 2.337.190 2.282.299 2.279.802 2.280.505 2.282.299 2.337.190 2.337.426
sextic 6 29.818.672 29.804.775 29.465.079 29.462.582 29.463.285 29.465.079 29.804.775 29.809.533


Literature




Character tables for chemically important point groups Character table for point group D2h Constructor University Bremen

Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement