Reduction formula for point group D2h



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
Cartesian 3N 144 0 0 0 0 8 0 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 138 2 2 2 0 8 0 0



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 19 19 17 17 17 17 19 19 144
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 19 18 16 16 17 16 18 18 138



Molecule Parameter
Number of Atoms (N) 48
Number of internal coordinates 138
Number of independant internal coordinates 19
Number of vibrational modes 138





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag B1g B2g B3g Au B1u B2u B3u Total
Linear (IR) 19 18 16 16 17 16 18 18 52 / 86
Quadratic (Raman) 19 18 16 16 17 16 18 18 69 / 69
IR + Raman - - - - 17 - - - 0* / 17
* 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 1 138 2 2 2 0 8 0 0
quadratic 2 9.591 71 71 71 69 101 69 69
cubic 3 447.580 140 140 140 0 640 0 0
quartic 4 15.777.195 2.555 2.555 2.555 2.415 4.815 2.415 2.415
quintic 5 448.072.338 4.970 4.970 4.970 0 25.752 0 0
sextic 6 10.679.057.389 62.125 62.125 62.125 57.155 148.291 57.155 57.155


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 19 18 16 16 17 16 18 18
quadratic 2 1.264 1.194 1.186 1.186 1.187 1.186 1.194 1.194
cubic 3 56.080 56.010 55.850 55.850 55.920 55.850 56.010 56.010
quartic 4 1.974.615 1.972.130 1.971.530 1.971.530 1.971.600 1.971.530 1.972.130 1.972.130
quintic 5 56.014.125 56.011.640 56.005.202 56.005.202 56.007.687 56.005.202 56.011.640 56.011.640
sextic 6 1.334.945.440 1.334.885.800 1.334.863.016 1.334.863.016 1.334.865.501 1.334.863.016 1.334.885.800 1.334.885.800


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