Reduction formula for point group D2h



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
Cartesian 3N 99 -1 -1 -1 -3 1 1 1
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 93 1 1 1 -3 1 1 1



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 12 12 12 12 12 13 13 13 99
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 12 11 11 11 12 12 12 12 93



Molecule Parameter
Number of Atoms (N) 33
Number of internal coordinates 93
Number of independant internal coordinates 12
Number of vibrational modes 93





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag B1g B2g B3g Au B1u B2u B3u Total
Linear (IR) 12 11 11 11 12 12 12 12 36 / 57
Quadratic (Raman) 12 11 11 11 12 12 12 12 45 / 48
IR + Raman - - - - 12 - - - 0* / 12
* 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 93 1 1 1 -3 1 1 1
quadratic 2 4.371 47 47 47 51 47 47 47
cubic 3 138.415 47 47 47 -145 47 47 47
quartic 4 3.321.960 1.128 1.128 1.128 1.320 1.128 1.128 1.128
quintic 5 64.446.024 1.128 1.128 1.128 -3.576 1.128 1.128 1.128
sextic 6 1.052.618.392 18.424 18.424 18.424 23.128 18.424 18.424 18.424


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 12 11 11 11 12 12 12 12
quadratic 2 588 541 541 541 540 540 540 540
cubic 3 17.319 17.272 17.272 17.272 17.320 17.320 17.320 17.320
quartic 4 416.256 415.128 415.128 415.128 415.080 415.080 415.080 415.080
quintic 5 8.056.152 8.055.024 8.055.024 8.055.024 8.056.200 8.056.200 8.056.200 8.056.200
sextic 6 131.594.008 131.575.584 131.575.584 131.575.584 131.574.408 131.574.408 131.574.408 131.574.408


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