Reduction formula for point group D2h



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
Cartesian 3N 90 0 0 -2 0 30 2 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 84 2 2 0 0 30 2 0



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 15 15 8 7 7 8 15 15 90
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 15 14 7 6 7 7 14 14 84



Molecule Parameter
Number of Atoms (N) 30
Number of internal coordinates 84
Number of independant internal coordinates 15
Number of vibrational modes 84





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag B1g B2g B3g Au B1u B2u B3u Total
Linear (IR) 15 14 7 6 7 7 14 14 35 / 49
Quadratic (Raman) 15 14 7 6 7 7 14 14 42 / 42
IR + Raman - - - - 7 - - - 0* / 7
* 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 84 2 2 0 0 30 2 0
quadratic 2 3.570 44 44 42 42 492 44 42
cubic 3 102.340 86 86 0 0 5.770 86 0
quartic 4 2.225.895 989 989 903 903 53.853 989 903
quintic 5 39.175.752 1.892 1.892 0 0 423.516 1.892 0
sextic 6 581.106.988 15.136 15.136 13.244 13.244 2.907.424 15.136 13.244


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 15 14 7 6 7 7 14 14
quadratic 2 540 497 385 384 385 385 497 497
cubic 3 13.546 13.503 12.082 12.039 12.082 12.082 13.503 13.503
quartic 4 285.678 284.732 271.516 271.473 271.516 271.516 284.732 284.732
quintic 5 4.950.618 4.949.672 4.844.266 4.843.320 4.844.266 4.844.266 4.949.672 4.949.672
sextic 6 73.012.444 72.998.254 72.275.182 72.274.236 72.275.182 72.275.182 72.998.254 72.998.254


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