Reduction formula for point group D2h



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
Cartesian 3N 36 -4 0 0 0 8 4 4
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 30 -2 2 2 0 8 4 4



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 6 4 4 4 2 4 6 6 36
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 6 3 3 3 2 3 5 5 30



Molecule Parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 6
Number of vibrational modes 30





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag B1g B2g B3g Au B1u B2u B3u Total
Linear (IR) 6 3 3 3 2 3 5 5 13 / 17
Quadratic (Raman) 6 3 3 3 2 3 5 5 15 / 15
IR + Raman - - - - 2 - - - 0* / 2
* 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 30 -2 2 2 0 8 4 4
quadratic 2 465 17 17 17 15 47 23 23
cubic 3 4.960 -32 32 32 0 208 72 72
quartic 4 40.920 152 152 152 120 792 256 256
quintic 5 278.256 -272 272 272 0 2.640 680 680
sextic 6 1.623.160 952 952 952 680 8.008 1.904 1.904


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 6 3 3 3 2 3 5 5
quadratic 2 78 58 52 52 51 54 60 60
cubic 3 668 616 598 598 580 600 650 650
quartic 4 5.350 5.146 5.012 5.012 4.994 5.046 5.180 5.180
quintic 5 35.316 34.840 34.486 34.486 34.316 34.520 35.146 35.146
sextic 6 204.814 203.386 201.860 201.860 201.690 202.166 203.692 203.692


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