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 0 -2 -2 0 12 2 2
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 0 0 0 12 2 2



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 6 6 3 3 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 5 2 2 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 5 2 2 2 3 5 5 13 / 17
Quadratic (Raman) 6 5 2 2 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 0 0 0 12 2 2
quadratic 2 465 17 15 15 15 87 17 17
cubic 3 4.960 32 0 0 0 472 32 32
quartic 4 40.920 152 120 120 120 2.112 152 152
quintic 5 278.256 272 0 0 0 8.184 272 272
sextic 6 1.623.160 952 680 680 680 28.336 952 952


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 6 5 2 2 2 3 5 5
quadratic 2 81 65 47 47 47 48 65 65
cubic 3 691 675 557 557 557 573 675 675
quartic 4 5.481 5.345 4.847 4.847 4.847 4.863 5.345 5.345
quintic 5 35.907 35.771 33.725 33.725 33.725 33.861 35.771 35.771
sextic 6 207.049 206.233 199.319 199.319 199.319 199.455 206.233 206.233


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