Reduction formula for point group D2h



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
Cartesian 3N 21 -3 -3 -3 -3 5 5 5
Translation 3 -1 -1 -1 -3 1 1 1
Rotation 3 -1 -1 -1 3 -1 -1 -1
Vibration 15 -1 -1 -1 -3 5 5 5



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 3 2 2 2 0 4 4 4 21
Translation 0 0 0 0 0 1 1 1 3
Rotation 0 1 1 1 0 0 0 0 3
Vibration 3 1 1 1 0 3 3 3 15



Molecule Parameter
Number of Atoms (N) 7
Number of internal coordinates 15
Number of independant internal coordinates 3
Number of vibrational modes 15





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag B1g B2g B3g Au B1u B2u B3u Total
Linear (IR) 3 1 1 1 0 3 3 3 9 / 6
Quadratic (Raman) 3 1 1 1 0 3 3 3 6 / 9
IR + Raman - - - - 0 - - - 0* / 0
* 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 15 -1 -1 -1 -3 5 5 5
quadratic 2 120 8 8 8 12 20 20 20
cubic 3 680 -8 -8 -8 -28 60 60 60
quartic 4 3.060 36 36 36 72 160 160 160
quintic 5 11.628 -36 -36 -36 -144 376 376 376
sextic 6 38.760 120 120 120 300 820 820 820


Decomposition into Irreducible representations
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 3 1 1 1 0 3 3 3
quadratic 2 27 13 13 13 9 15 15 15
cubic 3 101 75 75 75 63 97 97 97
quartic 4 465 367 367 367 327 389 389 389
quintic 5 1.563 1.393 1.393 1.393 1.317 1.523 1.523 1.523
sextic 6 5.235 4.765 4.765 4.765 4.545 4.895 4.895 4.895


Literature




Character tables for chemically important point groups Character table for point group D2h Jacobs University Bremen

Last update Mai, 23rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement