Reduction formula for point group D2h



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
Cartesian 3N 54 0 0 -2 0 18 2 0
Translation 3 -1 -1 -1 -3 1 1 1
Rotation 3 -1 -1 -1 3 -1 -1 -1
Vibration 48 2 2 0 0 18 2 0



Decomposition into Irreducible representations
Motion Ag B1g B2g B3g Au B1u B2u B3u Total
Cartesian 3N 9 9 5 4 4 5 9 9 54
Translation 0 0 0 0 0 1 1 1 3
Rotation 0 1 1 1 0 0 0 0 3
Vibration 9 8 4 3 4 4 8 8 48



Molecule Parameter
Number of Atoms (N) 18
Number of internal coordinates 48
Number of independant internal coordinates 9
Number of vibrational modes 48





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag B1g B2g B3g Au B1u B2u B3u Total
Linear (IR) 9 8 4 3 4 4 8 8 20 / 28
Quadratic (Raman) 9 8 4 3 4 4 8 8 24 / 24
IR + Raman - - - - 4 - - - 0* / 4
* 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 48 2 2 0 0 18 2 0
quadratic 2 1.176 26 26 24 24 186 26 24
cubic 3 19.600 50 50 0 0 1.410 50 0
quartic 4 249.900 350 350 300 300 8.670 350 300
quintic 5 2.598.960 650 650 0 0 45.594 650 0
sextic 6 22.957.480 3.250 3.250 2.600 2.600 211.922 3.250 2.600


Decomposition into Irreducible representations
Force field Tensor
Order
Ag B1g B2g B3g Au B1u B2u B3u
linear 1 9 8 4 3 4 4 8 8
quadratic 2 189 164 124 123 124 124 164 164
cubic 3 2.645 2.620 2.280 2.255 2.280 2.280 2.620 2.620
quartic 4 32.565 32.240 30.160 30.135 30.160 30.160 32.240 32.240
quintic 5 330.813 330.488 319.252 318.927 319.252 319.252 330.488 330.488
sextic 6 2.898.369 2.895.444 2.843.276 2.842.951 2.843.276 2.843.276 2.895.444 2.895.444


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