Reduction formula for point group D2



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x)
Cartesian 3N 54 0 0 -2
Translation (x,y,z) 3 -1 -1 -1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 48 2 2 0



Decomposition into Irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 13 14 14 13 54
Translation (x,y,z) 0 1 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 13 12 12 11 48



Molecule Parameter
Number of Atoms (N) 18
Number of internal coordinates 48
Number of independant internal coordinates 13
Number of vibrational modes 48





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B1 B2 B3 Total
Linear (IR) 13 12 12 11 35 / 13
Quadratic (Raman) 13 12 12 11 48 / 0
IR + Raman - 12 12 11 35 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) C2 (y) C2 (x)
linear 1 48 2 2 0
quadratic 2 1.176 26 26 24
cubic 3 19.600 50 50 0
quartic 4 249.900 350 350 300
quintic 5 2.598.960 650 650 0
sextic 6 22.957.480 3.250 3.250 2.600


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B1 B2 B3
linear 1 13 12 12 11
quadratic 2 313 288 288 287
cubic 3 4.925 4.900 4.900 4.875
quartic 4 62.725 62.400 62.400 62.375
quintic 5 650.065 649.740 649.740 649.415
sextic 6 5.741.645 5.738.720 5.738.720 5.738.395


Literature




Character tables for chemically important point groups Character table for point group D2 Jacobs University Bremen

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