Reduction formula for point group D2



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x)
Cartesian 3N 156 0 0 0
Translation (x,y,z) 3 -1 -1 -1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 150 2 2 2



Decomposition into Irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 39 39 39 39 156
Translation (x,y,z) 0 1 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 39 37 37 37 150



Molecule Parameter
Number of Atoms (N) 52
Number of internal coordinates 150
Number of independant internal coordinates 39
Number of vibrational modes 150





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B1 B2 B3 Total
Linear (IR) 39 37 37 37 111 / 39
Quadratic (Raman) 39 37 37 37 150 / 0
IR + Raman - 37 37 37 111 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) C2 (y) C2 (x)
linear 1 150 2 2 2
quadratic 2 11.325 77 77 77
cubic 3 573.800 152 152 152
quartic 4 21.947.850 3.002 3.002 3.002
quintic 5 675.993.780 5.852 5.852 5.852
sextic 6 17.463.172.650 79.002 79.002 79.002


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B1 B2 B3
linear 1 39 37 37 37
quadratic 2 2.889 2.812 2.812 2.812
cubic 3 143.564 143.412 143.412 143.412
quartic 4 5.489.214 5.486.212 5.486.212 5.486.212
quintic 5 169.002.834 168.996.982 168.996.982 168.996.982
sextic 6 4.365.852.414 4.365.773.412 4.365.773.412 4.365.773.412


Literature




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

Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement