Reduction formula for point group D2



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x)
Cartesian 3N 78 0 0 -6
Translation (x,y,z) 3 -1 -1 -1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 72 2 2 -4



Decomposition into Irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 18 21 21 18 78
Translation (x,y,z) 0 1 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 18 19 19 16 72



Molecule Parameter
Number of Atoms (N) 26
Number of internal coordinates 72
Number of independant internal coordinates 18
Number of vibrational modes 72





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B1 B2 B3 Total
Linear (IR) 18 19 19 16 54 / 18
Quadratic (Raman) 18 19 19 16 72 / 0
IR + Raman - 19 19 16 54 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) C2 (y) C2 (x)
linear 1 72 2 2 -4
quadratic 2 2.628 38 38 44
cubic 3 64.824 74 74 -156
quartic 4 1.215.450 740 740 970
quintic 5 18.474.840 1.406 1.406 -3.116
sextic 6 237.093.780 9.842 9.842 14.364


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B1 B2 B3
linear 1 18 19 19 16
quadratic 2 687 646 646 649
cubic 3 16.204 16.245 16.245 16.130
quartic 4 304.475 303.620 303.620 303.735
quintic 5 4.618.634 4.619.489 4.619.489 4.617.228
sextic 6 59.281.957 59.269.854 59.269.854 59.272.115


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