Reduction formula for point group D3



Characters for molecular motions
Motion E 2C3 (z) 3C'2
Cartesian 3N 39 0 -1
Translation (x,y,z) 3 0 -1
Rotation (Rx,Ry,Rz) 3 0 -1
Vibration 33 0 1



Decomposition into Irreducible representations
Motion A1 A2 E Total
Cartesian 3N 6 7 13 26
Translation (x,y,z) 0 1 1 2
Rotation (Rx,Ry,Rz) 0 1 1 2
Vibration 6 5 11 22



Molecule Parameter
Number of Atoms (N) 13
Number of internal coordinates 33
Number of independant internal coordinates 6
Number of vibrational modes 22





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E Total
Linear (IR) 6 5 11 16 / 6
Quadratic (Raman) 6 5 11 17 / 5
IR + Raman - - 11 11 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C3 (z) 3C'2
linear 1 33 0 1
quadratic 2 561 0 17
cubic 3 6.545 11 17
quartic 4 58.905 0 153
quintic 5 435.897 0 153
sextic 6 2.760.681 66 969


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 E
linear 1 6 5 11
quadratic 2 102 85 187
cubic 3 1.103 1.086 2.178
quartic 4 9.894 9.741 19.635
quintic 5 72.726 72.573 145.299
sextic 6 460.620 459.651 920.205


Literature




Character tables for chemically important point groups Character table for point group D3 Constructor University Bremen

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