Reduction formula for point group D2



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x)
Cartesian 3N 18 -6 0 0
Translation (x,y,z) 3 -1 -1 -1
Rotation (Rx,Ry)* 2 -2 0 0
Vibration 13 -3 1 1
* Linear molecule


Decomposition into Irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 3 3 6 6 18
Translation (x,y,z) 0 1 1 1 3
Rotation (Rx,Ry)* 0 0 1 1 2
Vibration 3 2 4 4 13
* Linear molecule


Molecule Parameter
Number of Atoms (N) 6
Number of internal coordinates 13
Number of independant internal coordinates 3
Number of vibrational modes 13





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B1 B2 B3 Total
Linear (IR) 3 2 4 4 10 / 3
Quadratic (Raman) 3 2 4 4 13 / 0
IR + Raman - 2 4 4 10 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) C2 (y) C2 (x)
linear 1 13 -3 1 1
quadratic 2 91 11 7 7
cubic 3 455 -25 7 7
quartic 4 1.820 60 28 28
quintic 5 6.188 -116 28 28
sextic 6 18.564 228 84 84


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B1 B2 B3
linear 1 3 2 4 4
quadratic 2 29 22 20 20
cubic 3 111 104 120 120
quartic 4 484 456 440 440
quintic 5 1.532 1.504 1.576 1.576
sextic 6 4.740 4.656 4.584 4.584


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