Reduction formula for point group D2



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x)
Cartesian 3N 15 -1 -1 -1
Translation (x,y,z) 3 -1 -1 -1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 9 1 1 1



Decomposition into Irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 3 4 4 4 15
Translation (x,y,z) 0 1 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 3 2 2 2 9



Molecule Parameter
Number of Atoms (N) 5
Number of internal coordinates 9
Number of independant internal coordinates 3
Number of vibrational modes 9





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B1 B2 B3 Total
Linear (IR) 3 2 2 2 6 / 3
Quadratic (Raman) 3 2 2 2 9 / 0
IR + Raman - 2 2 2 6 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) C2 (y) C2 (x)
linear 1 9 1 1 1
quadratic 2 45 5 5 5
cubic 3 165 5 5 5
quartic 4 495 15 15 15
quintic 5 1.287 15 15 15
sextic 6 3.003 35 35 35


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B1 B2 B3
linear 1 3 2 2 2
quadratic 2 15 10 10 10
cubic 3 45 40 40 40
quartic 4 135 120 120 120
quintic 5 333 318 318 318
sextic 6 777 742 742 742


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