Reduction formula for point group D2



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



Decomposition into Irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 18 20 20 20 78
Translation 0 1 1 1 3
Rotation 0 1 1 1 3
Vibration 18 18 18 18 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 18 18 18 54 / 18
Quadratic (Raman) 18 18 18 18 72 / 0
IR + Raman - 18 18 18 54 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) C2 (y) C2 (x)
linear 1 72 0 0 0
quadratic 2 2.628 36 36 36
cubic 3 64.824 0 0 0
quartic 4 1.215.450 666 666 666
quintic 5 18.474.840 0 0 0
sextic 6 237.093.780 8.436 8.436 8.436


Decomposition into Irreducible representations
Force field Tensor
Order
A B1 B2 B3
linear 1 18 18 18 18
quadratic 2 684 648 648 648
cubic 3 16.206 16.206 16.206 16.206
quartic 4 304.362 303.696 303.696 303.696
quintic 5 4.618.710 4.618.710 4.618.710 4.618.710
sextic 6 59.279.772 59.271.336 59.271.336 59.271.336


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