Reduction formula for point group D2



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x)
Cartesian 3N 120 0 0 0
Translation 3 -1 -1 -1
Rotation 3 -1 -1 -1
Vibration 114 2 2 2



Decomposition into Irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 30 30 30 30 120
Translation 0 1 1 1 3
Rotation 0 1 1 1 3
Vibration 30 28 28 28 114



Molecule Parameter
Number of Atoms (N) 40
Number of internal coordinates 114
Number of independant internal coordinates 30
Number of vibrational modes 114





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B1 B2 B3 Total
Linear (IR) 30 28 28 28 84 / 30
Quadratic (Raman) 30 28 28 28 114 / 0
IR + Raman - 28 28 28 84 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) C2 (y) C2 (x)
linear 1 114 2 2 2
quadratic 2 6.555 59 59 59
cubic 3 253.460 116 116 116
quartic 4 7.413.705 1.769 1.769 1.769
quintic 5 174.963.438 3.422 3.422 3.422
sextic 6 3.470.108.187 35.931 35.931 35.931


Decomposition into Irreducible representations
Force field Tensor
Order
A B1 B2 B3
linear 1 30 28 28 28
quadratic 2 1.683 1.624 1.624 1.624
cubic 3 63.452 63.336 63.336 63.336
quartic 4 1.854.753 1.852.984 1.852.984 1.852.984
quintic 5 43.743.426 43.740.004 43.740.004 43.740.004
sextic 6 867.553.995 867.518.064 867.518.064 867.518.064


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