Reduction formula for point group D2



Characters for molecular motions
Motion E C2 (z) C2 (y) C2 (x)
Cartesian 3N 39 -5 -5 -5
Translation (x,y,z) 3 -1 -1 -1
Rotation (Rx,Ry,Rz) 3 -1 -1 -1
Vibration 33 -3 -3 -3



Decomposition into Irreducible representations
Motion A B1 B2 B3 Total
Cartesian 3N 6 11 11 11 39
Translation (x,y,z) 0 1 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 6 9 9 9 33



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





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B1 B2 B3 Total
Linear (IR) 6 9 9 9 27 / 6
Quadratic (Raman) 6 9 9 9 33 / 0
IR + Raman - 9 9 9 27 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C2 (z) C2 (y) C2 (x)
linear 1 33 -3 -3 -3
quadratic 2 561 21 21 21
cubic 3 6.545 -55 -55 -55
quartic 4 58.905 225 225 225
quintic 5 435.897 -531 -531 -531
sextic 6 2.760.681 1.653 1.653 1.653


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A B1 B2 B3
linear 1 6 9 9 9
quadratic 2 156 135 135 135
cubic 3 1.595 1.650 1.650 1.650
quartic 4 14.895 14.670 14.670 14.670
quintic 5 108.576 109.107 109.107 109.107
sextic 6 691.410 689.757 689.757 689.757


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