Reduction formula for point group D2d



Characters for molecular motions
Motion E 2S4 C2 (z) 2C'2 2d
Cartesian 3N 99 -1 -1 -1 1
Translation (x,y,z) 3 -1 -1 -1 1
Rotation (Rx,Ry,Rz) 3 1 -1 -1 -1
Vibration 93 -1 1 1 1



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 12 12 12 13 25 74
Translation (x,y,z) 0 0 0 1 1 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 2
Vibration 12 11 12 12 23 70



Molecule Parameter
Number of Atoms (N) 33
Number of internal coordinates 93
Number of independant internal coordinates 12
Number of vibrational modes 70





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 12 11 12 12 23 35 / 35
Quadratic (Raman) 12 11 12 12 23 59 / 11
IR + Raman - 11 - 12 23 35 / 11



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2S4 C2 (z) 2C'2 2d
linear 1 93 -1 1 1 1
quadratic 2 4.371 1 47 47 47
cubic 3 138.415 -1 47 47 47
quartic 4 3.321.960 24 1.128 1.128 1.128
quintic 5 64.446.024 -24 1.128 1.128 1.128
sextic 6 1.052.618.392 24 18.424 18.424 18.424


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2 E
linear 1 12 11 12 12 23
quadratic 2 576 529 552 552 1.081
cubic 3 17.331 17.284 17.308 17.308 34.592
quartic 4 415.956 414.828 415.380 415.380 830.208
quintic 5 8.056.452 8.055.324 8.055.900 8.055.900 16.111.224
sextic 6 131.588.820 131.570.396 131.579.596 131.579.596 263.149.992


Literature




Character tables for chemically important point groups Character table for point group D2d Constructor University Bremen

Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement