Reduction formula for point group D2d



Characters for molecular motions
Motion E 2S4 C2 (z) 2C'2 2d
Cartesian 3N 66 0 -2 -2 6
Translation (x,y,z) 3 -1 -1 -1 1
Rotation (Rx,Ry,Rz) 3 1 -1 -1 -1
Vibration 60 0 0 0 6



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 9 7 6 10 17 49
Translation (x,y,z) 0 0 0 1 1 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 2
Vibration 9 6 6 9 15 45



Molecule Parameter
Number of Atoms (N) 22
Number of internal coordinates 60
Number of independant internal coordinates 9
Number of vibrational modes 45





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 9 6 6 9 15 24 / 21
Quadratic (Raman) 9 6 6 9 15 39 / 6
IR + Raman - 6 - 9 15 24 / 6



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2S4 C2 (z) 2C'2 2d
linear 1 60 0 0 0 6
quadratic 2 1.830 0 30 30 48
cubic 3 37.820 0 0 0 218
quartic 4 595.665 15 465 465 1.071
quintic 5 7.624.512 0 0 0 4.032
sextic 6 82.598.880 0 4.960 4.960 15.456


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2 E
linear 1 9 6 6 9 15
quadratic 2 252 213 228 237 450
cubic 3 4.782 4.673 4.673 4.782 9.455
quartic 4 74.904 74.136 74.361 74.664 148.800
quintic 5 954.072 952.056 952.056 954.072 1.906.128
sextic 6 10.330.584 10.320.376 10.322.856 10.328.104 20.648.480


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