Reduction formula for point group D4



Characters for molecular motions
Motion E 2C4 (z) C2 (z) 2C'2 2C''2
Cartesian 3N 48 0 0 0 0
Translation (x,y,z) 3 1 -1 -1 -1
Rotation (Rx,Ry,Rz) 3 1 -1 -1 -1
Vibration 42 -2 2 2 2



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 6 6 6 6 12 36
Translation (x,y,z) 0 1 0 0 1 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 2
Vibration 6 4 6 6 10 32



Molecule Parameter
Number of Atoms (N) 16
Number of internal coordinates 42
Number of independant internal coordinates 6
Number of vibrational modes 32





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 6 4 6 6 10 14 / 18
Quadratic (Raman) 6 4 6 6 10 28 / 4
IR + Raman - - - - 10 10 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C4 (z) C2 (z) 2C'2 2C''2
linear 1 42 -2 2 2 2
quadratic 2 903 3 23 23 23
cubic 3 13.244 -4 44 44 44
quartic 4 148.995 15 275 275 275
quintic 5 1.370.754 -26 506 506 506
sextic 6 10.737.573 37 2.277 2.277 2.277


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2 E
linear 1 6 4 6 6 10
quadratic 2 128 105 115 115 220
cubic 3 1.682 1.638 1.662 1.662 3.300
quartic 4 18.800 18.525 18.655 18.655 37.180
quintic 5 171.654 171.148 171.414 171.414 342.562
sextic 6 1.343.629 1.341.352 1.342.472 1.342.472 2.683.824


Literature




Character tables for chemically important point groups Character table for point group D4 Constructor University Bremen

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