Reduction formula for point group D4



Characters for molecular motions
Motion E 2C4 (z) C2 (z) 2C'2 2C''2
Cartesian 3N 15 1 -1 -3 -1
Translation (x,y,z) 3 1 -1 -1 -1
Rotation (Rx,Ry,Rz) 3 1 -1 -1 -1
Vibration 9 -1 1 -1 1



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 1 3 1 2 4 11
Translation (x,y,z) 0 1 0 0 1 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 2
Vibration 1 1 1 2 2 7



Molecule Parameter
Number of Atoms (N) 5
Number of internal coordinates 9
Number of independant internal coordinates 1
Number of vibrational modes 7





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 1 1 1 2 2 3 / 4
Quadratic (Raman) 1 1 1 2 2 6 / 1
IR + Raman - - - - 2 2 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C4 (z) C2 (z) 2C'2 2C''2
linear 1 9 -1 1 -1 1
quadratic 2 45 1 5 5 5
cubic 3 165 -1 5 -5 5
quartic 4 495 3 15 15 15
quintic 5 1.287 -3 15 -15 15
sextic 6 3.003 3 35 35 35


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2 E
linear 1 1 1 1 2 2
quadratic 2 9 4 6 6 10
cubic 3 21 21 19 24 40
quartic 4 72 57 63 63 120
quintic 5 162 162 156 171 318
sextic 6 398 363 379 379 742


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