Reduction formula for point group D4



Characters for molecular motions
Motion E 2C4 (z) C2 (z) 2C'2 2C''2
Cartesian 3N 72 0 0 -2 -2
Translation (x,y,z) 3 1 -1 -1 -1
Rotation (Rx,Ry,Rz) 3 1 -1 -1 -1
Vibration 66 -2 2 0 0



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 E Total
Cartesian 3N 8 10 9 9 18 54
Translation (x,y,z) 0 1 0 0 1 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 2
Vibration 8 8 9 9 16 50



Molecule Parameter
Number of Atoms (N) 24
Number of internal coordinates 66
Number of independant internal coordinates 8
Number of vibrational modes 50





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 E Total
Linear (IR) 8 8 9 9 16 24 / 26
Quadratic (Raman) 8 8 9 9 16 42 / 8
IR + Raman - - - - 16 16 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C4 (z) C2 (z) 2C'2 2C''2
linear 1 66 -2 2 0 0
quadratic 2 2.211 3 35 33 33
cubic 3 50.116 -4 68 0 0
quartic 4 864.501 21 629 561 561
quintic 5 12.103.014 -38 1.190 0 0
sextic 6 143.218.999 55 7.735 6.545 6.545


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2 E
linear 1 8 8 9 9 16
quadratic 2 298 265 280 280 544
cubic 3 6.272 6.272 6.274 6.274 12.512
quartic 4 108.427 107.866 108.136 108.136 215.968
quintic 5 1.513.016 1.513.016 1.513.035 1.513.035 3.025.456
sextic 6 17.906.628 17.900.083 17.903.328 17.903.328 35.802.816


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