Reduction formula for point group D4h



Characters for molecular motions
Motion E 2C4 (z) C2 2C'2 2C''2 i 2S4 h 2v 2d
Cartesian 3N 48 0 0 0 0 0 0 0 0 8
Translation 3 1 -1 -1 -1 -3 -1 1 1 1
Rotation 3 1 -1 -1 -1 3 1 -1 -1 -1
Vibration 42 -2 2 2 2 0 0 0 0 8



Decomposition into Irreducible representations
Motion A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu Total
Cartesian 3N 4 2 2 4 6 2 4 4 2 6 36
Translation 0 0 0 0 0 0 1 0 0 1 2
Rotation 0 1 0 0 1 0 0 0 0 0 2
Vibration 4 1 2 4 5 2 3 4 2 5 32



Molecule Parameter
Number of Atoms (N) 16
Number of internal coordinates 42
Number of independant internal coordinates 4
Number of vibrational modes 32





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu Total
Linear (IR) 4 1 2 4 5 2 3 4 2 5 8 / 24
Quadratic (Raman) 4 1 2 4 5 2 3 4 2 5 15 / 17
IR + Raman - 1 - - - 2 - 4 2 - 0* / 9
* Center of inversion: Mutual Exclusion Principle



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 2C4 (z) C2 2C'2 2C''2 i 2S4 h 2v 2d
linear 1 42 -2 2 2 2 0 0 0 0 8
quadratic 2 903 3 23 23 23 21 1 21 21 53
cubic 3 13.244 -4 44 44 44 0 0 0 0 256
quartic 4 148.995 15 275 275 275 231 11 231 231 1.095
quintic 5 1.370.754 -26 506 506 506 0 0 0 0 4.056
sextic 6 10.737.573 37 2.277 2.277 2.277 1.771 11 1.771 1.771 13.803


Decomposition into Irreducible representations
Force field Tensor
Order
A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu
linear 1 4 1 2 4 5 2 3 4 2 5
quadratic 2 76 46 56 64 110 52 59 59 51 110
cubic 3 873 787 799 863 1.650 809 851 863 799 1.650
quartic 4 9.596 9.127 9.247 9.463 18.590 9.204 9.398 9.408 9.192 18.590
quintic 5 86.334 85.067 85.200 86.214 171.281 85.320 86.081 86.214 85.200 171.281
sextic 6 673.984 668.952 669.952 672.960 1.341.912 669.645 672.400 672.520 669.512 1.341.912


Literature




Character tables for chemically important point groups Character table for point group D4h Jacobs University Bremen

Last update Mai, 23rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement