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 21 3 -3 -3 -1 -3 -1 5 5 3
Translation 3 1 -1 -1 -1 -3 -1 1 1 1
Rotation 3 1 -1 -1 -1 3 1 -1 -1 -1
Vibration 15 1 -1 -1 1 -3 -1 5 5 3



Decomposition into Irreducible representations
Motion A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu Total
Cartesian 3N 2 1 1 1 2 0 3 0 1 4 15
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 2 0 1 1 1 0 2 0 1 3 11



Molecule Parameter
Number of Atoms (N) 7
Number of internal coordinates 15
Number of independant internal coordinates 2
Number of vibrational modes 11





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu Total
Linear (IR) 2 0 1 1 1 0 2 0 1 3 5 / 6
Quadratic (Raman) 2 0 1 1 1 0 2 0 1 3 5 / 6
IR + Raman - 0 - - - 0 - 0 1 - 0* / 1
* 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 15 1 -1 -1 1 -3 -1 5 5 3
quadratic 2 120 0 8 8 8 12 0 20 20 12
cubic 3 680 0 -8 -8 8 -28 0 60 60 28
quartic 4 3.060 4 36 36 36 72 4 160 160 72
quintic 5 11.628 4 -36 -36 36 -144 -4 376 376 144
sextic 6 38.760 0 120 120 120 300 0 820 820 300


Decomposition into Irreducible representations
Force field Tensor
Order
A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu
linear 1 2 0 1 1 1 0 2 0 1 3
quadratic 2 16 4 11 9 13 4 8 5 7 15
cubic 3 55 33 46 42 75 29 51 34 46 97
quartic 4 247 171 218 196 367 159 199 168 190 389
quintic 5 804 674 759 719 1.393 646 776 671 747 1.523
sextic 6 2.670 2.330 2.565 2.435 4.765 2.250 2.470 2.295 2.425 4.895


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