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 36 4 -4 -4 0 0 0 8 8 4
Translation (x,y,z) 3 1 -1 -1 -1 -3 -1 1 1 1
Rotation (Rx,Ry,Rz) 3 1 -1 -1 -1 3 1 -1 -1 -1
Vibration 30 2 -2 -2 2 0 0 8 8 4



Decomposition into Irreducible representations
Motion A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu Total
Cartesian 3N 4 2 2 2 4 0 4 0 2 6 26
Translation (x,y,z) 0 0 0 0 0 0 1 0 0 1 2
Rotation (Rx,Ry,Rz) 0 1 0 0 1 0 0 0 0 0 2
Vibration 4 1 2 2 3 0 3 0 2 5 22



Molecule Parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 4
Number of vibrational modes 22





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu Total
Linear (IR) 4 1 2 2 3 0 3 0 2 5 8 / 14
Quadratic (Raman) 4 1 2 2 3 0 3 0 2 5 11 / 11
IR + Raman - 1 - - - 0 - 0 2 - 0* / 3
* 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 30 2 -2 -2 2 0 0 8 8 4
quadratic 2 465 1 17 17 17 15 -1 47 47 23
cubic 3 4.960 0 -32 -32 32 0 0 208 208 72
quartic 4 40.920 8 152 152 152 120 8 792 792 256
quintic 5 278.256 16 -272 -272 272 0 0 2.640 2.640 680
sextic 6 1.623.160 8 952 952 952 680 -8 8.008 8.008 1.904


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu
linear 1 4 1 2 2 3 0 3 0 2 5
quadratic 2 47 21 37 31 52 22 31 23 29 60
cubic 3 356 286 330 312 598 260 330 270 320 650
quartic 4 2.795 2.457 2.689 2.555 5.012 2.417 2.603 2.443 2.577 5.180
quintic 5 17.956 17.126 17.714 17.360 34.486 16.796 17.626 16.894 17.520 35.146
sextic 6 103.527 100.573 102.813 101.287 201.860 99.965 101.967 100.199 101.725 203.692


Literature




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

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