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 16 0 0
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 42 -2 2 2 2 0 0 16 0 0



Decomposition into Irreducible representations
Motion A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu Total
Cartesian 3N 4 4 4 4 4 2 2 2 2 8 36
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 3 4 4 3 2 1 2 2 7 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 3 4 4 3 2 1 2 2 7 8 / 24
Quadratic (Raman) 4 3 4 4 3 2 1 2 2 7 15 / 17
IR + Raman - 3 - - - 2 - 2 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 16 0 0
quadratic 2 903 3 23 23 23 21 1 149 21 21
cubic 3 13.244 -4 44 44 44 0 0 1.024 0 0
quartic 4 148.995 15 275 275 275 231 11 5.735 231 231
quintic 5 1.370.754 -26 506 506 506 0 0 27.568 0 0
sextic 6 10.737.573 37 2.277 2.277 2.277 1.771 11 117.483 1.771 1.771


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 3 4 4 3 2 1 2 2 7
quadratic 2 80 58 68 68 94 48 47 47 47 126
cubic 3 905 883 895 895 1.522 777 755 767 767 1.778
quartic 4 9.832 9.579 9.699 9.699 17.902 8.968 8.946 8.956 8.956 19.278
quintic 5 87.550 87.297 87.430 87.430 167.835 84.104 83.851 83.984 83.984 174.727
sextic 6 679.712 677.688 678.688 678.688 1.327.448 663.917 663.664 663.784 663.784 1.356.376


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