Reduction formula for point group C4



Characters for molecular motions
Motion E C4 C2 (C4)3
Cartesian 3N 21 3 -3 3
Translation 3 1 -1 1
Rotation 3 1 -1 1
Vibration 15 1 -1 1



Decomposition into Irreducible representations
Motion A B E Total
Cartesian 3N 6 3 6 15
Translation 1 0 1 2
Rotation 1 0 1 2
Vibration 4 3 4 11



Molecule Parameter
Number of Atoms (N) 7
Number of internal coordinates 15
Number of independant internal coordinates 4
Number of vibrational modes 11





Force field analysis


Allowed / forbidden vibronational transitions
Operator A B E Total
Linear (IR) 4 3 4 8 / 3
Quadratic (Raman) 4 3 4 11 / 0
IR + Raman 4 - 4 8 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E C4 C2 (C4)3
linear 1 15 1 -1 1
quadratic 2 120 0 8 0
cubic 3 680 0 -8 0
quartic 4 3.060 4 36 4
quintic 5 11.628 4 -36 4
sextic 6 38.760 0 120 0


Decomposition into Irreducible representations
Force field Tensor
Order
A B E
linear 1 4 3 4
quadratic 2 32 32 28
cubic 3 168 168 172
quartic 4 776 772 756
quintic 5 2.900 2.896 2.916
sextic 6 9.720 9.720 9.660


Literature




Character tables for chemically important point groups Character table for point group C4 Jacobs University Bremen

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