Reduction formula for point group Ci



Characters for molecular motions
Motion E i
Cartesian 3N 18 0
Translation (x,y,z) 3 -3
Rotation (Rx,Ry)* 2 2
Vibration 13 1
* Linear molecule


Decomposition into Irreducible representations
Motion Ag Au Total
Cartesian 3N 9 9 18
Translation (x,y,z) 0 3 3
Rotation (Rx,Ry)* 2 0 2
Vibration 7 6 13
* Linear molecule


Molecule Parameter
Number of Atoms (N) 6
Number of internal coordinates 13
Number of independant internal coordinates 7
Number of vibrational modes 13





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Au Total
Linear (IR) 7 6 6 / 7
Quadratic (Raman) 7 6 7 / 6
IR + Raman - - 0* / 0
* Center of inversion: Mutual Exclusion Principle



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E i
linear 1 13 1
quadratic 2 91 7
cubic 3 455 7
quartic 4 1.820 28
quintic 5 6.188 28
sextic 6 18.564 84


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Au
linear 1 7 6
quadratic 2 49 42
cubic 3 231 224
quartic 4 924 896
quintic 5 3.108 3.080
sextic 6 9.324 9.240


Literature




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

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