Reduction formula for point group Ci



Characters for molecular motions
Motion E i
Cartesian 3N 252 0
Translation (x,y,z) 3 -3
Rotation (Rx,Ry,Rz) 3 3
Vibration 246 0



Decomposition into Irreducible representations
Motion Ag Au Total
Cartesian 3N 126 126 252
Translation (x,y,z) 0 3 3
Rotation (Rx,Ry,Rz) 3 0 3
Vibration 123 123 246



Molecule Parameter
Number of Atoms (N) 84
Number of internal coordinates 246
Number of independant internal coordinates 123
Number of vibrational modes 246





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Au Total
Linear (IR) 123 123 123 / 123
Quadratic (Raman) 123 123 123 / 123
IR + Raman - - 0* / 0
* Center of inversion: Mutual Exclusion Principle



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E i
linear 1 246 0
quadratic 2 30.381 123
cubic 3 2.511.496 0
quartic 4 156.340.626 7.626
quintic 5 7.817.031.300 0
sextic 6 327.012.476.050 317.750


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Au
linear 1 123 123
quadratic 2 15.252 15.129
cubic 3 1.255.748 1.255.748
quartic 4 78.174.126 78.166.500
quintic 5 3.908.515.650 3.908.515.650
sextic 6 163.506.396.900 163.506.079.150


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