Reduction formula for point group Ci



Characters for molecular motions
Motion E i
Cartesian 3N 36 0
Translation (x,y,z) 3 -3
Rotation (Rx,Ry,Rz) 3 3
Vibration 30 0



Decomposition into Irreducible representations
Motion Ag Au Total
Cartesian 3N 18 18 36
Translation (x,y,z) 0 3 3
Rotation (Rx,Ry,Rz) 3 0 3
Vibration 15 15 30



Molecule Parameter
Number of Atoms (N) 12
Number of internal coordinates 30
Number of independant internal coordinates 15
Number of vibrational modes 30





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Au Total
Linear (IR) 15 15 15 / 15
Quadratic (Raman) 15 15 15 / 15
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 30 0
quadratic 2 465 15
cubic 3 4.960 0
quartic 4 40.920 120
quintic 5 278.256 0
sextic 6 1.623.160 680


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Au
linear 1 15 15
quadratic 2 240 225
cubic 3 2.480 2.480
quartic 4 20.520 20.400
quintic 5 139.128 139.128
sextic 6 811.920 811.240


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