Reduction formula for point group Ci



Characters for molecular motions
Motion E i
Cartesian 3N 9 -3
Translation (x,y,z) 3 -3
Rotation (Rx,Ry)* 2 2
Vibration 4 -2
* Linear molecule


Decomposition into Irreducible representations
Motion Ag Au Total
Cartesian 3N 3 6 9
Translation (x,y,z) 0 3 3
Rotation (Rx,Ry)* 2 0 2
Vibration 1 3 4
* Linear molecule


Molecule Parameter
Number of Atoms (N) 3
Number of internal coordinates 4
Number of independant internal coordinates 1
Number of vibrational modes 4





Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Au Total
Linear (IR) 1 3 3 / 1
Quadratic (Raman) 1 3 1 / 3
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 4 -2
quadratic 2 10 4
cubic 3 20 -6
quartic 4 35 9
quintic 5 56 -12
sextic 6 84 16


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
Ag Au
linear 1 1 3
quadratic 2 7 3
cubic 3 7 13
quartic 4 22 13
quintic 5 22 34
sextic 6 50 34


Literature




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

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