Reduction formula for point group C2h



Characters for molecular motions
Motion E C2 (z) i h
Cartesian 3N 120 0 0 8
Translation (x,y,z) 3 -1 -3 1
Rotation (Rx,Ry,Rz) 3 -1 3 -1
Vibration 114 2 0 8



Decomposition into Irreducible representations
Motion Ag Bg Au Bu Total
Cartesian 3N 32 28 28 32 120
Translation (x,y,z) 0 0 1 2 3
Rotation (Rx,Ry,Rz) 1 2 0 0 3
Vibration 31 26 27 30 114



Molecule Parameter
Number of Atoms (N) 40
Number of internal coordinates 114
Number of independant internal coordinates 31
Number of vibrational modes 114




Force field analysis


Allowed / forbidden vibronational transitions
Operator Ag Bg Au Bu Total
Linear (IR) 31 26 27 30 57 / 57
Quadratic (Raman) 31 26 27 30 57 / 57
IR + Raman - - - - 0* / 0
* Center of inversion: Mutual Exclusion Principle



Characters of symmetric powers for vibration representation
Force field Tensor
Order		 E C2 (z) i h
linear 1 114 2 0 8
quadratic 2 6.555 59 57 89
cubic 3 253.460 116 0 544
quartic 4 7.413.705 1.769 1.653 3.669
quintic 5 174.963.438 3.422 0 18.600
sextic 6 3.470.108.187 35.931 32.509 96.957


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order		 Ag Bg Au Bu
linear 1 31 26 27 30
quadratic 2 1.690 1.616 1.617 1.632
cubic 3 63.530 63.200 63.258 63.472
quartic 4 1.855.199 1.852.480 1.852.538 1.853.488
quintic 5 43.746.365 43.735.354 43.737.065 43.744.654
sextic 6 867.568.396 867.501.952 867.503.663 867.534.176


Literature



Character tables for chemically important point groups Character table for point group C2h Constructor University Bremen
Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement