Reduction formula for point group C2v



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



Decomposition into Irreducible representations
Motion A1 A2 B1 B2 Total
Cartesian 3N 34 26 30 30 120
Translation (x,y,z) 1 0 1 1 3
Rotation (Rx,Ry,Rz) 0 1 1 1 3
Vibration 33 25 28 28 114



Molecule Parameter
Number of Atoms (N) 40
Number of internal coordinates 114
Number of independant internal coordinates 33
Number of vibrational modes 114





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 B1 B2 Total
Linear (IR) 33 25 28 28 89 / 25
Quadratic (Raman) 33 25 28 28 114 / 0
IR + Raman 33 - 28 28 89 / 0



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


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 B1 B2
linear 1 33 25 28 28
quadratic 2 1.698 1.609 1.624 1.624
cubic 3 63.666 63.122 63.336 63.336
quartic 4 1.855.703 1.852.034 1.852.984 1.852.984
quintic 5 43.751.015 43.732.415 43.740.004 43.740.004
sextic 6 867.584.508 867.487.551 867.518.064 867.518.064


Literature




Character tables for chemically important point groups Character table for point group C2v Constructor University Bremen

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