Force field analysis for point group Cv


Number of atoms: 4


Your 3N representation

E 2C v
12 4+ 8cos() 4

can be reduced to

A1=+ A2=- E1= E2= E3= E4=
4 0 4 0 0 0

Substraction of translational and rotational contributions results in

A1=+ A2=- E1= E2= E3= E4=
3 0 2 0 0 0



Infrared and Raman activities (harmonic approximation)
Method A1=+ A2=- E1= E2= E3= E4=
Infrared + - + - - -
Raman + - + + - -

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 7 7 3
quadratic 49 28 9
cubic 343 84 19
quartic 2401 210 39
No. 1 : Total number of force constants .
No. 2 : Total number of force constants k.
No. 3 : Total number of nonvanishing force constants k.

Symmetry properties of force field parameters
Force field A1=+ A2=- E1= E2= E3= E4=
linear 3 0 2 0 0 0
quadratic 9 1 6 3 0 0
cubic 19 3 18 9 4 0
quartic 39 9 38 26 12 5

Number of independant internal coordinates 3

Literature




Character tables for chemically important point groups Computational Laboratory for Analysis, Modeling and Visualization Jacobs University Bremen