Reduction formula for point group O

Your representation

E 8C3 6C'2 6C4 3C2 =(C4)2
21 0 -1 3 -3

can be reduced to

A1 A2 E T1 T2
1 0 1 4 2

Substraction of translational and rotational contributions results in

A1 A2 E T1 T2
1 0 1 2 2



Force field analysis

Infrared and Raman activities (harmonic approximation)
Method A1 A2 E T1 T2
Infrared - - - + -
Raman + - + - +

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 15 15 1
quadratic 225 120 8
cubic 3375 680 31
quartic 50625 3060 142
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 E T1 T2
linear 1 0 1 2 2
quadratic 8 4 12 12 16
cubic 31 27 53 84 88
quartic 142 122 264 370 386

Number of independant internal coordinates 1

Literature




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