Reduction formula for point group O

Your representation

E 8C3 6C'2 6C4 3C2 =(C4)2
48 0 0 0 0

can be reduced to

A1 A2 E T1 T2
2 2 4 6 6

Substraction of translational and rotational contributions results in

A1 A2 E T1 T2
2 2 4 4 6



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 42 42 2
quadratic 1764 903 47
cubic 74088 13244 572
quartic 3111696 148995 6315
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 2 2 4 4 6
quadratic 47 34 81 105 115
cubic 572 552 1110 1638 1662
quartic 6315 6170 12485 18525 18655

Number of independant internal coordinates 2

Literature




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