Reduction formula for point group Td

Your representation

E 8C3 3C2 6S4 6d
15 0 -1 -1 3

can be reduced to

A1 A2 E T1 T2
1 0 1 1 3

Substraction of translational and rotational contributions results in

A1 A2 E T1 T2
1 0 1 0 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 9 9 1
quadratic 81 45 5
cubic 729 165 13
quartic 6561 495 33
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 0 2
quadratic 5 0 5 3 7
cubic 13 4 14 15 25
quartic 33 12 45 51 69

Number of independant internal coordinates 1

Literature




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