Reduction formula for point group Td

Your representation

E 8C3 3C2 6S4 6d
21 0 -3 -1 3

can be reduced to

A1 A2 E T1 T2
1 0 1 2 4

Substraction of translational and rotational contributions results in

A1 A2 E T1 T2
1 0 1 1 3



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 9
cubic 3375 680 36
quartic 50625 3060 151
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 1 3
quadratic 9 3 12 11 17
cubic 36 22 53 79 93
quartic 151 113 264 361 395

Number of independant internal coordinates 1

Literature




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