Reduction formula for point group Td

Your representation

E 8C3 3C2 6S4 6d
48 0 0 0 8

can be reduced to

A1 A2 E T1 T2
4 0 4 4 8

Substraction of translational and rotational contributions results in

A1 A2 E T1 T2
4 0 4 3 7



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 4
quadratic 1764 903 54
cubic 74088 13244 626
quartic 3111696 148995 6519
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 4 0 4 3 7
quadratic 54 27 81 97 123
cubic 626 498 1110 1586 1714
quartic 6519 5966 12485 18319 18861

Number of independant internal coordinates 4

Literature




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