Reduction formula for point group D2d

Your representation

E 2S4 C2 (z) 2C'2 2d
48 0 0 0 8

can be reduced to

A1 A2 B1 B2 E
8 4 4 8 12

Substraction of translational and rotational contributions results in

A1 A2 B1 B2 E
8 3 4 7 10



Force field analysis

Infrared and Raman activities (harmonic approximation)
Method A1 A2 B1 B2 E
Infrared - - - + +
Raman + - + + +

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 42 42 8
quadratic 1764 903 135
cubic 74088 13244 1736
quartic 3111696 148995 19004
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 B1 B2 E
linear 8 3 4 7 10
quadratic 135 97 108 123 220
cubic 1736 1586 1608 1714 3300
quartic 19004 18319 18451 18861 37180

Number of independant internal coordinates 8

Literature




Character tables for chemically important point groups Character table for point group D2d Jacobs University Bremen