Reduction formula for point group D2d

Your representation

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

can be reduced to

A1 A2 B1 B2 E
6 6 6 6 12

Substraction of translational and rotational contributions results in

A1 A2 B1 B2 E
6 5 6 5 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 6
quadratic 1764 903 127
cubic 74088 13244 1672
quartic 3111696 148995 18788
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 6 5 6 5 10
quadratic 127 105 116 115 220
cubic 1672 1650 1672 1650 3300
quartic 18788 18535 18667 18645 37180

Number of independant internal coordinates 6

Literature




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