Reduction formula for point group D4

Your representation

E 2C4 (z) C2 (z) 2C'2 2C''2
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 4 6 6 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 903 128
cubic 74088 13244 1682
quartic 3111696 148995 18800
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 4 6 6 10
quadratic 128 105 115 115 220
cubic 1682 1638 1662 1662 3300
quartic 18800 18525 18655 18655 37180

Number of independant internal coordinates 6

Literature




Character tables for chemically important point groups Character table for point group D4 Jacobs University Bremen