Reduction formula for point group D4

Your representation

E 2C4 (z) C2 (z) 2C'2 2C''2
21 3 -3 -3 -1

can be reduced to

A1 A2 B1 B2 E
2 4 1 2 6

Substraction of translational and rotational contributions results in

A1 A2 B1 B2 E
2 2 1 2 4



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 15 15 2
quadratic 225 120 20
cubic 3375 680 84
quartic 50625 3060 406
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 2 2 1 2 4
quadratic 20 12 16 16 28
cubic 84 84 80 88 172
quartic 406 370 386 386 756

Number of independant internal coordinates 2

Literature




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