Reduction formula for point group C4h

Your representation

E C4(z) C2 (C4)3 i (S4)3 h S4
21 3 -3 3 -3 -1 5 -1

can be reduced to

Ag Bg Eg Au Bu Eu
3 2 2 3 1 4

Substraction of translational and rotational contributions results in

Ag Bg Eg Au Bu Eu
2 2 1 2 1 3



Force field analysis

Infrared and Raman activities (harmonic approximation)
Method Ag Bg Eg Au Bu Eu
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 88
quartic 50625 3060 418
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 Ag Bg Eg Au Bu Eu
linear 2 2 1 2 1 3
quadratic 20 20 13 12 12 15
cubic 88 88 75 80 80 97
quartic 418 414 367 358 358 389

Number of independant internal coordinates 2

Literature




Character tables for chemically important point groups Character table for point group C4h Jacobs University Bremen