Reduction formula for point group C4v

Your representation

E 2C4 (z) C2 2v 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
7 3 4 8 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 7
quadratic 1764 903 135
cubic 74088 13244 1724
quartic 3111696 148995 18994
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 7 3 4 8 10
quadratic 135 98 107 123 220
cubic 1724 1596 1598 1726 3300
quartic 18994 18331 18439 18871 37180

Number of independant internal coordinates 7

Literature




Character tables for chemically important point groups Character table for point group C4v Jacobs University Bremen