Reduction formula for point group D4h

Your representation

E 2C4 (z) C2 2C'2 2C''2 i 2S4 h 2v 2d
21 3 -3 -3 -1 -3 -1 5 5 3

can be reduced to

A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu
2 1 1 1 2 0 3 0 1 4

Substraction of translational and rotational contributions results in

A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu
2 0 1 1 1 0 2 0 1 3



Force field analysis

Infrared and Raman activities (harmonic approximation)
Method A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu
Infrared - - - - - - + - - +
Raman + - + + + - - - - -

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 15 15 2
quadratic 225 120 16
cubic 3375 680 55
quartic 50625 3060 247
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 A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu
linear 2 0 1 1 1 0 2 0 1 3
quadratic 16 4 11 9 13 4 8 5 7 15
cubic 55 33 46 42 75 29 51 34 46 97
quartic 247 171 218 196 367 159 199 168 190 389

Number of independant internal coordinates 2

Literature




Character tables for chemically important point groups Character table for point group D4h Jacobs University Bremen