Reduction formula for point group D4h

Your representation

E 2C4 (z) C2 2C'2 2C''2 i 2S4 h 2v 2d
48 0 0 0 0 0 0 0 0 8

can be reduced to

A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu
4 2 2 4 6 2 4 4 2 6

Substraction of translational and rotational contributions results in

A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu
4 1 2 4 5 2 3 4 2 5



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 42 42 4
quadratic 1764 903 76
cubic 74088 13244 873
quartic 3111696 148995 9596
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 4 1 2 4 5 2 3 4 2 5
quadratic 76 46 56 64 110 52 59 59 51 110
cubic 873 787 799 863 1650 809 851 863 799 1650
quartic 9596 9127 9247 9463 18590 9204 9398 9408 9192 18590

Number of independant internal coordinates 4

Literature




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