Reduction formula for point group D2h

Your representation

E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
57 -3 -3 -3 -3 9 9 9

can be reduced to

Ag B1g B2g B3g Au B1u B2u B3u
9 6 6 6 3 9 9 9

Substraction of translational and rotational contributions results in

Ag B1g B2g B3g Au B1u B2u B3u
9 5 5 5 3 8 8 8



Force field analysis

Infrared and Raman activities (harmonic approximation)
Method Ag B1g B2g B3g Au B1u B2u B3u
Infrared - - - - - + + +
Raman + + + + - - - -

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 51 51 9
quadratic 2601 1326 204
cubic 132651 23426 3041
quartic 6765201 316251 40347
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 B1g B2g B3g Au B1u B2u B3u
linear 9 5 5 5 3 8 8 8
quadratic 204 158 158 158 147 167 167 167
cubic 3041 2877 2877 2877 2796 2986 2986 2986
quartic 40347 39336 39336 39336 38979 39639 39639 39639

Number of independant internal coordinates 9

Literature




Character tables for chemically important point groups Character table for point group D2h Jacobs University Bremen