Reduction formula for point group D2h

Your representation

E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
18 0 0 -2 0 6 2 0

can be reduced to

Ag B1g B2g B3g Au B1u B2u B3u
3 3 2 1 1 2 3 3

Substraction of translational and rotational contributions results in

Ag B1g B2g B3g Au B1u B2u B3u
3 2 1 0 1 1 2 2



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 12 12 3
quadratic 144 78 18
cubic 1728 364 60
quartic 20736 1365 216
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 3 2 1 0 1 1 2 2
quadratic 18 11 7 6 7 7 11 11
cubic 60 53 38 31 38 38 53 53
quartic 216 188 148 141 148 148 188 188

Number of independant internal coordinates 3

Literature




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