Reduction formula for point group D2h

Your representation

E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
24 0 -2 -2 0 4 6 2

can be reduced to

Ag B1g B2g B3g Au B1u B2u B3u
4 3 3 2 1 4 3 4

Substraction of translational and rotational contributions results in

Ag B1g B2g B3g Au B1u B2u B3u
4 2 2 1 1 3 2 3



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 18 18 4
quadratic 324 171 33
cubic 5832 1140 165
quartic 104976 5985 832
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 4 2 2 1 1 3 2 3
quadratic 33 19 21 17 17 22 19 23
cubic 165 137 143 125 125 153 137 155
quartic 832 725 755 703 703 765 725 777

Number of independant internal coordinates 4

Literature




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