Reduction formula for point group D2h

Your representation

E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
48 0 0 0 0 0 0 0

can be reduced to

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

Substraction of translational and rotational contributions results in

Ag B1g B2g B3g Au B1u B2u B3u
6 5 5 5 6 5 5 5



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 42 42 6
quadratic 1764 903 132
cubic 74088 13244 1672
quartic 3111696 148995 18843
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 6 5 5 5 6 5 5 5
quadratic 132 110 110 110 111 110 110 110
cubic 1672 1650 1650 1650 1672 1650 1650 1650
quartic 18843 18590 18590 18590 18612 18590 18590 18590

Number of independant internal coordinates 6

Literature




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