Reduction formula for point group D2h

Your representation

E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
72 0 0 0 0 8 8 8

can be reduced to

Ag B1g B2g B3g Au B1u B2u B3u
12 8 8 8 6 10 10 10

Substraction of translational and rotational contributions results in

Ag B1g B2g B3g Au B1u B2u B3u
12 7 7 7 6 9 9 9



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 66 66 12
quadratic 4356 2211 318
cubic 287496 50116 6422
quartic 18974736 864501 109047
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 12 7 7 7 6 9 9 9
quadratic 318 268 268 268 261 276 276 276
cubic 6422 6212 6212 6212 6158 6300 6300 6300
quartic 109047 107828 107828 107828 107550 108140 108140 108140

Number of independant internal coordinates 12

Literature




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