Reduction formula for point group D2h

Your representation

E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
54 0 0 -2 0 18 2 0

can be reduced to

Ag B1g B2g B3g Au B1u B2u B3u
9 9 5 4 4 5 9 9

Substraction of translational and rotational contributions results in

Ag B1g B2g B3g Au B1u B2u B3u
9 8 4 3 4 4 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 48 48 9
quadratic 2304 1176 189
cubic 110592 19600 2645
quartic 5308416 249900 32565
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 8 4 3 4 4 8 8
quadratic 189 164 124 123 124 124 164 164
cubic 2645 2620 2280 2255 2280 2280 2620 2620
quartic 32565 32240 30160 30135 30160 30160 32240 32240

Number of independant internal coordinates 9

Literature




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