Reduction formula for point group D2h

Your representation

E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
36 0 -4 0 0 12 0 4

can be reduced to

Ag B1g B2g B3g Au B1u B2u B3u
6 6 2 4 2 4 6 6

Substraction of translational and rotational contributions results in

Ag B1g B2g B3g Au B1u B2u B3u
6 5 1 3 2 3 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 30 30 6
quadratic 900 465 82
cubic 27000 4960 692
quartic 810000 40920 5498
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 1 3 2 3 5 5
quadratic 82 64 46 48 47 48 66 64
cubic 692 674 540 574 556 574 676 674
quartic 5498 5328 4830 4864 4846 4864 5362 5328

Number of independant internal coordinates 6

Literature




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