Reduction formula for point group D2h

Your representation

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

can be reduced to

Ag B1g B2g B3g Au B1u B2u B3u
6 4 4 4 3 5 5 5

Substraction of translational and rotational contributions results in

Ag B1g B2g B3g Au B1u B2u B3u
6 3 3 3 3 4 4 4



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 75
cubic 27000 4960 659
quartic 810000 40920 5283
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 3 3 3 3 4 4 4
quadratic 75 55 55 55 54 57 57 57
cubic 659 607 607 607 605 625 625 625
quartic 5283 5079 5079 5079 5061 5113 5113 5113

Number of independant internal coordinates 6

Literature




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