Reduction formula for point group D2h

Your representation

E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
21 -3 -1 -1 -3 5 3 3

can be reduced to

Ag B1g B2g B3g Au B1u B2u B3u
3 2 2 2 1 3 4 4

Substraction of translational and rotational contributions results in

Ag B1g B2g B3g Au B1u B2u B3u
3 1 1 1 1 2 3 3



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 15 15 3
quadratic 225 120 25
cubic 3375 680 97
quartic 50625 3060 443
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 3 1 1 1 1 2 3 3
quadratic 25 15 13 13 11 13 15 15
cubic 97 79 75 75 75 85 97 97
quartic 443 389 367 367 349 367 389 389

Number of independant internal coordinates 3

Literature




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