Reduction formula for point group D2h

Your representation

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

can be reduced to

Ag B1g B2g B3g Au B1u B2u B3u
3 2 2 2 0 4 4 4

Substraction of translational and rotational contributions results in

Ag B1g B2g B3g Au B1u B2u B3u
3 1 1 1 0 3 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 27
cubic 3375 680 101
quartic 50625 3060 465
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 0 3 3 3
quadratic 27 13 13 13 9 15 15 15
cubic 101 75 75 75 63 97 97 97
quartic 465 367 367 367 327 389 389 389

Number of independant internal coordinates 3

Literature




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