Reduction formula for point group D2h

Your representation

E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
60 0 0 0 0 4 4 4

can be reduced to

Ag B1g B2g B3g Au B1u B2u B3u
9 7 7 7 6 8 8 8

Substraction of translational and rotational contributions results in

Ag B1g B2g B3g Au B1u B2u B3u
9 6 6 6 6 7 7 7



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 54 54 9
quadratic 2916 1485 213
cubic 157464 27720 3531
quartic 8503056 395010 49815
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 6 6 6 6 7 7 7
quadratic 213 181 181 181 180 183 183 183
cubic 3531 3443 3443 3443 3441 3473 3473 3473
quartic 49815 49293 49293 49293 49263 49351 49351 49351

Number of independant internal coordinates 9

Literature




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