Reduction formula for point group D2h

Your representation

E C2 (z) C2 (y) C2 (x) i (xy) (xz) (yz)
48 0 0 0 0 0 8 8

can be reduced to

Ag B1g B2g B3g Au B1u B2u B3u
8 4 6 6 4 8 6 6

Substraction of translational and rotational contributions results in

Ag B1g B2g B3g Au B1u B2u B3u
8 3 5 5 4 7 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 42 42 8
quadratic 1764 903 140
cubic 74088 13244 1736
quartic 3111696 148995 19059
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 8 3 5 5 4 7 5 5
quadratic 140 102 110 110 103 118 110 110
cubic 1736 1586 1650 1650 1608 1714 1650 1650
quartic 19059 18374 18590 18590 18396 18806 18590 18590

Number of independant internal coordinates 8

Literature




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