Reduction formula for point group D6h

Your representation

E 2C6 (z) 2C3 C2 3C'2 3C''2 i 2S3 2S6 h (xy) 3d 3v
36 0 0 0 -4 0 0 0 0 12 0 4

can be reduced to

A1g A2g B1g B2g E1g E2g A1u A2u B1u B2u E1u E2u
2 2 0 2 2 4 0 2 2 2 4 2

Substraction of translational and rotational contributions results in

A1g A2g B1g B2g E1g E2g A1u A2u B1u B2u E1u E2u
2 1 0 2 1 4 0 1 2 2 3 2



Force field analysis

Infrared and Raman activities (harmonic approximation)
Method A1g A2g B1g B2g E1g E2g A1u A2u B1u B2u E1u E2u
Infrared - - - - - - - + - - + -
Raman + - - - + + - - - - - -

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 30 30 2
quadratic 900 465 34
cubic 27000 4960 237
quartic 810000 40920 1890
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 A1g A2g B1g B2g E1g E2g A1u A2u B1u B2u E1u E2u
linear 2 1 0 2 1 4 0 1 2 2 3 2
quadratic 34 16 14 16 32 48 16 17 22 20 44 31
cubic 237 219 170 204 370 455 179 197 228 226 448 377
quartic 1890 1720 1598 1632 3232 3608 1610 1628 1798 1764 3564 3236

Number of independant internal coordinates 2

Literature




Character tables for chemically important point groups Character table for point group D6h Jacobs University Bremen