Reduction formula for point group D6h

Your representation

E 2C6 (z) 2C3 C2 3C'2 3C''2 i 2S3 2S6 h (xy) 3d 3v
324 0 0 0 0 0 0 0 0 24 12 8

can be reduced to

A1g A2g B1g B2g E1g E2g A1u A2u B1u B2u E1u E2u
17 12 13 12 25 29 10 15 14 15 29 25

Substraction of translational and rotational contributions results in

A1g A2g B1g B2g E1g E2g A1u A2u B1u B2u E1u E2u
17 11 13 12 24 29 10 14 14 15 28 25



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 318 318 17
quadratic 101124 50721 2239
cubic 32157432 5410240 226229
quartic XXX*XXX*XXX*
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 17 11 13 12 24 29 10 14 14 15 28 25
quadratic 2239 2053 2099 2089 4190 4290 2083 2108 2113 2123 4238 4189
cubic 226229 225179 225272 225062 450307 451382 224827 225557 225574 225784 451327 450362
quartic XXX*XXX*XXX*XXX*XXX*XXX*XXX*XXX*XXX*XXX*XXX*XXX*
*Not calculated for systems with more than 75 atoms

Number of independant internal coordinates 17

Literature




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