Reduction formula for point group D5d

Your representation

E 2C5 2(C5)2 5C'2 i 2(S10)3 2S10 5d
120 0.0000 -0.0000 0 0 -0.0000 0.0000 8

can be reduced to

A1g A2g E1g E2g A1u A2u E1u E2u
8 4 12 12 4 8 12 12

Substraction of translational and rotational contributions results in

A1g A2g E1g E2g A1u A2u E1u E2u
8 3 11 12 4 7 11 12



Force field analysis

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

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 114 114 8
quadratic 12996 6555 368
cubic 1481544 253460 12837
quartic 168896016 7413705 372128
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 E1g E2g A1u A2u E1u E2u
linear 8 3 11 12 4 7 11 12
quadratic 368 294 662 660 318 333 650 649
cubic 12837 12507 25346 25347 12565 12779 25346 25347
quartic 372128 369409 741536 741535 370128 371078 741206 741204

Number of independant internal coordinates 8

Literature




Character tables for chemically important point groups Character table for point group D5d Jacobs University Bremen