Reduction formula for point group D5d

Your representation

E 2C5 2(C5)2 5C'2 i 2(S10)3 2S10 5d
36 3.2361 -1.2361 0 0 -0.0000 0.0000 4

can be reduced to

A1g A2g E1g E2g A1u A2u E1u E2u
3 1 4 3 1 3 4 3

Substraction of translational and rotational contributions results in

A1g A2g E1g E2g A1u A2u E1u E2u
3 0 3 3 1 2 3 3



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 30 30 3
quadratic 900 465 34
cubic 27000 4960 274
quartic 810000 40920 2154
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 3 0 3 3 1 2 3 3
quadratic 34 14 48 48 21 24 45 45
cubic 274 222 496 496 238 258 496 496
quartic 2154 1950 4104 4104 2014 2066 4080 4080

Number of independant internal coordinates 3

Literature




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