Reduction formula for point group D5d

Your representation

E 2C5 2(C5)2 5C'2 i 2(S10)3 2S10 5d
72 6.4721 -2.4721 0 0 -0.0000 0.0000 8

can be reduced to

A1g A2g E1g E2g A1u A2u E1u E2u
6 2 8 6 2 6 8 6

Substraction of translational and rotational contributions results in

A1g A2g E1g E2g A1u A2u E1u E2u
6 1 7 6 2 5 7 6



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 66 66 6
quadratic 4356 2211 138
cubic 287496 50116 2611
quartic 18974736 864501 43863
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 6 1 7 6 2 5 7 6
quadratic 138 88 224 224 102 117 218 217
cubic 2611 2401 5012 5011 2435 2577 5012 5011
quartic 43863 42644 86506 86506 42902 43492 86394 86394

Number of independant internal coordinates 6

Literature




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