Reduction formula for point group D5d

Your representation

E 2C5 2(C5)2 5C'2 i 2(S10)3 2S10 5d
180 0.0000 -0.0000 0 0 -0.0000 0.0000 4

can be reduced to

A1g A2g E1g E2g A1u A2u E1u E2u
10 8 18 18 8 10 18 18

Substraction of translational and rotational contributions results in

A1g A2g E1g E2g A1u A2u E1u E2u
10 7 17 18 8 9 17 18



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 174 174 10
quadratic 30276 15225 812
cubic 5268024 893200 44793
quartic 916636176 39524100 1978533
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 10 7 17 18 8 9 17 18
quadratic 812 720 1532 1530 756 759 1514 1513
cubic 44793 44525 89320 89321 44613 44705 89320 89321
quartic 1978533 1974261 3952793 3952792 1975880 1976148 3952028 3952026

Number of independant internal coordinates 10

Literature




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