Reduction formula for point group S10

Your representation

E C5 (C5)2 (C5)3 (C5)4 i (S10)7 (S10)9 S10 (S10)3
72 6.4721 -2.4721 -2.4721 6.4721 0 -0.0000 0.0000 0.0000 -0.0000

can be reduced to

Ag E1g E2g Au E1u E2u
8 8 6 8 8 6

Substraction of translational and rotational contributions results in

Ag E1g E2g Au E1u E2u
7 7 6 7 7 6



Force field analysis

Infrared and Raman activities (harmonic approximation)
Method Ag E1g E2g Au E1u E2u
Infrared - - - + + -
Raman + + + - - -

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 66 66 7
quadratic 4356 2211 226
cubic 287496 50116 5012
quartic 18974736 864501 86507
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 Ag E1g E2g Au E1u E2u
linear 7 7 6 7 7 6
quadratic 226 224 224 219 218 217
cubic 5012 5012 5011 5012 5012 5011
quartic 86507 86506 86506 86394 86394 86394

Number of independant internal coordinates 7

Literature




Character tables for chemically important point groups Character table for point group S10 Jacobs University Bremen