Reduction formula for point group C6h

Your representation

E C6(z) C3 C2 (C3)2 (C6)5 i (S3)5 (S6)5 h S6 S3
36 0 0 0 0 0 0 0 0 12 0 0

can be reduced to

Ag Bg E1g E2g Au Bu E1u E2u
4 2 2 4 2 4 4 2

Substraction of translational and rotational contributions results in

Ag Bg E1g E2g Au Bu E1u E2u
3 2 1 4 1 4 3 2



Force field analysis

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

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 30 30 3
quadratic 900 465 50
cubic 27000 4960 456
quartic 810000 40920 3610
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 Bg E1g E2g Au Bu E1u E2u
linear 3 2 1 4 1 4 3 2
quadratic 50 30 32 48 33 42 44 31
cubic 456 374 370 455 376 454 448 377
quartic 3610 3230 3232 3608 3238 3562 3564 3236

Number of independant internal coordinates 3

Literature




Character tables for chemically important point groups Character table for point group C6h Jacobs University Bremen