Reduction formula for point group C6v

Your representation

E 2C6 (z) 2C3 (z) C2 (z) 3v 3d
36 0 0 0 0 4

can be reduced to

A1 A2 B1 B2 E1 E2
4 2 2 4 6 6

Substraction of translational and rotational contributions results in

A1 A2 B1 B2 E1 E2
3 1 2 4 4 6



Force field analysis

Infrared and Raman activities (harmonic approximation)
Method A1 A2 B1 B2 E1 E2
Infrared + - - - + -
Raman + - - - + +

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 30 30 3
quadratic 900 465 51
cubic 27000 4960 434
quartic 810000 40920 3518
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 A1 A2 B1 B2 E1 E2
linear 3 1 2 4 4 6
quadratic 51 32 34 38 76 79
cubic 434 398 396 432 818 832
quartic 3518 3330 3362 3430 6796 6844

Number of independant internal coordinates 3

Literature




Character tables for chemically important point groups Character table for point group C6v Jacobs University Bremen