Reduction formula for point group C3v

Reduction formula for point group C_3v

Your representation

E	2C₃ (z)	3_v
9	0	3

can be reduced to

A₁	A₂	E
3	0	3

Infrared and Raman activities (harmonic approximation)
Method	A₁	A₂	E
Infrared	+	-	+
Raman	+	-	+

Number of force field parameters
Force field	No. 1	No. 2	No. 3
linear	9	9	3
quadratic	81	45	12
cubic	729	165	38
quartic	6561	495	102

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	E
linear	3	0	3
quadratic	12	3	15
cubic	38	19	54
quartic	102	63	165

Number of independant internal coordinates	3

J.K.G. Watson, J. Mol. Spec. 41 229 (1972)
The Numbers of Structural Parameters and Potential Constants of Molecules