Reduction formula for point group C4

Reduction formula for point group C₄

**Characters for molecular motions**
Motion	E	C₄	C₂	(C₄)³
Cartesian 3N	156	0	0	0
Translation (x,y,z)	3	1	-1	1
Rotation (R_x,R_y,R_z)	3	1	-1	1
Vibration	150	-2	2	-2

**Decomposition into Irreducible representations**
Motion	A	B	E	Total
Cartesian 3N	39	39	39	117
Translation (x,y,z)	1	0	1	2
Rotation (R_x,R_y,R_z)	1	0	1	2
Vibration	37	39	37	113

**Molecule Parameter**
Number of Atoms (N)	52
Number of internal coordinates	150
Number of independant internal coordinates	37
Number of vibrational modes	113

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A	B	E	Total
Linear (IR)	37	39	37	74 / 39
Quadratic (Raman)	37	39	37	113 / 0
IR + Raman	37	-	37	74 / 0

**Characters of symmetric powers for vibration representation**
Force field	Tensor Order	E	C₄	C₂	(C₄)³
linear	1	150	-2	2	-2
quadratic	2	11.325	3	77	3
cubic	3	573.800	-4	152	-4
quartic	4	21.947.850	42	3.002	42
quintic	5	675.993.780	-80	5.852	-80
sextic	6	17.463.172.650	118	79.002	118

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A	B	E
linear	1	37	39	37
quadratic	2	2.852	2.849	2.812
cubic	3	143.486	143.490	143.412
quartic	4	5.487.734	5.487.692	5.486.212
quintic	5	168.999.868	168.999.948	168.996.982
sextic	6	4.365.812.972	4.365.812.854	4.365.773.412

Literature

J.K.G. Watson, J. Mol. Spec. 41 229 (1972)
The Numbers of Structural Parameters and Potential Constants of Molecules
X.F. Zhou, P. Pulay. J. Comp. Chem. 10 No. 7, 935-938 (1989)
Characters for Symmetric and Antisymmetric Higher Powers of Representations:
Application to the Number of Anharmonic Force Constants in Symmetrical Molecules

Character tables for chemically important point groups

Character table for point group C4

Constructor University Bremen

Last update November, 13^th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement