Reduction formula for point group C3h

Reduction formula for point group C_3h

**Characters for molecular motions**
Motion	E	C₃(z)	(C₃)²	_h	S₃	(S₃)⁵
Cartesian 3N	33	0	0	7	-2	-2
Translation (x,y,z)	3	0	0	1	-2	-2
Rotation (R_x,R_y,R_z)	3	0	0	-1	2	2
Vibration	27	0	0	7	-2	-2

**Decomposition into Irreducible representations**
Motion	A'	E'	A''	E''	Total
Cartesian 3N	6	7	5	4	22
Translation (x,y,z)	0	1	1	0	2
Rotation (R_x,R_y,R_z)	1	0	0	1	2
Vibration	5	6	4	3	18

**Molecule Parameter**
Number of Atoms (N)	11
Number of internal coordinates	27
Number of independant internal coordinates	5
Number of vibrational modes	18

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A'	E'	A''	E''	Total
Linear (IR)	5	6	4	3	10 / 8
Quadratic (Raman)	5	6	4	3	14 / 4
IR + Raman	-	6	-	-	6 / 0

**Characters of symmetric powers for vibration representation**
Force field	Tensor Order	E	C₃(z)	(C₃)²	_h	S₃	(S₃)⁵
linear	1	27	0	0	7	-2	-2
quadratic	2	378	0	0	38	2	2
cubic	3	3.654	9	9	154	1	1
quartic	4	27.405	0	0	545	-4	-4
quintic	5	169.911	0	0	1.687	4	4
sextic	6	906.192	45	45	4.784	5	5

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A'	E'	A''	E''
linear	1	5	6	4	3
quadratic	2	70	69	56	57
cubic	3	638	633	586	582
quartic	4	4.657	4.659	4.478	4.476
quintic	5	28.601	28.599	28.036	28.038
sextic	6	151.846	151.821	150.248	150.228

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 C3h

Constructor University Bremen

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