Reduction formula for point group C2h

Reduction formula for point group C_2h

**Characters for molecular motions**
Motion	E	C₂ (z)	i	_h
Cartesian 3N	39	-1	-3	5
Translation (x,y,z)	3	-1	-3	1
Rotation (R_x,R_y,R_z)	3	-1	3	-1
Vibration	33	1	-3	5

**Decomposition into Irreducible representations**
Motion	A_g	B_g	A_u	B_u	Total
Cartesian 3N	10	8	9	12	39
Translation (x,y,z)	0	0	1	2	3
Rotation (R_x,R_y,R_z)	1	2	0	0	3
Vibration	9	6	8	10	33

**Molecule Parameter**
Number of Atoms (N)	13
Number of internal coordinates	33
Number of independant internal coordinates	9
Number of vibrational modes	33

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A_g	B_g	A_u	B_u	Total
Linear (IR)	9	6	8	10	18 / 15
Quadratic (Raman)	9	6	8	10	15 / 18
IR + Raman	-	-	-	-	0^* / 0

* Center of inversion: Mutual Exclusion Principle

**Characters of symmetric powers for vibration representation**
Force field	Tensor Order	E	C₂ (z)	i	_h
linear	1	33	1	-3	5
quadratic	2	561	17	21	29
cubic	3	6.545	17	-55	105
quartic	4	58.905	153	225	385
quintic	5	435.897	153	-531	1.141
sextic	6	2.760.681	969	1.653	3.325

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A_g	B_g	A_u	B_u
linear	1	9	6	8	10
quadratic	2	157	134	132	138
cubic	3	1.653	1.592	1.628	1.672
quartic	4	14.917	14.648	14.612	14.728
quintic	5	109.165	108.518	108.860	109.354
sextic	6	691.657	689.510	689.168	690.346

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 C2h

Constructor University Bremen

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