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	60	0	0	0
Translation (x,y,z)	3	-1	-3	1
Rotation (R_x,R_y,R_z)	3	-1	3	-1
Vibration	54	2	0	0

**Decomposition into Irreducible representations**
Motion	A_g	B_g	A_u	B_u	Total
Cartesian 3N	15	15	15	15	60
Translation (x,y,z)	0	0	1	2	3
Rotation (R_x,R_y,R_z)	1	2	0	0	3
Vibration	14	13	14	13	54

**Molecule Parameter**
Number of Atoms (N)	20
Number of internal coordinates	54
Number of independant internal coordinates	14
Number of vibrational modes	54

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A_g	B_g	A_u	B_u	Total
Linear (IR)	14	13	14	13	27 / 27
Quadratic (Raman)	14	13	14	13	27 / 27
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	54	2	0	0
quadratic	2	1.485	29	27	27
cubic	3	27.720	56	0	0
quartic	4	395.010	434	378	378
quintic	5	4.582.116	812	0	0
sextic	6	45.057.474	4.466	3.654	3.654

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A_g	B_g	A_u	B_u
linear	1	14	13	14	13
quadratic	2	392	364	365	364
cubic	3	6.944	6.916	6.944	6.916
quartic	4	99.050	98.644	98.672	98.644
quintic	5	1.145.732	1.145.326	1.145.732	1.145.326
sextic	6	11.267.312	11.263.252	11.263.658	11.263.252

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