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	54	0	0	18
Translation (x,y,z)	3	-1	-3	1
Rotation (R_x,R_y,R_z)	3	-1	3	-1
Vibration	48	2	0	18

**Decomposition into Irreducible representations**
Motion	A_g	B_g	A_u	B_u	Total
Cartesian 3N	18	9	9	18	54
Translation (x,y,z)	0	0	1	2	3
Rotation (R_x,R_y,R_z)	1	2	0	0	3
Vibration	17	7	8	16	48

**Molecule Parameter**
Number of Atoms (N)	18
Number of internal coordinates	48
Number of independant internal coordinates	17
Number of vibrational modes	48

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A_g	B_g	A_u	B_u	Total
Linear (IR)	17	7	8	16	24 / 24
Quadratic (Raman)	17	7	8	16	24 / 24
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	48	2	0	18
quadratic	2	1.176	26	24	186
cubic	3	19.600	50	0	1.410
quartic	4	249.900	350	300	8.670
quintic	5	2.598.960	650	0	45.594
sextic	6	22.957.480	3.250	2.600	211.922

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A_g	B_g	A_u	B_u
linear	1	17	7	8	16
quadratic	2	353	247	248	328
cubic	3	5.265	4.535	4.560	5.240
quartic	4	64.805	60.295	60.320	64.480
quintic	5	661.301	638.179	638.504	660.976
sextic	6	5.793.813	5.686.227	5.686.552	5.790.888

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