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

**Decomposition into Irreducible representations**
Motion	A_g	B_g	A_u	B_u	Total
Cartesian 3N	13	14	13	14	54
Translation (x,y,z)	0	0	1	2	3
Rotation (R_x,R_y,R_z)	1	2	0	0	3
Vibration	12	12	12	12	48

**Molecule Parameter**
Number of Atoms (N)	18
Number of internal coordinates	48
Number of independant internal coordinates	12
Number of vibrational modes	48

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A_g	B_g	A_u	B_u	Total
Linear (IR)	12	12	12	12	24 / 24
Quadratic (Raman)	12	12	12	12	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	0	0	0
quadratic	2	1.176	24	24	24
cubic	3	19.600	0	0	0
quartic	4	249.900	300	300	300
quintic	5	2.598.960	0	0	0
sextic	6	22.957.480	2.600	2.600	2.600

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A_g	B_g	A_u	B_u
linear	1	12	12	12	12
quadratic	2	312	288	288	288
cubic	3	4.900	4.900	4.900	4.900
quartic	4	62.700	62.400	62.400	62.400
quintic	5	649.740	649.740	649.740	649.740
sextic	6	5.741.320	5.738.720	5.738.720	5.738.720

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