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	15	-1	-3	5
Translation (x,y,z)	3	-1	-3	1
Rotation (R_x,R_y,R_z)	3	-1	3	-1
Vibration	9	1	-3	5

**Decomposition into Irreducible representations**
Motion	A_g	B_g	A_u	B_u	Total
Cartesian 3N	4	2	3	6	15
Translation (x,y,z)	0	0	1	2	3
Rotation (R_x,R_y,R_z)	1	2	0	0	3
Vibration	3	0	2	4	9

**Molecule Parameter**
Number of Atoms (N)	5
Number of internal coordinates	9
Number of independant internal coordinates	3
Number of vibrational modes	9

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A_g	B_g	A_u	B_u	Total
Linear (IR)	3	0	2	4	6 / 3
Quadratic (Raman)	3	0	2	4	3 / 6
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	9	1	-3	5
quadratic	2	45	5	9	17
cubic	3	165	5	-19	45
quartic	4	495	15	39	103
quintic	5	1.287	15	-69	211
sextic	6	3.003	35	119	399

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A_g	B_g	A_u	B_u
linear	1	3	0	2	4
quadratic	2	19	8	6	12
cubic	3	49	24	36	56
quartic	4	163	104	92	136
quintic	5	361	248	290	388
sextic	6	889	672	630	812

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