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	36	-4	0	0
Translation (x,y,z)	3	-1	-3	1
Rotation (R_x,R_y,R_z)	3	-1	3	-1
Vibration	30	-2	0	0

**Decomposition into Irreducible representations**
Motion	A_g	B_g	A_u	B_u	Total
Cartesian 3N	8	10	8	10	36
Translation (x,y,z)	0	0	1	2	3
Rotation (R_x,R_y,R_z)	1	2	0	0	3
Vibration	7	8	7	8	30

**Molecule Parameter**
Number of Atoms (N)	12
Number of internal coordinates	30
Number of independant internal coordinates	7
Number of vibrational modes	30

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A_g	B_g	A_u	B_u	Total
Linear (IR)	7	8	7	8	15 / 15
Quadratic (Raman)	7	8	7	8	15 / 15
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	30	-2	0	0
quadratic	2	465	17	15	15
cubic	3	4.960	-32	0	0
quartic	4	40.920	152	120	120
quintic	5	278.256	-272	0	0
sextic	6	1.623.160	952	680	680

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A_g	B_g	A_u	B_u
linear	1	7	8	7	8
quadratic	2	128	112	113	112
cubic	3	1.232	1.248	1.232	1.248
quartic	4	10.328	10.192	10.208	10.192
quintic	5	69.496	69.632	69.496	69.632
sextic	6	406.368	405.552	405.688	405.552

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