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	0	0	12
Translation (x,y,z)	3	-1	-3	1
Rotation (R_x,R_y,R_z)	3	-1	3	-1
Vibration	30	2	0	12

**Decomposition into Irreducible representations**
Motion	A_g	B_g	A_u	B_u	Total
Cartesian 3N	12	6	6	12	36
Translation (x,y,z)	0	0	1	2	3
Rotation (R_x,R_y,R_z)	1	2	0	0	3
Vibration	11	4	5	10	30

**Molecule Parameter**
Number of Atoms (N)	12
Number of internal coordinates	30
Number of independant internal coordinates	11
Number of vibrational modes	30

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A_g	B_g	A_u	B_u	Total
Linear (IR)	11	4	5	10	15 / 15
Quadratic (Raman)	11	4	5	10	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	12
quadratic	2	465	17	15	87
cubic	3	4.960	32	0	472
quartic	4	40.920	152	120	2.112
quintic	5	278.256	272	0	8.184
sextic	6	1.623.160	952	680	28.336

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A_g	B_g	A_u	B_u
linear	1	11	4	5	10
quadratic	2	146	94	95	130
cubic	3	1.366	1.114	1.130	1.350
quartic	4	10.826	9.694	9.710	10.690
quintic	5	71.678	67.450	67.586	71.542
sextic	6	413.282	398.638	398.774	412.466

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