Reduction formula for point group D2

Reduction formula for point group D₂

**Characters for molecular motions**
Motion	E	C₂ (z)	C₂ (y)	C₂ (x)
Cartesian 3N	78	-2	-2	-2
Translation (x,y,z)	3	-1	-1	-1
Rotation (R_x,R_y,R_z)	3	-1	-1	-1
Vibration	72	0	0	0

**Decomposition into Irreducible representations**
Motion	A	B₁	B₂	B₃	Total
Cartesian 3N	18	20	20	20	78
Translation (x,y,z)	0	1	1	1	3
Rotation (R_x,R_y,R_z)	0	1	1	1	3
Vibration	18	18	18	18	72

**Molecule Parameter**
Number of Atoms (N)	26
Number of internal coordinates	72
Number of independant internal coordinates	18
Number of vibrational modes	72

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A	B₁	B₂	B₃	Total
Linear (IR)	18	18	18	18	54 / 18
Quadratic (Raman)	18	18	18	18	72 / 0
IR + Raman	-	18	18	18	54 / 0

**Characters of symmetric powers for vibration representation**
Force field	Tensor Order	E	C₂ (z)	C₂ (y)	C₂ (x)
linear	1	72	0	0	0
quadratic	2	2.628	36	36	36
cubic	3	64.824	0	0	0
quartic	4	1.215.450	666	666	666
quintic	5	18.474.840	0	0	0
sextic	6	237.093.780	8.436	8.436	8.436

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A	B₁	B₂	B₃
linear	1	18	18	18	18
quadratic	2	684	648	648	648
cubic	3	16.206	16.206	16.206	16.206
quartic	4	304.362	303.696	303.696	303.696
quintic	5	4.618.710	4.618.710	4.618.710	4.618.710
sextic	6	59.279.772	59.271.336	59.271.336	59.271.336

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 D2

Constructor University Bremen

Last update November, 13^th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement