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	0	0	-2
Translation (x,y,z)	3	-1	-1	-1
Rotation (R_x,R_y,R_z)	3	-1	-1	-1
Vibration	72	2	2	0

**Decomposition into Irreducible representations**
Motion	A	B₁	B₂	B₃	Total
Cartesian 3N	19	20	20	19	78
Translation (x,y,z)	0	1	1	1	3
Rotation (R_x,R_y,R_z)	0	1	1	1	3
Vibration	19	18	18	17	72

**Molecule Parameter**
Number of Atoms (N)	26
Number of internal coordinates	72
Number of independant internal coordinates	19
Number of vibrational modes	72

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A	B₁	B₂	B₃	Total
Linear (IR)	19	18	18	17	53 / 19
Quadratic (Raman)	19	18	18	17	72 / 0
IR + Raman	-	18	18	17	53 / 0

**Characters of symmetric powers for vibration representation**
Force field	Tensor Order	E	C₂ (z)	C₂ (y)	C₂ (x)
linear	1	72	2	2	0
quadratic	2	2.628	38	38	36
cubic	3	64.824	74	74	0
quartic	4	1.215.450	740	740	666
quintic	5	18.474.840	1.406	1.406	0
sextic	6	237.093.780	9.842	9.842	8.436

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A	B₁	B₂	B₃
linear	1	19	18	18	17
quadratic	2	685	648	648	647
cubic	3	16.243	16.206	16.206	16.169
quartic	4	304.399	303.696	303.696	303.659
quintic	5	4.619.413	4.618.710	4.618.710	4.618.007
sextic	6	59.280.475	59.271.336	59.271.336	59.270.633

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