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	75	-1	-1	-1
Translation (x,y,z)	3	-1	-1	-1
Rotation (R_x,R_y,R_z)	3	-1	-1	-1
Vibration	69	1	1	1

**Decomposition into Irreducible representations**
Motion	A	B₁	B₂	B₃	Total
Cartesian 3N	18	19	19	19	75
Translation (x,y,z)	0	1	1	1	3
Rotation (R_x,R_y,R_z)	0	1	1	1	3
Vibration	18	17	17	17	69

**Molecule Parameter**
Number of Atoms (N)	25
Number of internal coordinates	69
Number of independant internal coordinates	18
Number of vibrational modes	69

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A	B₁	B₂	B₃	Total
Linear (IR)	18	17	17	17	51 / 18
Quadratic (Raman)	18	17	17	17	69 / 0
IR + Raman	-	17	17	17	51 / 0

**Characters of symmetric powers for vibration representation**
Force field	Tensor Order	E	C₂ (z)	C₂ (y)	C₂ (x)
linear	1	69	1	1	1
quadratic	2	2.415	35	35	35
cubic	3	57.155	35	35	35
quartic	4	1.028.790	630	630	630
quintic	5	15.020.334	630	630	630
sextic	6	185.250.786	7.770	7.770	7.770

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A	B₁	B₂	B₃
linear	1	18	17	17	17
quadratic	2	630	595	595	595
cubic	3	14.315	14.280	14.280	14.280
quartic	4	257.670	257.040	257.040	257.040
quintic	5	3.755.556	3.754.926	3.754.926	3.754.926
sextic	6	46.318.524	46.310.754	46.310.754	46.310.754

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