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	39	-5	-1	-1
Translation (x,y,z)	3	-1	-1	-1
Rotation (R_x,R_y,R_z)	3	-1	-1	-1
Vibration	33	-3	1	1

**Decomposition into Irreducible representations**
Motion	A	B₁	B₂	B₃	Total
Cartesian 3N	8	9	11	11	39
Translation (x,y,z)	0	1	1	1	3
Rotation (R_x,R_y,R_z)	0	1	1	1	3
Vibration	8	7	9	9	33

**Molecule Parameter**
Number of Atoms (N)	13
Number of internal coordinates	33
Number of independant internal coordinates	8
Number of vibrational modes	33

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A	B₁	B₂	B₃	Total
Linear (IR)	8	7	9	9	25 / 8
Quadratic (Raman)	8	7	9	9	33 / 0
IR + Raman	-	7	9	9	25 / 0

**Characters of symmetric powers for vibration representation**
Force field	Tensor Order	E	C₂ (z)	C₂ (y)	C₂ (x)
linear	1	33	-3	1	1
quadratic	2	561	21	17	17
cubic	3	6.545	-55	17	17
quartic	4	58.905	225	153	153
quintic	5	435.897	-531	153	153
sextic	6	2.760.681	1.653	969	969

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A	B₁	B₂	B₃
linear	1	8	7	9	9
quadratic	2	154	137	135	135
cubic	3	1.631	1.614	1.650	1.650
quartic	4	14.859	14.706	14.670	14.670
quintic	5	108.918	108.765	109.107	109.107
sextic	6	691.068	690.099	689.757	689.757

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