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	24	0	0	0
Translation (x,y,z)	3	-1	-1	-1
Rotation (R_x,R_y,R_z)	3	-1	-1	-1
Vibration	18	2	2	2

**Decomposition into Irreducible representations**
Motion	A	B₁	B₂	B₃	Total
Cartesian 3N	6	6	6	6	24
Translation (x,y,z)	0	1	1	1	3
Rotation (R_x,R_y,R_z)	0	1	1	1	3
Vibration	6	4	4	4	18

**Molecule Parameter**
Number of Atoms (N)	8
Number of internal coordinates	18
Number of independant internal coordinates	6
Number of vibrational modes	18

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A	B₁	B₂	B₃	Total
Linear (IR)	6	4	4	4	12 / 6
Quadratic (Raman)	6	4	4	4	18 / 0
IR + Raman	-	4	4	4	12 / 0

**Characters of symmetric powers for vibration representation**
Force field	Tensor Order	E	C₂ (z)	C₂ (y)	C₂ (x)
linear	1	18	2	2	2
quadratic	2	171	11	11	11
cubic	3	1.140	20	20	20
quartic	4	5.985	65	65	65
quintic	5	26.334	110	110	110
sextic	6	100.947	275	275	275

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A	B₁	B₂	B₃
linear	1	6	4	4	4
quadratic	2	51	40	40	40
cubic	3	300	280	280	280
quartic	4	1.545	1.480	1.480	1.480
quintic	5	6.666	6.556	6.556	6.556
sextic	6	25.443	25.168	25.168	25.168

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