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	48	0	0	0
Translation (x,y,z)	3	-1	-1	-1
Rotation (R_x,R_y,R_z)	3	-1	-1	-1
Vibration	42	2	2	2

**Decomposition into Irreducible representations**
Motion	A	B₁	B₂	B₃	Total
Cartesian 3N	12	12	12	12	48
Translation (x,y,z)	0	1	1	1	3
Rotation (R_x,R_y,R_z)	0	1	1	1	3
Vibration	12	10	10	10	42

**Molecule Parameter**
Number of Atoms (N)	16
Number of internal coordinates	42
Number of independant internal coordinates	12
Number of vibrational modes	42

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A	B₁	B₂	B₃	Total
Linear (IR)	12	10	10	10	30 / 12
Quadratic (Raman)	12	10	10	10	42 / 0
IR + Raman	-	10	10	10	30 / 0

**Characters of symmetric powers for vibration representation**
Force field	Tensor Order	E	C₂ (z)	C₂ (y)	C₂ (x)
linear	1	42	2	2	2
quadratic	2	903	23	23	23
cubic	3	13.244	44	44	44
quartic	4	148.995	275	275	275
quintic	5	1.370.754	506	506	506
sextic	6	10.737.573	2.277	2.277	2.277

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A	B₁	B₂	B₃
linear	1	12	10	10	10
quadratic	2	243	220	220	220
cubic	3	3.344	3.300	3.300	3.300
quartic	4	37.455	37.180	37.180	37.180
quintic	5	343.068	342.562	342.562	342.562
sextic	6	2.686.101	2.683.824	2.683.824	2.683.824

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