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	57	-3	-3	-3
Translation (x,y,z)	3	-1	-1	-1
Rotation (R_x,R_y,R_z)	3	-1	-1	-1
Vibration	51	-1	-1	-1

**Decomposition into Irreducible representations**
Motion	A	B₁	B₂	B₃	Total
Cartesian 3N	12	15	15	15	57
Translation (x,y,z)	0	1	1	1	3
Rotation (R_x,R_y,R_z)	0	1	1	1	3
Vibration	12	13	13	13	51

**Molecule Parameter**
Number of Atoms (N)	19
Number of internal coordinates	51
Number of independant internal coordinates	12
Number of vibrational modes	51

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A	B₁	B₂	B₃	Total
Linear (IR)	12	13	13	13	39 / 12
Quadratic (Raman)	12	13	13	13	51 / 0
IR + Raman	-	13	13	13	39 / 0

**Characters of symmetric powers for vibration representation**
Force field	Tensor Order	E	C₂ (z)	C₂ (y)	C₂ (x)
linear	1	51	-1	-1	-1
quadratic	2	1.326	26	26	26
cubic	3	23.426	-26	-26	-26
quartic	4	316.251	351	351	351
quintic	5	3.478.761	-351	-351	-351
sextic	6	32.468.436	3.276	3.276	3.276

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A	B₁	B₂	B₃
linear	1	12	13	13	13
quadratic	2	351	325	325	325
cubic	3	5.837	5.863	5.863	5.863
quartic	4	79.326	78.975	78.975	78.975
quintic	5	869.427	869.778	869.778	869.778
sextic	6	8.119.566	8.116.290	8.116.290	8.116.290

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