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	252	0	0	0
Translation (x,y,z)	3	-1	-1	-1
Rotation (R_x,R_y,R_z)	3	-1	-1	-1
Vibration	246	2	2	2

**Decomposition into Irreducible representations**
Motion	A	B₁	B₂	B₃	Total
Cartesian 3N	63	63	63	63	252
Translation (x,y,z)	0	1	1	1	3
Rotation (R_x,R_y,R_z)	0	1	1	1	3
Vibration	63	61	61	61	246

**Molecule Parameter**
Number of Atoms (N)	84
Number of internal coordinates	246
Number of independant internal coordinates	63
Number of vibrational modes	246

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A	B₁	B₂	B₃	Total
Linear (IR)	63	61	61	61	183 / 63
Quadratic (Raman)	63	61	61	61	246 / 0
IR + Raman	-	61	61	61	183 / 0

**Characters of symmetric powers for vibration representation**
Force field	Tensor Order	E	C₂ (z)	C₂ (y)	C₂ (x)
linear	1	246	2	2	2
quadratic	2	30.381	125	125	125
cubic	3	2.511.496	248	248	248
quartic	4	156.340.626	7.874	7.874	7.874
quintic	5	7.817.031.300	15.500	15.500	15.500
sextic	6	327.012.476.050	333.250	333.250	333.250

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A	B₁	B₂	B₃
linear	1	63	61	61	61
quadratic	2	7.689	7.564	7.564	7.564
cubic	3	628.060	627.812	627.812	627.812
quartic	4	39.091.062	39.083.188	39.083.188	39.083.188
quintic	5	1.954.269.450	1.954.253.950	1.954.253.950	1.954.253.950
sextic	6	81.753.368.950	81.753.035.700	81.753.035.700	81.753.035.700

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