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	84	0	0	0
Translation (x,y,z)	3	-1	-1	-1
Rotation (R_x,R_y,R_z)	3	-1	-1	-1
Vibration	78	2	2	2

**Decomposition into Irreducible representations**
Motion	A	B₁	B₂	B₃	Total
Cartesian 3N	21	21	21	21	84
Translation (x,y,z)	0	1	1	1	3
Rotation (R_x,R_y,R_z)	0	1	1	1	3
Vibration	21	19	19	19	78

**Molecule Parameter**
Number of Atoms (N)	28
Number of internal coordinates	78
Number of independant internal coordinates	21
Number of vibrational modes	78

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A	B₁	B₂	B₃	Total
Linear (IR)	21	19	19	19	57 / 21
Quadratic (Raman)	21	19	19	19	78 / 0
IR + Raman	-	19	19	19	57 / 0

**Characters of symmetric powers for vibration representation**
Force field	Tensor Order	E	C₂ (z)	C₂ (y)	C₂ (x)
linear	1	78	2	2	2
quadratic	2	3.081	41	41	41
cubic	3	82.160	80	80	80
quartic	4	1.663.740	860	860	860
quintic	5	27.285.336	1.640	1.640	1.640
sextic	6	377.447.148	12.300	12.300	12.300

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A	B₁	B₂	B₃
linear	1	21	19	19	19
quadratic	2	801	760	760	760
cubic	3	20.600	20.520	20.520	20.520
quartic	4	416.580	415.720	415.720	415.720
quintic	5	6.822.564	6.820.924	6.820.924	6.820.924
sextic	6	94.371.012	94.358.712	94.358.712	94.358.712

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