Reduction formula for point group D3

Reduction formula for point group D₃

**Characters for molecular motions**
Motion	E	2C₃ (z)	3C'₂
Cartesian 3N	108	0	-4
Translation (x,y,z)	3	0	-1
Rotation (R_x,R_y,R_z)	3	0	-1
Vibration	102	0	-2

**Decomposition into Irreducible representations**
Motion	A₁	A₂	E	Total
Cartesian 3N	16	20	36	72
Translation (x,y,z)	0	1	1	2
Rotation (R_x,R_y,R_z)	0	1	1	2
Vibration	16	18	34	68

**Molecule Parameter**
Number of Atoms (N)	36
Number of internal coordinates	102
Number of independant internal coordinates	16
Number of vibrational modes	68

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A₁	A₂	E	Total
Linear (IR)	16	18	34	52 / 16
Quadratic (Raman)	16	18	34	50 / 18
IR + Raman	-	-	34	34 / 0

**Characters of symmetric powers for vibration representation**
Force field	Tensor Order	E	2C₃ (z)	3C'₂
linear	1	102	0	-2
quadratic	2	5.253	0	53
cubic	3	182.104	34	-104
quartic	4	4.780.230	0	1.430
quintic	5	101.340.876	0	-2.756
sextic	6	1.807.245.622	595	26.182

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A₁	A₂	E
linear	1	16	18	34
quadratic	2	902	849	1.751
cubic	3	30.310	30.414	60.690
quartic	4	797.420	795.990	1.593.410
quintic	5	16.888.768	16.891.524	33.780.292
sextic	6	301.220.893	301.194.711	602.415.009

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 D3

Constructor University Bremen

Last update November, 13^th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement