Reduction formula for point group D3

Reduction formula for point group D₃

**Characters for molecular motions**
Motion	E	2C₃ (z)	3C'₂
Cartesian 3N	102	0	0
Translation (x,y,z)	3	0	-1
Rotation (R_x,R_y,R_z)	3	0	-1
Vibration	96	0	2

**Decomposition into Irreducible representations**
Motion	A₁	A₂	E	Total
Cartesian 3N	17	17	34	68
Translation (x,y,z)	0	1	1	2
Rotation (R_x,R_y,R_z)	0	1	1	2
Vibration	17	15	32	64

**Molecule Parameter**
Number of Atoms (N)	34
Number of internal coordinates	96
Number of independant internal coordinates	17
Number of vibrational modes	64

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A₁	A₂	E	Total
Linear (IR)	17	15	32	47 / 17
Quadratic (Raman)	17	15	32	49 / 15
IR + Raman	-	-	32	32 / 0

**Characters of symmetric powers for vibration representation**
Force field	Tensor Order	E	2C₃ (z)	3C'₂
linear	1	96	0	2
quadratic	2	4.656	0	50
cubic	3	152.096	32	98
quartic	4	3.764.376	0	1.274
quintic	5	75.287.520	0	2.450
sextic	6	1.267.339.920	528	22.050

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A₁	A₂	E
linear	1	17	15	32
quadratic	2	801	751	1.552
cubic	3	25.409	25.311	50.688
quartic	4	628.033	626.759	1.254.792
quintic	5	12.549.145	12.546.695	25.095.840
sextic	6	211.234.521	211.212.471	422.446.464

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