Reduction formula for point group T

Reduction formula for point group T

**Characters for molecular motions**
Motion	E	4C₃	4(C₃)²	3C₂
Cartesian 3N	84	0	0	0
Translation (x,y,z)	3	0	0	-1
Rotation (R_x,R_y,R_z)	3	0	0	-1
Vibration	78	0	0	2

**Decomposition into Irreducible representations**
Motion	A	E	T	Total
Cartesian 3N	7	7	21	35
Translation (x,y,z)	0	0	1	1
Rotation (R_x,R_y,R_z)	0	0	1	1
Vibration	7	7	19	33

**Molecule Parameter**
Number of Atoms (N)	28
Number of internal coordinates	78
Number of independant internal coordinates	7
Number of vibrational modes	33

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A	E	T	Total
Linear (IR)	7	7	19	19 / 14
Quadratic (Raman)	7	7	19	33 / 0
IR + Raman	-	-	19	19 / 0

**Characters of symmetric powers for vibration representation**
Force field	Tensor Order	E	4C₃	4(C₃)²	3C₂
linear	1	78	0	0	2
quadratic	2	3.081	0	0	41
cubic	3	82.160	26	26	80
quartic	4	1.663.740	0	0	860
quintic	5	27.285.336	0	0	1.640
sextic	6	377.447.148	351	351	12.300

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A	E	T
linear	1	7	7	19
quadratic	2	267	267	760
cubic	3	6.884	6.858	20.520
quartic	4	138.860	138.860	415.720
quintic	5	2.274.188	2.274.188	6.820.924
sextic	6	31.457.238	31.456.887	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 T

Constructor University Bremen

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