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

**Decomposition into Irreducible representations**
Motion	A	E	T	Total
Cartesian 3N	21	21	63	105
Translation (x,y,z)	0	0	1	1
Rotation (R_x,R_y,R_z)	0	0	1	1
Vibration	21	21	61	103

**Molecule Parameter**
Number of Atoms (N)	84
Number of internal coordinates	246
Number of independant internal coordinates	21
Number of vibrational modes	103

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A	E	T	Total
Linear (IR)	21	21	61	61 / 42
Quadratic (Raman)	21	21	61	103 / 0
IR + Raman	-	-	61	61 / 0

**Characters of symmetric powers for vibration representation**
Force field	Tensor Order	E	4C₃	4(C₃)²	3C₂
linear	1	246	0	0	2
quadratic	2	30.381	0	0	125
cubic	3	2.511.496	82	82	248
quartic	4	156.340.626	0	0	7.874
quintic	5	7.817.031.300	0	0	15.500
sextic	6	327.012.476.050	3.403	3.403	333.250

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A	E	T
linear	1	21	21	61
quadratic	2	2.563	2.563	7.564
cubic	3	209.408	209.326	627.812
quartic	4	13.030.354	13.030.354	39.083.188
quintic	5	651.423.150	651.423.150	1.954.253.950
sextic	6	27.251.125.252	27.251.121.849	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 T

Constructor University Bremen

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