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	57	0	0	-3
Translation (x,y,z)	3	0	0	-1
Rotation (R_x,R_y,R_z)	3	0	0	-1
Vibration	51	0	0	-1

**Decomposition into Irreducible representations**
Motion	A	E	T	Total
Cartesian 3N	4	4	15	23
Translation (x,y,z)	0	0	1	1
Rotation (R_x,R_y,R_z)	0	0	1	1
Vibration	4	4	13	21

**Molecule Parameter**
Number of Atoms (N)	19
Number of internal coordinates	51
Number of independant internal coordinates	4
Number of vibrational modes	21

Force field analysis

**Allowed / forbidden vibronational transitions**
Operator	A	E	T	Total
Linear (IR)	4	4	13	13 / 8
Quadratic (Raman)	4	4	13	21 / 0
IR + Raman	-	-	13	13 / 0

**Characters of symmetric powers for vibration representation**
Force field	Tensor Order	E	4C₃	4(C₃)²	3C₂
linear	1	51	0	0	-1
quadratic	2	1.326	0	0	26
cubic	3	23.426	17	17	-26
quartic	4	316.251	0	0	351
quintic	5	3.478.761	0	0	-351
sextic	6	32.468.436	153	153	3.276

Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field	Tensor Order	A	E	T
linear	1	4	4	13
quadratic	2	117	117	325
cubic	3	1.957	1.940	5.863
quartic	4	26.442	26.442	78.975
quintic	5	289.809	289.809	869.778
sextic	6	2.706.624	2.706.471	8.116.290

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