Grouptheoretical Analysis

Grouptheoretical Analysis

Composition Input Structure

Atomic Number	Atomic Symbol	Isotope	Isotope Mass	Isotope Abundance	Number Atoms	Mass
9	F	19	18.9984	100.0000	6	113.9904
16	S	32	31.9721	94.9900	1	31.9721

Total					7	145.9625
Isotopomer Natural Abundance (%)					94.9900

Determined Point Group: O_h

Representation Γ_N

**Characters of reducible representation**
E	8C₃	6C₂	6C₄	3C₂	i	6S₄	8S₆	3σ_h	6σ_d
7	1	1	3	3	1	1	1	5	3

**Direct sum of irreducible representation**
A_1g	A_2g	E_g	T_1g	T_2g	A_1u	A_2u	E_u	T_1u	T_2u
2	0	1	0	0	0	0	0	1	0

**Properties of derivatives and isotopomers by single substitution, h(O_h)=48**
Atom Set^*	Site Symmetry^**	h(Site Symmetry)	Identical Atoms^***	Element	Chrial	Polar	Isotopomer
Atom Set^*	Site Symmetry^**	h(Site Symmetry)	Identical Atoms^***	Element	Chrial	Polar	Isotope	Mass	Abundance^****
1	O_h	48	1	S	no	no	³⁴S ³³S ³⁶S	147.9583 146.9619 149.9575	4.2500 0.7500 0.010000
2	C_4v	8	6	F	no	yes	-	-	-
Total Number of Atoms:			7	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group O_h
***Calculated as h( O_h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

**Numbers of isomers by substitution**
Replacement	Pattern	Achiral Isomers	Chiral Isomer Pairs
Single	X	2	0
Double	X₂	3	0
Double	XY	4	0
Triple	X₃	4	0
Triple	X₂Y	7	0
Triple	XYZ	9	1
Quadruple	X₄	4	0
Quadruple	X₃Y	8	0
Quadruple	X₂Y₂	10	1
Quadruple	X₂YZ	13	3
Quadruple	WXYZ	15	10
Quintuple	X₅	3	0
Quintuple	VWXYZ	15	45
Sextuple	X₆	2	0
Sextuple	UVWXYZ	0	105

Further Reading

P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
Isomer Counting using Point Group Symmetry

Representation Γ_3N

**Characters of reducible representation**
E	8C₃	6C₂	6C₄	3C₂	i	6S₄	8S₆	3σ_h	6σ_d
21	0	-1	3	-3	-3	-1	0	5	3

**Direct sum of irreducible representation**
A_1g	A_2g	E_g	T_1g	T_2g	A_1u	A_2u	E_u	T_1u	T_2u
1	0	1	1	1	0	0	0	3	1

Molecular motions and force field analysis

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