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	5	94.9920
16	S	32	31.9721	94.9900	1	31.9721
17	Cl	35	34.9689	75.7600	1	34.9689

Total					7	161.9329
Isotopomer Natural Abundance (%)					71.9644

Determined Point Group: C_4v

Representation Γ_N

**Characters of reducible representation**
E	2C₄	C₂	2σ_v	2σ_d
7	3	3	5	3

**Direct sum of irreducible representation**
A₁	A₂	B₁	B₂	E
4	0	1	0	1

**Properties of derivatives and isotopomers by single substitution, h(C_4v)=8**
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	C_4v	8	1	S	no	yes	³⁴S ³³S ³⁶S	163.9287 162.9323 165.9279	3.2198 0.5682 0.007576
2	C_4v	8	1	Cl	no	yes	³⁷Cl	163.9300	23.0256
3	C_s	2	4	F	no	yes	-	-	-
4	C_4v	8	1	F	no	yes	-	-	-
Total Number of Atoms:			7	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group C_4v
***Calculated as h( C_4v)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

**Numbers of isomers by substitution**
Replacement	Pattern	Achiral Isomers	Chiral Isomer Pairs
Single	X	4	0
Double	X₂	8	0
Double	XY	13	1
Triple	X₃	11	0
Triple	X₂Y	22	4
Triple	XYZ	33	12
Quadruple	X₄	11	0
Quadruple	X₃Y	26	6
Quadruple	X₂Y₂	32	12
Quadruple	X₂YZ	46	31
Quadruple	WXYZ	60	75
Quintuple	X₅	8	0
Quintuple	VWXYZ	60	285
Sextuple	X₆	4	0
Sextuple	UVWXYZ	0	630

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	2C₄	C₂	2σ_v	2σ_d
21	3	-3	5	3

**Direct sum of irreducible representation**
A₁	A₂	B₁	B₂	E
5	1	2	1	6

Molecular motions and force field analysis

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