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
54	Xe	132	131.9042	26.9000	1	131.9042

Total					7	245.8946
Isotopomer Natural Abundance (%)					26.9000

Determined Point Group: C_3v

Representation Γ_N

**Characters of reducible representation**
E	2C₃	3σ_v
7	1	3

**Direct sum of irreducible representation**
A₁	A₂	E
3	0	2

**Properties of derivatives and isotopomers by single substitution, h(C_3v)=6**
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_3v	6	1	Xe	no	yes	¹²⁹Xe ¹³¹Xe ¹³⁴Xe ¹³⁶Xe ¹³⁰Xe ¹²⁸Xe ¹²⁴Xe ¹²⁶Xe	242.8952 244.8955 247.8958 249.8976 243.8939 241.8940 237.8963 239.8947	26.4000 21.2000 10.4000 8.9000 4.1000 1.9100 0.100000 0.090000
2	C_s	2	3	F	no	yes	-	-	-
3	C_s	2	3	F	no	yes	-	-	-
Total Number of Atoms:			7	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group C_3v
***Calculated as h( C_3v)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

**Numbers of isomers by substitution**
Replacement	Pattern	Achiral Isomers	Chiral Isomer Pairs
Single	X	3	0
Double	X₂	5	1
Double	XY	6	4
Triple	X₃	7	3
Triple	X₂Y	9	13
Triple	XYZ	6	32
Quadruple	X₄	7	3
Quadruple	X₃Y	12	18
Quadruple	X₂Y₂	14	28
Quadruple	X₂YZ	12	64
Quadruple	WXYZ	0	140
Quintuple	X₅	5	1
Quintuple	VWXYZ	0	420
Sextuple	X₆	3	0
Sextuple	UVWXYZ	0	840

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	2C₃	3σ_v
21	0	3

**Direct sum of irreducible representation**
A₁	A₂	E
5	2	7

Molecular motions and force field analysis

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