Grouptheoretical Analysis

Grouptheoretical Analysis

Composition Input Structure

Atomic Number	Atomic Symbol	Isotope	Isotope Mass	Isotope Abundance	Number Atoms	Mass
1	H	1	1.0078	99.9844	2	2.0157
8	O	16	15.9949	99.7620	2	31.9898

Total					4	34.0055
Isotopomer Natural Abundance (%)					99.4935

Determined Point Group: C₂

Representation Γ_N

**Characters of reducible representation**
E	C₂
4	0

**Direct sum of irreducible representation**
A	B
2	2

**Properties of derivatives and isotopomers by single substitution, h(C₂)=2**
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	C₁	1	2	H	yes	yes	²H	35.0118	0.031047
2	C₁	1	2	O	yes	yes	¹⁸O ¹⁷O	36.0097 35.0097	0.3989 0.075795
Total Number of Atoms:			4	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group C₂
***Calculated as h( C₂)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

**Numbers of isomers by substitution**
Replacement	Pattern	Chiral Isomers
Single	X	2
Double	X₂	4
Double	XY	6
Triple	X₃	2
Triple	X₂Y	6
Triple	XYZ	12
Quadruple	X₄	1
Quadruple	X₃Y	2
Quadruple	X₂Y₂	4
Quadruple	X₂YZ	6
Quadruple	WXYZ	12
Quintuple	X₅	0
Quintuple	VWXYZ	0
Sextuple	X₆	0
Sextuple	UVWXYZ	0

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	C₂
12	0

**Direct sum of irreducible representation**
A	B
6	6

Molecular motions and force field analysis

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