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	1	1.0078
8	O	16	15.9949	99.7620	1	15.9949
17	Cl	35	34.9689	75.7600	1	34.9689

Total					3	51.9716
Isotopomer Natural Abundance (%)					75.5679

Determined Point Group: C_s

Representation Γ_N

**Characters of reducible representation**
E	σ_h
3	3

**Direct sum of irreducible representation**
A'	A''
3	0

**Properties of derivatives and isotopomers by single substitution, h(C_s)=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	C_s	2	1	H	no	yes	²H	52.9779	0.011790
2	C_s	2	1	O	no	yes	¹⁸O ¹⁷O	53.9758 52.9758	0.1515 0.028784
3	C_s	2	1	Cl	no	yes	³⁷Cl	53.9686	24.1785
Total Number of Atoms:			3	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group C_s
***Calculated as h( C_s)/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	3	0
Double	XY	6	0
Triple	X₃	1	0
Triple	X₂Y	3	0
Triple	XYZ	6	0
Quadruple	X₄	0	0
Quadruple	X₃Y	0	0
Quadruple	X₂Y₂	0	0
Quadruple	X₂YZ	0	0
Quadruple	WXYZ	0	0
Quintuple	X₅	0	0
Quintuple	VWXYZ	0	0
Sextuple	X₆	0	0
Sextuple	UVWXYZ	0	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	σ_h
9	3

**Direct sum of irreducible representation**
A'	A''
6	3

Molecular motions and force field analysis

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