Grouptheoretical Analysis

Grouptheoretical Analysis

Composition Input Structure

Atomic Number	Atomic Symbol	Isotope	Isotope Mass	Isotope Abundance	Number Atoms	Mass
16	S	32	31.9721	94.9900	6	191.8324

Total					6	191.8324
Isotopomer Natural Abundance (%)					73.4628

Determined Point Group: D_3d

Representation Γ_N

**Characters of reducible representation**
E	2C₃	3C'₂	i	2S₆	3σ_d
6	0	0	0	0	2

**Direct sum of irreducible representation**
A_1g	A_2g	E_g	A_1u	A_2u	E_u
1	0	1	0	1	1

**Properties of derivatives and isotopomers by single substitution, h(D_3d)=12**
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	6	S	no	yes	³⁴S ³³S ³⁶S	193.8282 192.8318 195.8274	19.7210 3.4802 0.046402
Total Number of Atoms:			6	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group D_3d
***Calculated as h( D_3d)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

**Numbers of isomers by substitution**
Replacement	Pattern	Achiral Isomers	Chiral Isomer Pairs
Single	X	1	0
Double	X₂	2	1
Double	XY	1	2
Triple	X₃	2	1
Triple	X₂Y	2	4
Triple	XYZ	0	10
Quadruple	X₄	2	1
Quadruple	X₃Y	2	4
Quadruple	X₂Y₂	4	7
Quadruple	X₂YZ	2	14
Quadruple	WXYZ	0	30
Quintuple	X₅	1	0
Quintuple	VWXYZ	0	60
Sextuple	X₆	1	0
Sextuple	UVWXYZ	0	60

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	3C'₂	i	2S₆	3σ_d
18	0	0	0	0	2

**Direct sum of irreducible representation**
A_1g	A_2g	E_g	A_1u	A_2u	E_u
2	1	3	1	2	3

Molecular motions and force field analysis

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