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	8	255.7766

Total					8	255.7766
Isotopomer Natural Abundance (%)					66.2862

Determined Point Group: D_4d

Representation Γ_N

**Characters of reducible representation**
E	2S₈	2C₄	2(S₈)³	C₂	4C'₂	4σ_d
8	0.000	0	0.000	0	0	2

**Direct sum of irreducible representation**
A₁	A₂	B₁	B₂	E₁	E₂	E₃
1	0	0	1	1	1	1

**Properties of derivatives and isotopomers by single substitution, h(D_4d)=16**
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	8	S	no	yes	³⁴S ³³S ³⁶S	257.7724 256.7760 259.7716	23.7260 4.1869 0.055826
Total Number of Atoms:			8	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group D_4d
***Calculated as h( D_4d)/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	2
Double	XY	1	3
Triple	X₃	3	2
Triple	X₂Y	3	9
Triple	XYZ	0	21
Quadruple	X₄	3	5
Quadruple	X₃Y	3	16
Quadruple	X₂Y₂	6	27
Quadruple	X₂YZ	3	51
Quadruple	WXYZ	0	105
Quintuple	X₅	3	2
Quintuple	VWXYZ	0	420
Sextuple	X₆	2	2
Sextuple	UVWXYZ	0	1.260

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	2S₈	2C₄	2(S₈)³	C₂	4C'₂	4σ_d
24	0.000	0	-0.000	0	0	2

**Direct sum of irreducible representation**
A₁	A₂	B₁	B₂	E₁	E₂	E₃
2	1	1	2	3	3	3

Molecular motions and force field analysis

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