Grouptheoretical Analysis

Grouptheoretical Analysis

Composition Input Structure

Atomic Number	Atomic Symbol	Isotope	Isotope Mass	Isotope Abundance	Number Atoms	Mass
6	C	12	12.0000	98.9000	16	192.0000
16	S	32	31.9721	94.9900	8	255.7766

Total					24	447.7766
Isotopomer Natural Abundance (%)					55.5346

Determined Point Group: D_8h

Representation Γ_N

**Characters of reducible representation**
E	2C₈	2C₄	2(C₈)³	C₂	4C'₂	4C''₂	i	2(S₈)³	2S₄	2S₈	σ_h	4σ_v	4σ_d
24	0.000	0	0.000	0	4	2	0	0.000	0	0.000	24	4	2

**Direct sum of irreducible representation**
A_1g	A_2g	B_1g	B_2g	E_1g	E_2g	E_3g	A_1u	A_2u	B_1u	B_2u	E_1u	E_2u	E_3u
3	0	2	1	0	3	0	0	0	0	0	3	0	3

**Properties of derivatives and isotopomers by single substitution, h(D_8h)=32**
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_2v	4	8	C	no	yes	¹³C	448.7799	4.9414
2	C_2v	4	8	C	no	yes	¹³C	448.7799	4.9414
3	C_2v	4	8	S	no	yes	³⁴S ³³S ³⁶S	449.7724 448.7760 451.7716	19.8776 3.5078 0.046771
Total Number of Atoms:			24	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group D_8h
***Calculated as h( D_8h)/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	25	0
Double	XY	38	0
Triple	X₃	143	0
Triple	X₂Y	398	0
Triple	XYZ	765	0
Quadruple	X₄	712	0
Quadruple	X₃Y	2.693	0
Quadruple	X₂Y₂	4.080	0
Quadruple	X₂YZ	8.008	0
Quadruple	WXYZ	15.945	0
Quintuple	X₅	2.739	0
Quintuple	VWXYZ	318.780	0
Sextuple	X₆	8.581	0
Sextuple	UVWXYZ	6.056.820	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	2C₈	2C₄	2(C₈)³	C₂	4C'₂	4C''₂	i	2(S₈)³	2S₄	2S₈	σ_h	4σ_v	4σ_d
72	0.000	0	-0.000	0	-4	-2	0	-0.000	0	0.000	24	4	2

**Direct sum of irreducible representation**
A_1g	A_2g	B_1g	B_2g	E_1g	E_2g	E_3g	A_1u	A_2u	B_1u	B_2u	E_1u	E_2u	E_3u
3	3	3	3	3	6	3	0	3	1	2	6	3	6

Molecular motions and force field analysis

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