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	16	16.1252
6	C	12	12.0000	98.9000	16	192.0000
92	U	238	238.0508	99.2745	1	238.0508

Total					33	446.1760
Isotopomer Natural Abundance (%)					82.9649

Determined Point Group: D₈

Representation Γ_N

**Characters of reducible representation**
E	2C₈	2C₄	2(C₈)³	C₂	4C'₂	4C''₂
33	1.000	1	1.000	1	1	1

**Direct sum of irreducible representation**
A₁	A₂	B₁	B₂	E₁	E₂	E₃
3	2	2	2	4	4	4

**Properties of derivatives and isotopomers by single substitution, h(D₈)=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	D₈	16	1	U	yes	no	²³⁵U ²³⁴U	443.1691 442.1662	0.6017 0.004596
2	C₁	1	16	C	yes	yes	¹³C	447.1793	14.7642
3	C₁	1	16	H	yes	yes	²H	447.1823	0.2071
Total Number of Atoms:			33	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group D₈
***Calculated as h( D₈)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

**Numbers of isomers by substitution**
Replacement	Pattern	Chiral Isomers
Single	X	3
Double	X₂	42
Double	XY	66
Triple	X₃	350
Triple	X₂Y	1.032
Triple	XYZ	2.046
Quadruple	X₄	2.626
Quadruple	X₃Y	10.230
Quadruple	X₂Y₂	15.480
Quadruple	X₂YZ	30.690
Quadruple	WXYZ	61.380
Quintuple	X₅	14.902
Quintuple	VWXYZ	1.780.020
Sextuple	X₆	69.538
Sextuple	UVWXYZ	49.840.560

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
99	2.414	1	-0.414	-1	-1	-1

**Direct sum of irreducible representation**
A₁	A₂	B₁	B₂	E₁	E₂	E₃
6	7	6	6	13	12	12

Molecular motions and force field analysis

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