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	10	10.0783
6	C	12	12.0000	98.9000	10	120.0000
26	Fe	56	55.9349	91.7540	1	55.9349

Total					21	186.0132
Isotopomer Natural Abundance (%)					82.0182

Determined Point Group: D₅

Representation Γ_N

**Characters of reducible representation**
E	2C₅	2(C₅)²	5C'₂
21	1.000	1.000	1

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

**Properties of derivatives and isotopomers by single substitution, h(D₅)=10**
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	D₅	10	1	Fe	yes	no	⁵⁴Fe ⁵⁷Fe ⁵⁸Fe	184.0179 187.0136 188.0115	5.2248 1.8942 0.2521
2	C₁	1	10	C	yes	yes	¹³C	187.0165	9.1224
3	C₁	1	10	H	yes	yes	²H	187.0195	0.1280
Total Number of Atoms:			21	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group D₅
***Calculated as h( D₅)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

**Numbers of isomers by substitution**
Replacement	Pattern	Chiral Isomers
Single	X	3
Double	X₂	26
Double	XY	42
Triple	X₃	138
Triple	X₂Y	404
Triple	XYZ	798
Quadruple	X₄	621
Quadruple	X₃Y	2.394
Quadruple	X₂Y₂	3.636
Quadruple	X₂YZ	7.182
Quadruple	WXYZ	14.364
Quintuple	X₅	2.059
Quintuple	VWXYZ	244.188
Sextuple	X₆	5.488
Sextuple	UVWXYZ	3.907.008

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	2C₅	2(C₅)²	5C'₂
63	1.618	-0.618	-1

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

Molecular motions and force field analysis

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