Direct sum of irreducible representation

A	E*	T
8	8	24

Properties of derivatives and isotopomers by single substitution, h(T)=12

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	C1	1	12	C	yes	yes	13C	1404.9459	6.8731
2	C1	1	12	C	yes	yes	13C	1404.9459	6.8731
3	C1	1	12	C	yes	yes	13C	1404.9459	6.8731
4	C1	1	12	C	yes	yes	13C	1404.9459	6.8731
5	C1	1	12	C	yes	yes	13C	1404.9459	6.8731
6	C1	1	12	F	yes	yes	-	-	-
7	C1	1	12	F	yes	yes	-	-	-
8	C1	1	12	F	yes	yes	-	-	-
Total Number of Atoms:			96	✅ Correct Number of Atoms found

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

Numbers of isomers by substitution

Replacement	Pattern	Chiral Isomers
Single	X	8
Double	X2	392
Double	XY	760
Triple	X3	11.928
Triple	X2Y	35.720
Triple	XYZ	71.440
Quadruple	X4	277.112
Quadruple	X3Y	1.107.320
Quadruple	X2Y2	1.661.544
Quadruple	X2YZ	3.321.960
Quadruple	WXYZ	6.643.920
Quintuple	X5	5.093.672
Quintuple	VWXYZ	611.240.640
Sextuple	X6	77.258.680
Sextuple	UVWXYZ	55.622.898.240

Further Reading

• P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
  Isomer Counting using Point Group Symmetry
  
  

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Representation Γ_3N