Direct sum of irreducible representation

Ag	Au
8	8

Properties of derivatives and isotopomers by single substitution, h(C_i)=2

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	C1	1	2	C	yes	yes	13C	151.0198	2.0960
2	C1	1	2	C	yes	yes	13C	151.0198	2.0960
3	C1	1	2	O	yes	yes	18O 17O	152.0207 151.0207	0.3778 0.071782
4	C1	1	2	H	yes	yes	2H	151.0227	0.029403
5	C1	1	2	O	yes	yes	18O 17O	152.0207 151.0207	0.3778 0.071782
6	C1	1	2	H	yes	yes	2H	151.0227	0.029403
7	C1	1	2	O	yes	yes	18O 17O	152.0207 151.0207	0.3778 0.071782
8	C1	1	2	H	yes	yes	2H	151.0227	0.029403
Total Number of Atoms:			16	✅ Correct Number of Atoms found

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

Numbers of isomers by substitution

Replacement	Pattern	Achiral Isomers	Chiral Isomer Pairs
Single	X	0	8
Double	X2	8	56
Double	XY	0	120
Triple	X3	0	280
Triple	X2Y	0	840
Triple	XYZ	0	1.680
Quadruple	X4	28	896
Quadruple	X3Y	0	3.640
Quadruple	X2Y2	56	5.432
Quadruple	X2YZ	0	10.920
Quadruple	WXYZ	0	21.840
Quintuple	X5	0	2.184
Quintuple	VWXYZ	0	262.080
Sextuple	X6	56	3.976
Sextuple	UVWXYZ	0	2.882.880

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