Direct sum of irreducible representation

A'	A''
8	0

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

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	Cs	2	1	C	no	yes	13C	57.0296	1.0727
2	Cs	2	1	C	no	yes	13C	57.0296	1.0727
3	Cs	2	1	C	no	yes	13C	57.0296	1.0727
4	Cs	2	1	O	no	yes	18O 17O	58.0305 57.0304	0.1934 0.036737
5	Cs	2	1	H	no	yes	2H	57.0325	0.015048
6	Cs	2	1	H	no	yes	2H	57.0325	0.015048
7	Cs	2	1	H	no	yes	2H	57.0325	0.015048
8	Cs	2	1	H	no	yes	2H	57.0325	0.015048
Total Number of Atoms:			8	✅ Correct Number of Atoms found

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

Numbers of isomers by substitution

Replacement	Pattern	Achiral Isomers	Chiral Isomer Pairs
Single	X	8	0
Double	X2	28	0
Double	XY	56	0
Triple	X3	56	0
Triple	X2Y	168	0
Triple	XYZ	336	0
Quadruple	X4	70	0
Quadruple	X3Y	280	0
Quadruple	X2Y2	420	0
Quadruple	X2YZ	840	0
Quadruple	WXYZ	1.680	0
Quintuple	X5	56	0
Quintuple	VWXYZ	6.720	0
Sextuple	X6	28	0
Sextuple	UVWXYZ	20.160	0

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