Direct sum of irreducible representation

Ag	Bg	Au	Bu
8	0	0	8

Properties of derivatives and isotopomers by single substitution, h(C_2h)=4

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	Cs	2	2	C	no	yes	13C	131.0565	2.0193
2	Cs	2	2	N	no	yes	15N	131.0501	0.6669
3	Cs	2	2	C	no	yes	13C	131.0565	2.0193
4	Cs	2	2	C	no	yes	13C	131.0565	2.0193
5	Cs	2	2	C	no	yes	13C	131.0565	2.0193
6	Cs	2	2	H	no	yes	2H	131.0594	0.028327
7	Cs	2	2	H	no	yes	2H	131.0594	0.028327
8	Cs	2	2	H	no	yes	2H	131.0594	0.028327
Total Number of Atoms:			16	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group C_2h
***Calculated as h( C_2h)/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	64	0
Double	XY	120	0
Triple	X3	280	0
Triple	X2Y	840	0
Triple	XYZ	1.680	0
Quadruple	X4	924	0
Quadruple	X3Y	3.640	0
Quadruple	X2Y2	5.488	0
Quadruple	X2YZ	10.920	0
Quadruple	WXYZ	21.840	0
Quintuple	X5	2.184	0
Quintuple	VWXYZ	262.080	0
Sextuple	X6	4.032	0
Sextuple	UVWXYZ	2.882.880	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